A Level Physics Skills, Practicals and Analysis Defnitions Signifcant Figures alculating !rrors 2 Lines o# $est Fit %radient !&uations 2 )ernier alli'ers and Micrometers Rearranging Rearranging + Deriving !&uations
Prefxes Signifcant Figures 2 "denti#ying !rrors %radients "nter'reting %ra'hs Descri*ing !x !x'eriments
Means and Anomalous Results alculating !rrors Points Plotting %radients !&uations (angents Descri*ing !x !x'eriments 2
Rearranging Rearranging + Deriving !&uations 2
nits
Photon !nergy .uarks, /adrons and Le'tons (he (hreshold (hreshold Fre&uency Fre&uency Line S'ectra de $roglie -avelength "0) %ra'hs 1hms La3 Light Dependent Resistors (hermistor (hermometer (hermometer Resistivity o# o''er Resistivity o# o''er Resistivity of a Metal Wire Series and Parallel ircuits EMF and nternal Resistance !MF and "nternal Resistance Potential Dividers 1scillosco'e (races
Analysis Analysis Analysis Analysis Analysis Practical Analysis Practical Practical Practical Analysis Practical Practical Practical Analysis Practical Analysis
$raking Force "m'ulse ircular Motion Finding g 3ith a Sim'le Pendulum Finding k 3ith a Mass and S'ring S"M #scillations of a Spring $ Shaped %endulum Dam'ing (he %ravitational onstant onstant %ravitational Potential 9e'lers (hird La3 !lectric Potential Finding :; a'acitance Discharging a'acitors a'acitor (ime onstant &apacitor Discharge Mass S'ectrometer Magnetic Flux Density (rans#ormers (rans#ormers
Analysis Analysis Practical Practical Practical Practical Practical Analysis Analysis Analysis Analysis Analysis Analysis Analysis Practical Analysis Practical Analysis Analysis Analysis
Skills
Resolving Forces to fnd -eight Moments Rolling Down a Ramp Acceleration Due to %ravity (erminal )elocity Bouncing Ball -ork Done onservation o# !nergy (he S'ring onstant Finding the 4oung Modulus Finding the 4oung Modulus Loading and nloading The Speed of Waves in Water !lectromagnetic S'eed Phase Di5erence o# Pendulums Sound -aves in a olumn o# Air Finding the Refractive nde! Finding th the Re#ractive "n "ndex "nter#erence o# Sound Laser Di5raction (he 6uclear Radius onstant Radioactive Decay /al#0Li#e and the Decay onstant (he "nverse S&uare La3 $inding !nergy !7mc2 "deal %ases Finding A*solute 8ero Finding A*solute 8ero S'ecifc /eat a'acity
Defnitions
6< D-4!R Defne the #ollo3ing 3ords= "nde'endent varia*le
De'endent varia*le
Practical Practical Practical Practical Practical Practical Practical Analysis Practical Practical Analysis Practical Practical Analysis Practical Analysis Practical Analysis Analysis Practical Analysis Practical Analysis Analysis Analysis Analysis Analysis Practical Analysis Practical
ontrol varia*le
Random error
ontinuous varia*le
Systematic error
Discrete varia*le
8ero error
1rdered varia*le
Mean value
ategoric varia*le
Anomalous results
Accuracy
Line o# *est ft
Precision
%radient
Relia*ility
40"nterce't 40"nterce't
ali*ration /o3 do you im'rove the 'recision o# a reading> /o3 do could you im'rove the relia*ility o# your results> "# a 3eighing scale read 2;g 3hen nothing 3as 'laced on it ho3 3ould you descri*e it> "# you used this to fnd the masses o# di5erent sam'les o# metal 3hat ty'e o# error 3ould it 'roduce> /o3 could you calculate the true value #or each o# the masses> /o3 do you calculate a mean value o# ? readings> "# all your readings are to 2 signifcant fgures ho3 many sig fg can your mean value *e> -hy> -hich ty'e o# varia*le 3ould the #ollo3ing *e classed as= /eight in cm>
Favourite chocolate *ar>
%ender>
urrent in Am's>
Dress si@e>
Smelliness>
Attractiveness>
Age in days>
Distance in m>
'/>
$rightness>
Pressure in Pa>
)olume o# 12 'roduced in m >
Loudness>
(em'erature (em'erature in Fahrenheit> Fahrenheit>
(0Shirt (0Shirt si@e>
"# T re'resents re'resents the true value 3hich o# the gra'hs *elo3 re'resents= A< Precise and accurate>
< Accurate *ut not 'recise>
$< Precise *ut not accurate>
D< 6either accurate nor 'recise>
Skills 6< D-4!R
Prefxes
ontrol varia*le
Random error
ontinuous varia*le
Systematic error
Discrete varia*le
8ero error
1rdered varia*le
Mean value
ategoric varia*le
Anomalous results
Accuracy
Line o# *est ft
Precision
%radient
Relia*ility
40"nterce't 40"nterce't
ali*ration /o3 do you im'rove the 'recision o# a reading> /o3 do could you im'rove the relia*ility o# your results> "# a 3eighing scale read 2;g 3hen nothing 3as 'laced on it ho3 3ould you descri*e it> "# you used this to fnd the masses o# di5erent sam'les o# metal 3hat ty'e o# error 3ould it 'roduce> /o3 could you calculate the true value #or each o# the masses> /o3 do you calculate a mean value o# ? readings> "# all your readings are to 2 signifcant fgures ho3 many sig fg can your mean value *e> -hy> -hich ty'e o# varia*le 3ould the #ollo3ing *e classed as= /eight in cm>
Favourite chocolate *ar>
%ender>
urrent in Am's>
Dress si@e>
Smelliness>
Attractiveness>
Age in days>
Distance in m>
'/>
$rightness>
Pressure in Pa>
)olume o# 12 'roduced in m >
Loudness>
(em'erature (em'erature in Fahrenheit> Fahrenheit>
(0Shirt (0Shirt si@e>
"# T re'resents re'resents the true value 3hich o# the gra'hs *elo3 re'resents= A< Precise and accurate>
< Accurate *ut not 'recise>
$< Precise *ut not accurate>
D< 6either accurate nor 'recise>
Skills 6< D-4!R
Prefxes
In Physics we have to deal with quantities from the very large to the very small. A prex is something that goes in front of a unit and acts as a multiplier. multiplier. This sheet will give you practice at converting gures between prexes.
Sym'ol
(ame
What it means
P
'eta
B;BC
(
tera
B;B2
%
giga
B;G
M
mega
k
kilo
"ow to convert
B ;; ; ;; ;; ;; ; ;; ;; ;
xB;;;
B ;; ;; ;; ; ;; ;; ;
E B; ;;
xB;;;
B; ;; ;; ; ;; ;
E B ;; ;
xB;;;
B;H
B; ; ;; ;;
E B; ; ;
xB;;;
B;
B; ;;
E B ;; ;
xB;;;
B
E B ;; ;
xB;;;
m
m i l li
B;0
; <; ; B
E B ;; ;
xB;;;
I
micro
B;0H
; <; ; ; ; ; B
E B; ;;
xB;;;
n
nano
B;0G
; <; ; ; ; ; ; ; ; B
E B; ;;
xB;;;
'
'ico
B;0B2
; <; ; ; ; ; ; ; ; ; ; ; B
E B ;; ;
xB;;;
#
#emto
B;0BC
E B;;;
;<;;;;;;;;;;;;;;B
onvert the fgures into the 'refxes re&uired< s ms )s
ns
ps
B?
m
*m
mm
Mm
+m
Mg
mg
g
+g
m,
),
n,
*,
B2KJ ;<2GC CJ<2
*g G?
, ;<;;;;;;HJK
Skills
6< D-4!R
Means and Anomalous Results
For each set of values calculate the mean and then calculate the mean ignoring any anomalous results.
?BC2 GC
. 2GGH G2C
. / H
/ ?;BK G2H
Mean
0 H2
Mean
. / 0 1 B?; 22; G; BK; B?; CH;; ?B2;; CKH;; ?K;; CK;; ;
Mean
Skills
Signifcant Figures
6< D-4!R
$alue
For each value state how many signicant gures it is stated to. Sig Sig Sig $alue $alue $alue Figs Figs Figs
2
B;HH
BK;;
;<;J
2<;
K2
2
HG2?
2<;;
JC;;;;
2
;<;;H
;
B;
CG;H
G
;<?
2;;;;;
HJBJ
C?
B2
;
Sig Figs
Add the values below then write the answer to the appropriate number of signicant gures Total to correct $alue $alue . $alue / Total $alue sig 2gs
CB
B
<2
JB?H
2
B2
2;
BK
;
B
B;
B<;H2
G<;J
;
JGJH2
2H;BJ
2<;CK
K
;<;;2
B;H
B2<;
?
CK;;
BC2
;
;
;
?G22KK
B2;;;
ultiply the values below then write the answer to the appropriate number of signicant gures Total to correct sig $alue $alue . Total $alue 2gs
;
B<2
K
J
2
B
GJ
?;<;B
;
H?<2
!ivide value" by value # then write the answer to the appropriate number of signicant gures Total to correct sig $alue $alue . Total $alue 2gs
C<
J?K
JKB
H
GB x B;2
BK;
C
22 x B;0
K<B?
Skills
Signifcant Figures 2
6< D-4!R
$alue
For each value state how many signicant gures it is stated to. Sig Sig Sig $alue $alue $alue Figs Figs Figs
2
HKGHJB
B;;;;;
H
B;;
CHKHC
K
J
2?
B
H?;;
BJ
C
BK2
KJC
2
?<2HJ
G?
;<;C
2
;<;2
G?<;
;
Sig Figs
$alculate the mean of the values below then write the answer to the appropriate number of signicant gures Mean to correct sig $alue $alue . $alue / Mean $alue 2gs
B
B
2
?C
2GG
?B;
C;;
H;;
G;;
<;K
?
J2;
?GK
BHK
BHCC
2GGH
B?;
;<2;
G2C
CH;;
2H;BJ
BG
;
22K
K;
B
GBH;
2;BB
?
H2
B2J
2H
BCC
BB
B
J;;HC
J2<K
CBB
2HJ;KKJ
B
KKK
BB;
GKH
;
H2
J2HBHB
2CBCJ
?H
2HJ;J
B;B?
J<G
?KK
B;C2G
J;
;
B?;
B
B
CK;;
?;2
?
;<B?
JGJH2
2H
B
2HJ;G;B
B
G
2H;
Skills
alculating !rrors
6< D-4!R
$aria'l e
$omplete the table. Reading Mean $alue / BBG
A
Reading B2B
Reading . BBK
B
CGG
H2
C
<
$aria'l e
3ncertainty
CG
$omplete the table. Reading Mean $alue / BJ
D
Reading BJ
Reading . BJ
E
?2
?2
?2
F
<2K
G
JCJ JB? JG %hat would be the percentage error in the following quantities&
$aria'l e
$omplete the table. Reading Mean $alue / CKBG
H
Reading CK2;C
Reading . CK;G
I
K2<
KB
K2
J
BGKC
BGKK
BGK;
K
4 3ncertainty
3ncertainty
3ncertainty
? BG 2J %hat would be the percentage error in the following quantities&
4 3ncertainty
4 3ncertainty
Skills
alculating !rrors 2
6< D-4!R
$omplete the table.
$aria'l e
-
.
/
0
L
BB
BB
BB
B;
M
KC
22
?;K
2K
N
2JH
2J2G
2J?
2H?
O
CB;B
CB;K
C;;
C;GK
P
B2C
BJ
BHJ
B?2
Q
HB2?
HBBK
HCB;
HB2
R
<2G
<2G
<2G
<2G
S
?CKG
?H;H
?H??
?CGH
T
?BJ
?KK
?H;
?CH
U
B
<;HB
<;KC
B
V
2J?
K
2JJ
W
Mean $alue
3ncertainty
%hat would be the percentage error in the following quantities&
4 3ncertainty
Skills 6< D-4!R
"denti#ying !rrors
For each of the measurements listed below identify the most li'ely source of error what type of error this is and one method of reducing it.
Measurement A range o# values are o*tained #or the length o# a co''er 3ire
(he reading #or the current through a 3ire is ;
A *eaker o# hot 3ater le#t on the desk a''ears to have gained tem'erature
A mass o# a *eaker sho3s di5erent values on di5erent *alances
A range o# values are o*tained #or the *ounce *ack height o# a dro''ed *all
A #e3 grou's o*tain di5erent gra'hs o# resistance vs light intensity #or an LDR
(he time 'eriod time o# one oscillationN o# a 'endulum
A range o# values are o*tained #or the time a 'arachute takes to reach the ground #rom ;
Skills
Source
Type
Points Plotting
6< D-4!R
(ou are going to practice plotting points on a graph. This s'ill carries up to ) mar's in the I*A.
! a!is
y a!is
! a!is
y a!is
! a!is
y a!is
;
2
;<?
B
;
2
;<2J
B<G
;
B
;
B
;<G
2
;<2H
2<22
;
2
;
B<2
;<B
2
;<2G
B
;<J
B
;
2<H
;
B
;<22
2
;
2<2
;
B<2J
;
B
;
B
;<2?
B
;
B
;
2
;
B
2
2
2<2
2
B
B
B
B<2 ;<2
Skills
;
;
;
;
;
Lines o# $est Fit
6< D-4!R
!raw a line of best t for each of the graphs. 2C
C
2;
?
BC
B;
2
C
B
;
; ;
;
B
B
2
2
A
A
?
?
C
;
C;
2C
?;
2;
A;
BC
2;
B;
B;
C
; C
B;
BC
2;
2C
A;
AC
?;
?C
C;
; ;
C
B; BC 2; 2C ; C ?; ?C C;
B
B
2
2
?
?
C
H;
C
C;
?
?;
A;
2 2;
B
B;
;
;
;
C
B; BC 2; 2C ; C ?; ?C C;
;
B
2
A
?
C
Skills
%radients
6< D-4!R
$alculate the gradients of the graphs below. %or' out the equation for the line.
C; ;; 2C; 2;; BC; B;; C; ; C; B;; BC; 2;; 2C; ;; C; ?;; ?C; C;; ;
B2;
02 ;
C
B;
BC
2;
2C
B;;
0? 0H
K;
0K 0B;
H;
0B2 0B?
?;
0BH 0BK
2; ?
02;
C
H
J
K
G
B;
BB
B2
?
;
;
A 2
;
2
;<;K
B
;<;H
B ;
;
;<2
;
;
;
;
;
;
BJ
BK
BG
2;
2B
22
2
2?
Skills 6< D-4!R
E5uation
%radient !&uations $omplete the table below about graphs and gradients +raph Rearrange +radient E5uation y 'lotted on the y axis m x 'lotted on the x axis y axis 7 V x axis 7 I y axis 7 t x axis 7 Q y axis 7 l x axis 7 R y axis 7 V x axis 7 I y axis 7 E/t x axis 7 V y axis 7 E K x axis 7 f y axis 7 1 /v x axis 7 m y axis 7 mg x axis 7 E P y axis 7 x axis 7 1 /F y axis 7 1 /! x axis 7 f y axis 7 " x axis 7 1 /t y axis 7 v# x axis 7 $ y axis 7 v x axis 7 $ y axis 7 ! x axis 7 %
R
ntercept
c
0
Skills 6< D-4!R
E5uation
%radient !&uations 2 $omplete the table below about graphs and gradients +raph Rearrange +radient E5uation y 'lotted on the y axis m x 'lotted on the x axis y axis 7 V x axis 7 I y axis 7 v x axis 7 F/m y axis 7 & x axis 7 F/m y axis 7 l x axis 7 g y axis 7 T 2 x axis 7 m y axis 7 M x axis 7 g y axis 7 F x axis 7 '/& # y axis 7 V x axis 7 Q y axis 7 ln (Q/Q0) x axis 7 t y axis 7 ( x axis 7 N y axis 7 N P x axis 7 N S y axis 7 R) x axis 7 A y axis 7 T x axis 7 V y axis 7 T x axis 7 Q
R
ntercept
c
0
Skills
"nter'reting %ra'hs
6< D-4!R
+xplain the relationship between the two variables shown in the graphs below. Descri*e the general trendOrelationshi'"denti#y sections o# highestOlo3est gradient .uote any signifcant numerical valuesalculate any gradients you can
"eight 6cm7
2;;
?
BC;
A
B;;
Diameter of %arachute (eeded 6m7
2
C;
B
;
;
;
C
B;
BC
2;
;
,ge 6years7
C
Mass of Load 6*g7
B;;
B;
K;
K; Temp erature 6&7
H; ?;
Relative Strength of +ravity
;
2; ;
02;
B C 2 C A < < B 2
; B;2;;?;C;H;J;K; Time 6minutes7
Distance from the Surface of the Earth 6Radii
2C
B;;
2;
K;
BC
Bacteria +rowth from Test Spot 6cm7
H;
B;
Rate of En8yme ,ctivity
?;
C 2;
;
;
B; ;
;
Time ncu'ated 6days7
B;;
Temp erature 6&7
H
C
C
?
?
Distance from Start 6m7
C;
A
A
$elocity 6m9s7
2
2
B
B
;
; ;
C
B;
BC
Time 6s7
2;
;
C
B;
Time 6s7
BC
2;
Skills
(angents
6< D-4!R
!raw tangents to the line at the following values along the x,axis- 22C, H;, H; and B;C B ;
0;<2
G;
BK;
2J;
H;
?C;
C?;
H;
J2;
KB;
G;;
GG;
B;K;
0;
!raw a tangent to the line and calculate its gradient at the following x,axis values; 0B;
; ;
B
2
A
?
C
0B;
02;
02;
0A;
0A;
0?;
0?;
0C;
0C;
0H;
0H;
0J;
0J;
0K;
0K;
0G;
0G;
0B;;
0B;;
;
B
2
2<; and
A
?
C
B
C;
B2;
?C B;;
?; C
K;
; 2C
H;
2; ?;
BC B;
2;
C ;
; ;
B
2
2<2 and ?<;
Skills
?
C
;
B
2
B
?
6< D-4!R
)ernier alli'ers and Micrometers
*tate the reading on the ernier $allipers to the left and the micrometers to the right.
Skills 6< D-4!R
Descri*ing !x'eriments
The last question of the I*A often requires the description of an experiment to support a theory.
$hange / %hich variables will you 'eep the same and which will you change& 0ange / 1ive specic values for the variables you will use. $alculate / %hat will you calculate or plot& $onclude / %hat result will help you either prove or disprove the theory&
+&SE:A student suggests that i# an egg 3as dro''ed #rom di5erent heights the area o# s'latter 3ould increase as the height increases *ut only until a certain 'oint< /o3 could you investigate this> +&SE:"s the ight time o# a 'a'er 'lane directly 'ro'ortional to the angle o# the nose * N, the sine o# the angle sin* N or neither> +&SE:-hat is the relationshi' *et3een the time that a f@@y 'o' *ottle is shook u' #or and the volume o# li&uid that is lost 3hen the *ottle is o'ened> 3-: /o3 could you investigate the theory that the sur#ace tem'erature o# a resistor is directly 'ro'ortional to the current o3ing through it> 3-: A *attery 3ith internal resistance r is connected in series 3ith a resistor o# resistance R< A student suggests that the 'o3er o# the resistor 3ill *e a maximum 3hen it has a value e&ual to the internal resistance o# the *attery< 3-: /o3 could you investigate the connection *et3een the tem'erature at 3hich a resistor sto's o*eying 1hms la3 and the value o# the resistor> 3-: (he 'hotoelectric e5ect ex'eriment is set u' so that 'hotoelectrons are released< /o3 could you 'rove that the intensity does a5ect the rate o# electron emission *ut only 3hen a*ove the threshold #re&uency> 3-: A 'otato can *e used as a *attery i# electrodes o# co''er and @inc are inserted into it< !x'lain ho3 you could fnd the internal resistance and the em# o# the 'otato using resistors o# C di5erent values< 3-: /o3 could you fnd the relationshi' *et3een the resistivity o# a metal and the tem'erature> 3.: -ater is 'laced in a 'lastic tray, one end it raised, dro''ed and the s'eed o# the 3ater 3ave is measured< A student suggests that the s'eed o# the 3ave de'ends on the height o# the 3ater in the tray< /o3 could you 'rove this> 3.: A cylinder o# solid metal is rolled do3n a ram' and the s'eed is calculated #rom the distance rolled and the time taken to roll< (here is a suggestion that i# the cylinder 3as hollo3 it 3ould *e a5ect more *y the air resistance< /o3 could you investigate this> 3.: /o3 could you investigate 3hether or not the critical angle o# a Pers'ex *lock is a5ected *y the colour o# light that is incident on the *lock> 3.: A #ello3 scientist suggests that the 4oung modulus o# a material de'ends on the tem'erature o# the material< /o3 could you fnd any 'ossi*le relationshi' *et3een the varia*les> 3.: A s'eaker is attached to the to' o# an o'en glass tu*e and set to give out a sound o# fxed #re&uency< (he *ottom o# the tu*e is 'laced in 3ater and the height is adQusted until the frst harmonic is heard< (here is a claim that the height 3ill vary de'ending on the diameter o# the glass tu*e< /o3 could you investigate this>
Skills 6< D-4!R
Descri*ing !x'eriments 2
The last question of the I*A often requires the description of an experiment to support a theory. $hange / %hich variables will you 'eep the same and which will you change& 0ange / 1ive specic values for the variables you will use. $alculate / %hat will you calculate or plot& $onclude / %hat result will help you either prove or disprove the theory&
,S: !x'lain ho3 it is 'ossi*le to fnd the resistivity o# a conducting material at room tem'erature< (he material is a cylinder o# radius r and length l < ,S: Descri*e the ex'eriment and accom'anying calculationsOgra'hs to fnd the 4oung modulus o# a material o# original length l and cross sectional area A< ,S: !x'lain ho3 to fnd the s'ring constant o# a metal s'ring 3ith fve B;;g masses and a ; cm ruler< ,S: Descri*e the ex'erimental set u' and the gra'h you 3ould dra3 to fnd the re#ractive index o# a trans'arent material< /o3 3ould your gra'h give you an ans3er> 30: A mass and s'ring system is set u' 3ith a 'iece o# card 'laced *et3een t3o o# the masses< (he time 'eriod o# this dam'ed system is measured< "t is suggested that the area o# the card does not a5ect the time 'eriod *ut the sha'e o# the card does, ho3 could you investigate this> 30: A 'endulum and a massOs'ring system are set u' to have the same time 'eriod o# oscillation< 4ou are to investigate 3hich S/M system 3ill su5er the greatest degree o# dam'ing and conclude 3hich 3ill sto' frst< 30: A ca'acitor has the ca'acitance and maximum voltage 'rinted on the casing< /o3 could you investigate that this 3as the largest voltage allo3ed *e#ore the ca'acitor *reaks> 30: ar A is crashed into stationary car $< /o3 could you investigate the theory that the collisions 3ill *e elastic 3hen car $ has less mass than car A *ut inelastic 3hen car $ has an e&ual or greater mass than car A> 30: /o3 could you investigate 3hether the angle a 'endulum is dis'laced #rom a5ects the time 'eriod> 30: A student suggests that the eciency o# a trans#ormer is directly 'ro'ortional to the diameter o# the 3ire 3hich is 3ra''ed around the 'rimary coil< /o3 could you 'rove this theory, 3hat 3ould you 'lot on a gra'h and 3hat result 3ould su''ort the theory> 31: A student uses a %M tu*e to investigate the inverse s&uare la3< /o3 could she investigate i# the inverse s&uare la3 holds true in all direction #rom an al'ha source> 31: !x'lain ho3 it is 'ossi*le to fnd the a*solute @ero tem'erature using air tra''ed in a glass tu*e in a science la* 3hich is 3ell a*ove the value itsel#< 31: /o3 could you fnd the constant o# 'ro'ortionality *et3een the volume o# a gas and the tem'erature 3hen investigating harles gas la3>
31: -ith the use o# a *lock o# ice, a tem'erature 'ro*e and $unsen *urner that 'rovides a constant energy su''ly, ex'lain ho3 you could fnd out ho3 many times *igger the s'ecifc latent heat o# va'orisation is than the s'ecifc latent heat o# #usion<
Skills
Rearranging + Deriving !&uations
6< D-4!R
Rearrange su*Qect
to make " the
Su*stitute this into Su*stitute this into the e&uation Su*stitute this into the e&uation
se
to sim'li#y the e&uation
Su*stitute
into the e&uation
Multi'ly out the *rackets Su*stitute this into the e&uation Rearrange the e&uation to fnd the angle to the rd maxima
Su*stitute
into the e&uation
Su*stitute
into the e&uation
Su*stitute
se
into the e&uation
to remove t #rom the e&uation
Sim'li#y this
!lastic energy is converted into kinetic Make v2 the su*Qect Re'lace this 3ith "# +7; rearrange the e&uation to make " the su*Qect se
to make F the su*Qect
alculate the !nergy stored using the distance moved is
Skills
i#
Rearranging + Deriving !&uations 2
6< D-4!R
(he centri'etal #orce o# a satellite is due to the gravitational #orce *et3een it and the 'lanet Sim'li#y the e&uation and much as you can and rearrange to make & the su*Qect se
to remove v #rom the e&uation
Sim'li#y the e&uation and use re'lace , se
to
to remove f #rom the e&uation
Rearrange su*Qect
to make
the
Make the su*Qect Rearrange the e&uation to make t the su*Qect (he centri'etal #orce o# a charged 'article is due to the magnetic #orce acting on it Rearrange the e&uation to make Q the su*Qect Su*stitute se
into the e&uation to remove B #rom the e&uation
Rearrange su*Qect Make
Su*stitute
Rearrange
to make
the
the su*Qect
into the e&uation
to make T the su*Qect
Su*stitute this into the e&uation
"# the V is volume o# a cu*e o# side l , rearrange the e&uation to make F the su*Qect
Skills 6< D-4!R
nits
%rite down the standard units for the following quantities. !nergy Density !nergy Stored -avelength (ensile Strength Force on a Moving harge Fre&uency (ensile Stress Magnetic Flux urrent Re#ractive "ndex Magnetic Flux Density Potential Di5erence Momentum Magnetic Flux Linkage Resistance "m'ulse "nduced !MF !MF Angular Dis'lacement "ntensity Resistivity Angular S'eed Activity Po3er (ime Period /al# Li#e Moment %ravitational Field Pressure )elocity Strength )olume Acceleration %ravitational Potential (em'erature Mass !lectric Field Strength S'ecifc /eat a'acity -eight !lectric Potential S'ecifc Latent Force a'acitance -ork Done (ime onstant There are 2 base units 3*I units4 which all other units can be derived from. Length in metre, mMass in kilogram, kg(ime in second, s!lectric urrent in am'ere, A (hermodynamic (em'erature in kelvin, 9Amount o# Su*stance in mole, molLuminous "ntensity in candela, cd %rite down the units for the following quantities in *I units. Area 4oung Modulus )olume !lastic !nergy Stored urrent Fre&uency )oltage -avelength Resistance Re#ractive "ndex Resistivity Momentum Po3er Force !nergy "m'ulse Distance Plancks onstant S'eed De $roglie -avelength Acceleration Angular Dis'lacement Force Angular )elocity -ork Done entri'etal Acceleration !nergy entri'etal Force Moment %ravitational Field onstant -eight %ravitational Potential Po3er !lectric Field Strength %ravitational Field Strength !lectric Potential Pressure Permittivity o# Free S'ace Density a'acitance S'ring onstant (ime onstant (ensile Stress !nergy Stored in a a'acitor (ensile Strain Magnetic Flux Density
Force on a Moving harge Magnetic Flux "nduced !MF Activity
$inding !nergy Molar %as onstant S'ecifc /eat a'acity S'ecifc Latent /eat
Practical
Photon !nergy
6< D-4!R
(ou are going to use the minimum voltages required for di5erent 6+!s to emit light to calculate Plan'7s constant8 -
E5uipment List Po3er Pack )oltmeter Ammeter
Photon !nergy Array $lack Plastic (u*e Leads
Tas* •
• •
• • • • • •
onnect the 'o3er 'ack to the Photon !nergy Array and ensure that the correct terminals are connected together< Select a voltage o# C)< onnect the voltmeter and ammeter to the Photon !nergy Array< (urn the 'otential divider dial all the 3ay to the le#t and select the L!D o# 3avelength ?; nm< alculate the #re&uency, f , o# the light it 3ill emit< Place the *lack tu*e over the L!D and vie3 #rom the other end< (urn the 'otential divider dial until light is only Qust emitted< Record the voltmeter reading< (ake re'eat readings and calculate the mean voltage, , #or that L!D< Re'eat this #or L!Ds o# 3avelengths C;C, CH;, HBC, HCC, KJC and GC; nm<
•
Dis'lay your results #or each L!D in a ta*le including a column o# e , 3here e is the charge o# an electron and is the mean voltage< Plot a gra'h o# e on the y0axis against f on the x0axis<
•
Dra3 a line o# *est ft #or your data<
•
,fter the E!periment -hat 3as the 'recision o# the voltmeter> se the 'recision to calculate the uncertainty in your frst reading #or the voltage o# the L!D 3ith 3avelength C;C< -hat is the 'ercentage uncertainty> alculate the uncertainty in your value o# the mean voltage #or this L!D< -hat is the 'ercentage uncertainty> se the 'recision to calculate the uncertainty in your frst reading #or the voltage o# the L!D 3ith 3avelength H;C< -hat is the 'ercentage uncertainty> alculate the uncertainty in your value o# the mean voltage #or this L!D< -hat is the 'ercentage uncertainty> se your gra'h to comment on the relia*ility o# your results< alculate the gradient o# your line o# *est ft< -hat is the di5erence *et3een your value and the acce'ted value o# H alculate the 'ercentage di5erence *et3een your gradient and the acce'ted value< (heory states that the line 3ill have an e&uation o# , extra'olate your line o# *est ft so it cuts the y axis, does your gra'h su''ort the theory> -hy O 3hy not> -hat do you think 3as the largest source o# error in the ex'eriment>
!x'lain your ans3er< -hat is the name give to this ty'e o# error>
Analysis 6< D-4!R
.uarks, /adrons and Le'tons
(ou are going to use data on the fundamental particles to nd the theoretical masses of some 9adrons.
E!perimental Data %article
Mean Mass 6Me$7
Mass 6Me$7
u
?
C
C<
d
J
G
K
s
BJ 2
BC
BC C
c
BH BJ
B? ?2
B ?? B
'
?B 2H
?? 2
? BG 2
t
BGC;; ;
BJ?;; ;
BJB;; ;
e
;
;
;
;
B;?
B ; C
B;H
<
BK 2
BK C?
B HC ?
3ncertainty in Mass
%ercentage 3ncertainty in Mean
,nalysis alculate the mean masses #or each o# the 'articles< alculate the uncertainty in the mass reading #or each 'article< (his is e&ual to hal# the range o# the valuesN< -hat is this as a 'ercentage o# the mean> Divide the uncertainty *y the mean value then multi'ly *y B;;N< -hich has the lo3est 'ercentage uncertainty in the mean m ean value> /o3 can 3e descri*e this value> -hat is the &uark com'osition o# a 'roton> se the mean values to calculate the theoretical mass o# a 'roton< -hat is the 'ercentage uncertainty in this value> 4ou 4ou should add the 'ercentage uncertainties o# the &uarks usedN< (he actual rest mass o# a 'roton is GK< Me)< Me)< -hat is the di5erence di5erence *et3een this and your theoretical value> -hat is the &uark com'osition o# a neutron> se the mean values to calculate the theoretical mass o# a neutron< -hat is the 'ercentage uncertainty in this value> (he actual rest mass o# a neutron is GG -hat is the &uark com'osition o# a neutral 'ion> se the mean values to calculate the theoretical mass o# a neutral 'ion< -hat is the 'ercentage uncertainty in this value> (he actual rest mass o# a ;is BC<; Me)< Me)< -hat is the di5erence *et3een this and your theoretical value> -hat is the &uark com'osition o# a 'ositive 'ion> se the mean values to calculate the theoretical mass o# a 'ositive 'ion< -hat is the 'ercentage uncertainty in this value>
(he actual rest mass o# a Tis BG -hat is the &uark com'osition o# a 'ositive kaon> se the mean values to calculate the theoretical mass o# a 'ositive kaon< -hat is the 'ercentage uncertainty in this value> (he actual rest mass o# a 9 T is ?G -hat is the &uark com'osition o# a neutral kaon> se the mean values to calculate the theoretical mass o# a neutral kaon< -hat is the 'ercentage uncertainty in this value> (he actual rest mass o# a 9 ; is ?GJ
Analysis
(he (hreshold (hreshold Fr Fre&uency
6< D-4!R
(ou are going to analyse data from an experiment investigating the photoelectric e5ect. :sing the wavelengths of the photons used and the speeds of the emerging electrons you will determine the threshold frequency of the metal.
E!perimental Data /ere are the measured s'eeds o# the emerging 'hotoelectrons #rom the sur#ace o# the metal< (he Planck onstant 7 H1 m9s7 Wavelength= ! 6nm7 ;;
K
K
K
K
2 ;;
B2<;J
B2<;J
B 2 <; G
B 2 <; K
B C;
B?
B?
B G <2 2
B ?
B 2;
BJ<;C
BJ<;G
B J <; H
B J <; H
B ;;
BG
BG<;J
B G <; J
B G <; K
Wavelength= ! 6nm7
Fre5uency= f 6 ! ->-1 "87
Mean Speed= v 6 ! ->1 m9s7
Mean E K 6 ! ->?-@ A7
;; 2;; BC; B2; B;;
,nalysis -hat 3ere the de'endent and inde'endent varia*les in this investigation> se to calculate the #re&uency o# the 'hotons #or each 3avelength< alculate the mean s'eed o# the electrons given out #or each 3avelength< se
to calculate the mean kinetic energy E K N o# the emerging 'hotoelectrons
Plot a gra'h o# kinetic energy on the y0axisN against the #re&uency on the x0axisN< Dra3 a line o# *est ft and extra'olate this to so it cuts the x0axis< alculate the gradient o# your line< (heory states that the gradient should *e e&ual to the Planck constant< constant< -hat is the di5erence di5erence *et3een you gradient and the acce'ted value> -hat is the 'ercentage di5erence o# your value #rom the acce'ted value>
(he threshold #re&uency #re&uency o# the metal can *e o*tained #rom #rom your x0interce't o# your gra'h< -hat value did you o*tain #or the threshold #re&uency> (he acce'ted value is ; alculate the 'ercentage di5erence #rom the acce'ted value< sing either your gra'h or the e&uation calculate the 3ork #unction, φ 0BG (he acce'ted value is 2 -hat is the 'ercentage di5erence o# your value #rom the acce'ted value> alculate the uncertainty in the s'eed #or the data #rom 'hotons o# 3avelength BC; nm< -hat is this as a 'ercentage o# the mean s'eed>
Analysis
Line S'ectra
6< D-4!R
(ou are going to analyse the frequencies of photons emitted when w hen electrons ma'e transitions between di5erent energy levels in 9ydrogen atoms. (he Paschen Paschen Series Fre5uency= f Mean f 6! ->-0 "87 6! ->-0 "87
Transit ion HV
2
2
2
CV
2 < G
2<2K
2 < C
?V
B
B
B
Fre5uency= f 6! ->-0 "87
Transit ion
(he $almer Series Mean f 6! ->-0 "87
HV2
J <2 J
J<
J < H
CV2
H
J<2H
H
?V2
H <2
H
H
V2
?
?
?
Fre5uency= f 6! ->-1 "87
Transit ion
(he Lyman Lyman Series Mean f 6! ->-1 "87
HVB
< C
<;B
<2 B
CVB
<2?
<; C
?VB
2
VB
2
2
<; 2
Wavelength = ! 6nm7
Energy Dierence 6e$7
Wavelength = ! 6nm7
Energy Dierence 6e$7
Wavelength = ! 6nm7
Energy Dierence 6e$7
2VB
2 < J 2
For each transition calculate the mean #re&uency o# the 'hoton emitted< se the 3ave s'eed e&uation,
to calculate the 3avelength o# the 'hoton<
sing calculate the energy o# the 'hoton in Uoules< onvert this to electronvolts and record it in the ta*le<
-hat is the uncertainty in the #re&uency o# the ? V transition> alculate this as a 'ercentage o# the mean #re&uency #or this transition< -hat is the uncertainty in the #re&uency o# the C V 2 transition> alculate this as a 'ercentage o# the smallest #re&uency #or this transition< -hat is the uncertainty in the #re&uency o# the H V B transition> alculate this as a 'ercentage o# the largest #re&uency #or this transition< For each transition state 3hat ty'e o# 'hoton #rom the !M S'ectrum is emitted< For 'hotons in the )isi*le Light region o# the !M S'ectrum state 3hich colour the 'hoton 3ould *e< "# the ground state n7BN has an energy o# B
Analysis 6< D-4!R
de $roglie -avelength
+lectrons were accelerated to a range of speed and their de ;roglie wavelengths were measured. :se this experimental data to nd a value for Planc'7s constant.
E!perimental Data /ere are the measured 3avelengths o# the electrons travelling at certain velocities< !lectron rest mass 7 G
$elocity= v 6m9s7
De Broglie Wavelength= ! 6! ->?0 m7
C
B?
B?
B?
H
B2<;B
B2
B2<2;
J
B;<G
B;<K
B;
K
G<;G
G<;C
G
G
K<2G
K<;B
J
B;
J<B
J
J<G
Mean ! 6! ->?0 m7
,nalysis -hat is the inde'endent varia*le in this investigation> -hat is the de'endent varia*le in this investigation> -hat is the 'recision o# the 3avelength measurements> -hat is the 'recision o# the velocity measurements> -hat is the uncertainty in the velocity measurements> alculate the 'ercentage uncertainty in the velocity measurement o# K mOs alculate the mean values o# the de $roglie 3avelength #or each velocity< For each mean value calculate B O !< alculate the uncertainty in the measurement o# ! 3hen v is C mOs< -hat is this as a 'ercentage o# the mean value> alculate the uncertainty in the measurement o# ! 3hen v is J mOs< -hat is this as a 'ercentage o# the mean value> alculate the uncertainty in the measurement o# ! 3hen v is G mOs<
./!
6 m?-7
-hat is this as a 'ercentage o# the mean value> Plot a gra'h o# v against B O ! and dra3 a line o# *est ft< Does the line 'ass through the origin> Should it> !x'lain your ans3er< alculate the gradient o# your line o# *est ft<
"# v and B O ! are linked *y the e&uation , 3hat does the gradient o# your line o# *est ft re'resent> se your gradient to calculate a value o# Plancks constant, -< (he acce'ted value is H -hat is this as a 'ercentage o# the acce'ted value>
Practical
"0) %ra'hs
6< D-4!R
(ou are going to carry out an investigation to nd the I, graphs of three components.
E5uipment List $attery or Po3er Pack Leads 3ith rocodile li's )oltmeter Ammeter Multimeter
)aria*le Resistor Resistor Filament Lam' Diode Sa#ety Resistor at least B;;XN
Tas*
•
Set u' the a''ro'riate circuit #or the com'onent you are investigating< For the diode ex'eriment it is vital to include a sa#ety resistor< hange the 'otential di5erence V N across the com'onents #rom @ero to the maximum availa*le #rom the 'o3er su''ly< Measure the current I N #or each '
•
-rite do3n the 'recision o# your meters<
•
•
•
•
(ake re'eat reading and calculate a mean value
•
Record your results in a ta*le<
•
Plot a gra'h o# I on the y0axisN against V <
,fter the E!periment -hat 3as the inde'endent varia*le in your investigation> -hat did you use to measure this and 3hat 3as the 'recision o# this 'iece o# e&ui'ment> -hat 3as the de'endent varia*le in your investigation> -hat did you use to measure this and 3hat 3as the 'recision o# this 'iece o# e&ui'ment> "# your voltmeter measures a ' -hat is the name give to the ty'e o# error res'onsi*le #or the s'read o# results in your ammeter readings> R!S"S(1R
-hat is the uncertainty in the current #or the greatest ' alculate this as a 'ercentage o# the mean current at this ' -hat resistance does your gra'h suggest that the resistor has> alculate the distance *et3een the actual value and the value o*tained #rom your gra'h< -hat is this as a 'ercentage o# the actual value> F"LAM!6( LAMP At 3hat ' -hat is the gradient o# the line 3hen it did o*ey 1hms la3> -hat resistance does your gra'h suggest that the lam' has> D"1D! -hat #eature o# your gra'h sho3s that the com'onent is a semiconducting diode> Does the diode a''ear to o*ey 1hms la3 at any 'oint on the gra'h> alculate the gradient and use this to calculate the resistance o# the diode during this 'eriod<
Analysis 6< D-4!R
1hms La3
A resistor of un'nown resistance was connected to a variable power supply. The current through8 I 8 and potential di5erence across8 V 8 were measured. (ou will use this information to calculate the resistance8 R8 of the resistor.
E!perimental Data %otential Dierence= V 6$7 G
B
&urrent= I 6,7 B<2H ;
Mean &urrent= I 6,7
Resistance= R 6C7
,nalysis om'lete the ta*le *e calculating the mean values o# V and I < -hat is the 'recision o# the voltmeter> -hat is the 'recision o# the ammeter> -hat is the uncertainty in the largest 'ositive 'otential di5erence> alculate this as a 'ercentage o# the mean 'otential di5erence< -hat is the uncertainty in the smallest negative 'otential di5erence> alculate this as a 'ercentage o# the mean 'otential di5erence< -hat is the uncertainty in the smallest 'ositive current> alculate this as a 'ercentage o# the mean current< -hat is the uncertainty in the largest negative current> alculate this as a 'ercentage o# the mean current<
B<2? B<;B ;
-hich ty'e o# error is res'onsi*le #or the di5erences in the 'otential di5erence and current measurements> Plot a gra'h o# I on the y axisN against V on the x axisN< Does your line o# *est ft 'ass through the origin> Should it> !x'lain your ans3er< -hat does the gradient o# your gra'h re'resent> alculate the gradient o# your line o# *est ft< se the gradient to calculate the resistance, R, o# the resistor< (he given value o# the resistor is J<Y, 3hat is the di5erence *et3een your value and the given value> -hat is this as a 'ercentage o# the acce'ted value> om'lete the ta*le using the e&uation to calculate R< alculate the mean value o# resistance #rom the ta*le< -hat is the uncertainty o# the mean resistance> -hat is the di5erence *et3een the acce'ted value given a*ove and the value you calculated #rom the ta*le> alculate this as a 'ercentage o# the acce'ted value<
(ou are going to investigate how much light passes through a number of layers of tracing paper using a bright light source and a light dependent resistor.
E5uipment List LDR Leads S3itch $atteryOPo3er Pack )oltmeter
Ammeter ;cm Ruler (racing Pa'er Scissors Desk Lam'
Tas* •
Set u' a suita*le circuit using the a''aratus 'rovided to determine the resistance o# the LDR< Dra3 a diagram o# your circuit sho3ing your 'o3er su''ly, s3itch and meters<
•
Position the lam' at a distance given *y your su'ervisor so that it #ully illuminates the LDR<
•
S3itch it on and determine the resistance R0 o# the LDR<
•
•
•
• • •
•
Do not change the distance 'etween the lamp and the LDR in the remainder of the e!periment: Place a small 'iece o# tracing 'a'er over the LDR so that only light that 'asses through the 'a'er reaches its light sensitive sur#ace< (ake readings to determine the ne3 resistance o# the LDR< Re'eat the LDR resistance determination #or a range o# values o# 1, 3here 1 is the num*er o# layers o# tracing 'a'er *et3een the LDR and the lam'< (ake re'eat readings< Present all o# your measurements in a ta*le< For each value o# 1 calculate R = R1 – R0, 3here R1 is the LDR resistance 3ith 1 layers o# 'a'er< se your results to 'lot a gra'h o# Ragainst 1< Dra3 a lineOcurve o# *est ft<
,fter the E!periment -hat 3as the inde'endent varia*le in your investigation> /o3 many di5erent values did you use #or this varia*le>
-as this enough values> Uusti#y your ans3er< -hat 3as the de'endent varia*le in your investigation> /o3 did you calculate this> -hat 3as the 'recision o# the ammeter> -hat 3as the 'recision o# the voltmeter> se your ra3 data to calculate the uncertainty in the current 3hen 1 7 ?< -hat is this as a 'ercentage o# the mean current> se your ra3 data to calculate the uncertainty in the voltage 3hen 1 7 ?< -hat is this as a 'ercentage o# the mean voltage> -hat is the 'ercentage uncertainty in the resistance calculated #rom these t3o values> -hat does your gra'h sho3> Descri*e any #eatures and ex'lain any relationshi's< Does your gra'h su''ort the theory that as light intensity increases the resistance o# the LDR decreases> -hyO3hy not> /o3 could you fnd the thickness o# a single 'iece o# tracing 'a'er> !x'lain ho3 your ex'erimental set u' and gra'h could *e used as a &uality control measurement in tracing 'a'er manu#acturing<
Practical 6< D-4!R
(hermistor (hermometer
(ou are going to calibrate a thermistor to be used as a thermometer and use it to nd the temperature of a liquid.
E5uipment List $attery or Po3er 'ack Leads 3ith rocodile li's )oltmeter Ammeter Multimeter
(hermistor ali*rated (hermometer $eaker 9ettle Plastic $ag
Tas* •
Put the thermistor in a 3ater'roo# 'lastic *ag and 'lace it into a *eaker<
•
-rite do3n the 'recision o# the thermometer<
•
Pour B;;ml *oiling hot 3ater into the *eaker<
•
Stir the 3ater and measure the tem'erature T o# the 3ater, the 'otential di5erence V and the current I < Record your results in a ta*le<
•
For every B; Z dro' in tem'erature measure I and V <
•
-rite do3n the 'recision o# the ammeter and voltmeter<
•
alculate the resistance R o# the thermistor at each tem'erature using the e&uation V = IR
•
Re'eat the ex'eriment t3ice and determine the average resistance at each tem'erature<
•
Plot a gra'h o# resistance R against tem'erature T <
•
,fter the E!periment -hat 3as the inde'endent varia*le in your investigation> /o3 did you measure this> -hat 3as the de'endent varia*le in your investigation> /o3 did you measure this>
Descri*e the gra'h you dre3 #rom your results< se your gra'h to comment on the relia*ility o# your results< /o3 could you im'rove the relia*ility o# your results> Ask your su'ervisor to 'rovide you 3ith a *eaker o# hot 3ater< se your thermistor circuit and record the current and voltage o# the 3ater and ask your su'ervisor to measure the tem'erature using the cali*rated thermometer< alculate the resistance o# the thermistor< se your gra'h to fnd the tem'erature o# the 3ater< -hat is the di5erence *et3een your value #or the tem'erature and your su'ervisors value> alculate the 'ercentage di5erence *et3een your value and your su'ervisors value< For the largest tem'erature reading use your ra3 data to calculate the uncertainty in the current reading< alculate this as a 'ercentage o# the mean current at this tem'erature< For the smallest tem'erature reading use your ra3 data to calculate the uncertainty in the voltage reading< alculate this as a 'ercentage o# the mean voltage at this tem'erature< For the middle tem'erature reading use your ra3 data to calculate the uncertainty in the current reading< alculate this as a 'ercentage o# the lo3est voltage reading at this tem'erature< For the middle tem'erature reading use your ra3 data to calculate the uncertainty in the voltage reading< alculate this as a 'ercentage o# the smallest voltage reading at this tem'erature< /o3 could you increase the 'recision o# your results>
Practical 6< D-4!R
Resistivity o# o''er
(ou are going to carry out an experiment to determine the resistivity of a copper.
E5uipment List $attery Leads 3ith rocodile li's )oltmeter Ammeter
Multimeter Rulers ;cm and BmN )ernier alli'ers o''er -ire
Tas* • •
• •
•
•
• •
•
ut a section o# co''er 3ire Qust over Bm in length< Measure the diameter o# the 3ire in a num*er o# 'laces along the 3ire< Record your readings< alculate the cross sectional area o# the 3ire< Set u' a circuit 3ith the *attery, ammeter and co''er 3ire in series< onnect a voltmeter to measure the 'd across the 3ire< AdQust the 3ire so only Bm o# the co''er 3ire is in the circuit< Record the current and the 'otential di5erence< S-"(/ 1FF 1R D"S166!( (/! $A((!R4 $!(-!!6 R!AD"6%S (ake re'eat readings and calculate the mean values #or your readings< Re'eat this to take readings o# current and 'otential di5erence #or di5erence lengths o# co''er 3ire< alculate the resistance #rom the mean values<
•
Plot a gra'h o# the resistance on the y0axisN and the length o# co''er 3ire on the x0axisN
•
alculate the gradient o# the line< se this to calculate the resistivity o# co''er<
,fter the E!periment -hat -hat -hat -hat -hat -hat
3as the inde'endent varia*le in your investigation> did you use to measure this> 3as the 'recision o# this 'iece o# e&ui'ment> 3as the de'endent varia*le in your investigation> did you use to measure this> 3as the 'recision o# this 'iece o# e&ui'ment>
se your ra3 data to calculate the uncertainty in your largest measurement o# the current< 6o3 calculate the 'ercentage uncertainty in this measurement< se your ra3 data to calculate the uncertainty in the corres'onding measurement o# the 'otential di5erence< 6o3 calculate the 'ercentage uncertainty in this measurement< -hat is the 'ercentage uncertainty in the resistance calculated #rom these measurements> se your gra'h to comment on the relia*ility o# your results< /o3 could you increase the relia*ility o# your results> /o3 could you increase the 'recision o# your results> "# your voltmeter measures a 'otential di5erence o# ;<2; ) 3hen the *attery 3as disconnected, 3hat is the name given to this ty'e o# error> -hat is the name give to the ty'e o# error res'onsi*le #or the s'read o# results in your voltmeter readings #or ;cm> -hy do you think you 3ere instructed to s3itch o5 or disconnect the *attery *et3een measurements>
Analysis
Resistivity o# o''er
6< D-4!R
!i5erent lengths of copper wire were used to nd its resistivity. A potential di5erence was applied across the wires and the current through them was recorded. The wire had a diameter of <.= mm.
E!perimental Data /ere is the ex'erimental data collected #rom the di5erent lengths o# co''er 3ire< Length p:d:= V &urrent= I Mean &urrent= I Resistance= R = l 6m$7 6,7 6,7 6C7 6m7 B<;;
C?
2
B
B
2<;;
C?
B<;2B
B<;;?
B<;B?
<;;
C?
;
;
;
?<;;
C?
;
;
;
C<;;
C?
;<GC
;
;
H<;;
C?
;<?J
;<
;<?
,nalysis alculate the cross0sectional area o# the 3ire using the e&uation
alculate the mean value o# current #or each o# the di5erent lengths o# 3ire< se the e&uation
to calculate the resistance o# each o# the di5erent lengths o# 3ire<
-hat is the 'recision o# the length measurements> -hat is the smallest division on the ruler used to measure it> -hat is the 'recision o# the voltmeter used> alculate the uncertainty in the current 3hen the 3ire is 2<;; m long< -hat is this as a 'ercentage o# the mean current> -hat 3ould *e the 'ercentage uncertainty in the corres'onding value o# R> alculate the uncertainty in the current 3hen the 3ire is ?<;; m long< -hat is this as a 'ercentage o# the mean current> -hat 3ould *e the 'ercentage uncertainty in the corres'onding value o# R> alculate the uncertainty in the current 3hen the 3ire is H<;; m long< -hat is this as a 'ercentage o# the mean current> -hat 3ould *e the 'ercentage uncertainty in the corres'onding value o# R> Plot a gra'h o# R y axisN against l and dra3 a line o# *est ft< Does your line o# *est ft 'ass through the origin> Should it> !x'lain your ans3er< "# the e&uation linking R and l is , 3hat does the gradient o# your line re'resent> alculate the gradient o# your line o# *est ft< se the gradient to fnd the value o# resistivity< (he acce'ted value o# the resistivity o# co''er at 2; Z is B alculate this as a 'ercentage o# the acce'ted value<
Practical 6< D-4!R
Resistivity o# a Metal -ire
(ou are going to investigate the variation with length of the resistance of the wire supplied
E5uipment List $attery Leads 3ith rocodile li's )oltmeter Ammeter
Multimeter Rulers ;cm and BmN )ernier alli'ers o''er -ire
Tas* •
• •
•
• •
om'lete the circuit as sho3n in the diagram *elo3= crocodile cli's [, 4 and P are already in 'lace 3ith leads attached< Record the 'recision o# your voltmeter and your ammeter S3itch on the 'o3er su''ly and adQust the varia*le resistor i# you are using one in your circuit, or the voltage control on the 'o3er su''ly i# you do not have a varia*le resistor, so that the current, I , sho3n on the ammeter is ;:1> , 'efore reading the voltmeter 1*serve ho3 the 'd, V , *et3een [ and P varies #or di5erent lengths L o# 3ire *et3een [ and P< Decide on a range o# values #or L #or 3hich you 3ill measure V . Pre'are a ta*le to record all o# your measurements #or L and ) and include a column #or the resistance, R, o# the 3ire *et3een [ and P<
•
•
arry out your ex'eriment and com'lete your ta*le< Dra3 a gra'h to sho3 ho3 R 'lotted on the vertical axisN varies 3ith L<
,fter the E!periment -hat 3as the inde'endent varia*le in your investigation> -hat did you use to measure this> -hat 3as the 'recision o# this 'iece o# e&ui'ment> -hat 3as the de'endent varia*le in your investigation> -hat did you use to measure this> -hat 3as the 'recision o# this 'iece o# e&ui'ment> se your ra3 data to calculate the uncertainty in your largest measurement o# the mean 'd, V 6o3 calculate the 'ercentage uncertainty in this measurement< -hat is the uncertainty in your value #or the current, I > 6o3 calculate the 'ercentage uncertainty in this measurement< -hat is the 'ercentage uncertainty in the resistance calculated #rom these measurements> se your gra'h to comment on the relia*ility o# your results< /o3 could you increase the relia*ility o# your results> /o3 could you increase the 'recision o# your results> alculate the gradient o# the gra'h> -hat does the gradient re'resent> -hat value do you get #or the resistivity o# the 3ire>
Practical
Series and Parallel ircuits
6< D-4!R
(ou are going to carry out an experiment to investigate how the theoretical value of resistors in series and parallel di5ers from values obtained experimentally.
E5uipment List $attery or Po3er Pack Leads 3ith rocodile li's )oltmeter
Ammeter Multimeter Resistors o# at least K di5erent valuesN
Tas* •
S-"(/ 1FF 1R D"S166!( (/! $A((!R4 $!(-!!6 R!AD"6%S<
•
Set u' a circuit 3ith t3o resistors in series, a 'o3er su''ly, a voltmeter and an ammeter<
•
Dra3 a diagram o# the circuit you used<
•
-rite do3n the 'recision o# the instruments used<
•
alculate the theoretical value #or the total resistance o# the resistors<
•
(ake readings o# the 'otential di5erence and the current o# the circuit<
•
alculate the total resistance o# the resistors
•
Re'eat the ex'eriment 3ith di5erent values o# R B and R2<
•
Set u' a similar circuit 3ith t3o resistors in 'arallel<
•
Record all o# your results in t3o ta*les like the one *elo3< RB XN
R2 XN
R (1(AL XN theoretical
'
urrent I AN
R (1(AL XN measured
,fter the E!periment Series Look at the data 3ith the lo3est theoretical total resistance< -hat is the uncertainty in the ' alculate the 'ercentage uncertainty in this reading< -hat is the di5erence *et3een the actual value and the theoretical value #or the total resistance> alculate this as a 'ercentage o# the theoretical value< Look at the data 3ith the second highest theoretical total resistance< -hat is the uncertainty in the current reading> alculate the 'ercentage uncertainty in this reading< -hat is the di5erence *et3een the actual value and the theoretical value #or the total resistance> alculate this as a 'ercentage o# the theoretical value< -hich set o# data has a smaller 'ercentage di5erence> -hat 3ord can 3e use this to descri*e this result>
,fter the E!periment %arallel Look at the data 3ith the second lo3est theoretical total resistance< -hat is the uncertainty in the ' alculate the 'ercentage uncertainty in this reading< -hat is the di5erence *et3een the actual value and the theoretical value #or the total resistance> alculate this as a 'ercentage o# the theoretical value< Look at the data 3ith the highest theoretical total resistance< -hat is the uncertainty in the current reading> alculate the 'ercentage uncertainty in this reading< -hat is the di5erence *et3een the actual value and the theoretical value #or the total resistance> alculate this as a 'ercentage o# the theoretical value< -hat do you think is res'onsi*le #or the di5erence *et3een the theoretical and actual values>
Practical 6< D-4!R
!MF and "nternal Resistance
(ou are going to carry out an experiment to investigate the relationship between the terminal potential di5erence across and the current through a cell or battery when connected to a range of di5erent value resistors.
E5uipment List $attery Leads 3ith rocodile li's )oltmeter
Ammeter Multimeter Resistors o# K di5erent valuesN
Tas* • •
• •
S-"(/ 1FF 1R D"S166!( (/! $A((!R4 $!(-!!6 R!AD"6%S Set u' a circuit 3ith the *attery, ammeter and a resistor in series< onnect a voltmeter to measure the 'd across the cell terminals< -rite do3n the 'recision o# the instruments used< For each resistor, record the current and terminal 'd values in a suita*le ta*le< "nclude the resistor value in the ta*le< (ake readings #or the eight di5erent resistors 'rovided<
• • •
•
(ake re'eat readings Dra3 a circuit diagram o# the circuit you used< Plot a gra'h o# the terminal 'd on the y0axisN and the current on the x0axisN and dra3 a line o# *est ft< alculate the gradient o# the line and the y interce't<
,fter the E!periment -hat 3as the inde'endent varia*le in your investigation> /o3 did you vary this> -hat did you use to measure this> -hat 3as the 'recision o# this 'iece o# e&ui'ment> -hat 3as the de'endent varia*le in your investigation> -hat did you use to measure this> -hat 3as the 'recision o# this 'iece o# e&ui'ment> se the 'recision o# your e&ui'ment to calculate the 'ercentage uncertainty o# your smallest measurement o# the current< se the 'recision o# your e&ui'ment to calculate the 'ercentage uncertainty o# your smallest measurement o# the 'otential di5erence< -hich is the greater source o# uncertainty> -hy> se your ra3 data to calculate the uncertainty in your largest measurement o# the current< 6o3 calculate the 'ercentage uncertainty in this measurement< se your ra3 data to calculate the uncertainty in your largest measurement o# the 'otential di5erence< 6o3 calculate the 'ercentage uncertainty in this measurement< se your gra'h to comment on the relia*ility o# your results< /o3 could you increase the relia*ility o# your results> /o3 could you increase the 'recision o# your results> -hy do you think you 3ere instructed to s3itch o5 or disconnect the *attery *et3een measurements>
Analysis 6< D-4!R
!MF and "nternal Resistance
A battery was connected to a resistor8 the current was measured through the circuit and the potential di5erence was measured at the terminals of the battery. ;y varying the resistor value it is possible to nd the +F and internal resistance of the battery.
E!perimental Data /ere is the ex'erimental data collected #rom using di5erent external resistors< Resista Mean Terminal p:d:= &urrent Mean p:d:= nce= &urrent= R
67
V
I
V
6$7
6,7
6$7
B
B<2
B
B<22
B<;J
B
B<;G
B
B<2H
B<C
B<2H
;
;
;
2<2
B<
B<?
B<B
;
;
;
<
B<K
B<J
B<K
;<G
;
;
I
6,7
?
B<G
B
B
;<2
;<2G
;<2G
H
B
B
B
;<2B
;<2B
;<22
B;
B
B
B
;
;
;
22
B
B
B
;<;J
;<;K
;<;J
,nalysis Dra3 the circuit used in this investigation< alculate the mean ' -hat is the inde'endent varia*le in this investigation> -hat is the de'endent varia*le in this investigation> alculate the uncertainty in the largest mean value o# ' alculate the uncertainty in the ' alculate the uncertainty in the smallest mean value o# current< -hat is this as a 'ercentage o# the mean> alculate the uncertainty in the current 3hen the resistance 3as H Plot a gra'h o# V against I on the x axisN and dra3 a line o# *est ft< "# V and I are connected *y the e&uation , 3hat does the gradient o# the line re'resent> alculate the gradient o# your line o# *est ft< -hat does the y0interce't o# your line re'resent> -rite do3n the value o# the y0interce't #rom your gra'h< "# the internal resistance 3as increased 3hat e5ect 3ould this have one your gra'h>
Practical 6< D-4!R
Potential Dividers
(ou are going to carry out an experiment to investigate the relationship between the value of rst resistor and the potential di5erence across the second resistor.
E5uipment List $attery or Po3er Pack Leads 3ith rocodile li's )oltmeter x2
Ammeter Multimeter Resistors o# at least K di5erent valuesN
Tas* •
S-"(/ 1FF 1R D"S166!( (/! $A((!R4 $!(-!!6 R!AD"6%S<
•
Set u' a circuit as sho3n in the diagram 3ith R1 7 B; kX and R2 7 C; kX<
•
Record the '
•
Record the '
•
-rite do3n the 'recision o# the instruments used<
•
9ee' R2 the same *ut re'lace R1 3ith resistors o# other values<
•
For each R1 record the V OUT and take re'eat readings<
•
For each value o# R1 calculate R1+ R2 and
•
Record all o# your results in one ta*le<
•
Plot a gra'h o# V OUT on the y0axisN against line o# *est ft<
and dra3 a
,fter the E!periment -hat assum'tion did 3e make in this investigation> -hat ty'e o# error is res'onsi*le #or the s'read in values or V OUT #or each value o# R1> "# the voltmeter measured a ' /o3 many di5erence values o# R1 did you use> !x'lain 3hy this 3as or 3asnt enough values< -hat is the uncertainty in V OUT #or the largest value o# R1> alculate this as a 'ercentage o# the mean value o# V OUT <
(he relationshi' that links the V OUT 3ith the values o# R1 and R2 is < se this to fnd the e&uation o# your line o# *est ft and state 3hat the gradient o# the line o# *est re'resents< Does your gra'h su''ort this e&uation> !x'lain your ans3er< alculate the theoretical value o# the gradient< alculate the gradient o# your line o# *est ft #rom the gra'h< -hat is the di5erence *et3een the theoretical value #or the gradient and the value o*tained #rom the gra'h> alculate this as 'ercentage o# the theoretical value< se your gra'h to comment on the relia*ility o# your results< /o3 could you increase the relia*ility o# your results> /o3 could you increase the 'recision o# your results> -hy do you think you 3ere instructed to s3itch o5 or disconnect the *attery *et3een measurements>
Analysis
1scillosco'e (races
6< D-4!R
An oscilloscope was used to determine the overall potential di5erence of ve batteries which were added to a circuit one at a time. The volts>div is set at " and the time base is set at # seconds. C ? 2 B ; 0B 02
;
C
B;
BC
2;
2C
;
-rite do3n the voltages o# the fve *atteries, ho3 long they are in the circuit *e#ore the next one is added and the direction it is 'laced in< 9ere is the oscilloscope traces for the potential di5erence of an alternating supply. The volts>div is set at # and the time base is set at ? ms. B;
;
0B;
-hat is the 'eak voltage, 'eak to 'eak voltage and the time 'eriod>/o3 long does the 3hole trace re'resent>
The volts>div is set at @ and the time base is set at <.ms. -hat is the 'eak voltage, 'eak to 'eak voltage and the time 'eriod>/o3 long does the 3hole trace re'resent>
The volts>div is set at ". and the time base is set at <. s. -hat is the 'eak voltage, 'eak to 'eak voltage and the time 'eriod>/o3 long does the 3hole trace re'resent>
Practical 6< D-4!R
Resolving Forces to fnd -eight
(ou are going to carry out an experiment using two force meters and Pythagoras to nd the weight and mass of a can containing and un'nown amount of water.
E5uipment List lam' stand x2N $oss and lam' x2N Force meter, B;6 x2N Protractor
String an o# unkno3n mass Pa'er cli' Rulers Bm and ;cmN
Tas*
•
•
•
•
ut a length o# string a''roximately ;
•
Raise the #orce meter on the le#t until the right #orce meter is 'er'endicular to the desk to'< Measure the angle * 3ith a 'rotractor and state its 'recision<
•
Measure the tensions T and F #rom the #orce meters<
•
Re'eat the ex'eriment #or di5erent values o# * and record your results in a ta*le<
•
For each value o# * construct a triangle o# #orces and determine the 3eight, W , o# the can<
•
From each value o# the 3eight, W 8 calculate the mass, m o# the can<
•
se each #orce meter to fnd the average 3eight o# the can and #rom this fnd the mass<
•
,fter the E!periment "n your investigation 3hat 3ere the inde'endent and de'endent varia*les> -hat is the uncertainty in your measurements o# the angle * > For the smallest value o# * calculate the 'ercentage uncertainty< /o3 could you increase the relia*ility o# your results> /o3 could you increase the 'recision o# your measurements #or the angle * and #or the #orces T and F > Ask your su'ervisor to use a cali*rated electronic scale to measure the mass o# the can< alculate the average value o# the mass #rom the di5erent values o# * that you used< -hat is the di5erence *et3een your value and your su'ervisors> alculate this as a 'ercentage o# your su'ervisors value< -hat is the di5erence *et3een your value and the value you calculated at the end o# the investigation> hoose a set o# results #or any value o# * and calculate F cos * < (his value should *e e&ual to the corres'onding value o# T 3hen the system in in e&uili*rium< -hat is the di5erence *et3een T and F cos * > alculate this as a 'ercentage o# T < For the same set o# results calculate F sin * < (his value should *e e&ual to the 3eight o# the can 3hen the system is in e&uili*rium< -hat is the di5erence *et3een F sin * and the actual 3eight o# the can> -hat could have caused this di5erence>
Practical 6< D-4!R
Moments
(ou are going to carry out an experiment to investigate the e5ect that position of mass suspension has on the dip of a ruler.
E5uipment List -ooden metre ruler x2N % lam' Masses C;g x BN
Masses B;;g x B;N Mass hanger Ru**er *and
Tas*
•
sing the % clam' attach one o# the rulers to your desk so that Kcm rests on the sur#ace and the remainder stick out unsu''orted< (he 'oint 3here the ruler frst 'rotrudes #rom the desk shall *e called the 'ivot< Measure the height o# the #ree end o# the ruler #rom the oor< (ake re'eat readings and record this result< Set u' the masses and hanger so that they have a com*ined mass o# C;;g<
•
se the ru**er *and to attach the mass hanger to the ruler<
•
Position it at various distances #rom the 'ivot<
•
•
•
•
For each distance #rom the 'ivot measure the height o# the #ree end o# the ruler and use it to calculate the di' o# the ruler< (ake re'eat readings and record your results in a ta*le<
•
Plot a gra'h o# distance #rom 'ivot on the x axisN against the di' o# the ruler<
•
Dra3 a line or curve o# *est ft<
•
6o3 'osition the C;;g hanger at a distance o# B;cm #rom the 'ivot<
•
alculate the moment and measure the di'<
•
•
Re'eat this #or various masses and distances #rom the 'ivot *ut a''lying the same moment each time< Record your results #or this 'art o# the investigation in a se'arate ta*le<
,fter the E!periment "n the frst 'art o# the investigation 3hat 3as the inde'endent varia*le> -hat 3as the de'endent varia*le and ho3 did you measure it> -hat 3as the 'recision o# the instrument you used> -hat is the uncertainty in the di' measurement #or your greatest distance #rom the 'ivot> alculate this as a 'ercentage o# the mean di' #or this distance< -hat is the uncertainty in the di' measurement #or your second smallest distance #rom the 'ivot> alculate this as a 'ercentage o# the largest di' measured #or this distance< -hat is the uncertainty in the di' measurement #or the middle value #or the distance #rom the 'ivot> alculate this as a 'ercentage o# the smallest di' measured #or this distance< !x'lain the relationshi' your gra'h suggest *et3een the distance # rom the 'ivot and the di' caused in the ruler< /o3 could you increase the relia*ility o# your results> /o3 could you increase the 'recision o# your results> -hat conclusion can you make #rom the second 'art o# the investigation> -hen calculating the #orce a''lied 3hat value did you use #or g > sing the correct scientifc terminology ex'lain 3hy it is *etter to use a value o# G -hat results 3ould suggest the o''osite>
Practical 6< D-4!R
Rolling Do3n a Ram'
(ou are going to carry out an experiment to investigate the acceleration due to gravity using a section of dowel rolling down a ramp which in inclined at an angle of * to the bench.
E5uipment List Ram' 3ith su''ort and #eet Protractor Section o# do3el
Sto' clock Rulers ;cm and BmN
Tas* •
Set u' the ram' *y attaching one end to the lo3est 'art o# the su''ort<
•
Measure the angle the ram' makes 3ith the desk<
•
State the 'recision o# the 'rotractor< 'rotractor<
•
Measure the time, t , that the cylinder takes to roll di5erent distances, $, do3n the ram'<
•
(ake (ake re'eat readings readings #or each distance you choose<
•
Present all your measurements in a ta*le<
•
For each value o# $, calculate t 2 and include these values in your ta*le<
•
Plot a gra'h o# t 2 on the y0axisN against $<
•
State the 'recision o# the sto' clock that you used in this ex'eriment<
,fter the E!periment -hat -hat -hat -hat -hat -hat
3as the inde'endent varia*le in i n your investigation> did you use to measure this> 3as the 'recision o# this 'iece o# e&ui'ment> 3as the de'endent varia*le in your investigation> did you use to measure this> 3as the 'recision o# this 'iece o# e&ui'ment>
Suggest t3o reasons 3hy re'eat timings at each distance 3ould *e ex'ected to s'read a*out a mean value< se the s'read o# your results to calculate the uncertainty in your measurement o# t #or #or your= Largest value o# s< Smallest value o# s< Middle value o# s< sing the $+v"t e&uations e&uations calculate the value o# " #or your middle value o# $< alculate the value o# " sin * < "# this value should *e the acceleration due to gravity, G se your gra'h to comment on the relia*ility o# your results< alculate the gradient o# your gra'h< (heory states that the e&uation e&uation #or the line is= , does your gra'h su''ort this theory> se your value #or the gradient o# the line to calculate the value o# "< -hat is the di5erence o# this value #rom your value o# " #rom a*ove> A student 'redicts that a hollo3 cylinder 3ill roll more slo3ly do3n a slo'e than a solid cylinder o# the same radius< Descri*e an ex'eriment to test this theory< theory<
Practical 6< D-4!R
Acceleration Due to %ravity
(ou are going to carr carry y out an experiment to nd the acceleration due to gravity of a falling ball. (ou (ou will then compare this to the theoretical value.
E5uipment List (a*le (a*le tennis *all (ennis (ennis *all $all o# scre3ed u' 'a'er
(a'e (a'e measure Sto' clock Post0it notes or other sticky markers
Tas* • •
• •
se the ta'er measure to mark heights *et3een and C metres me tres #rom the oor< oor< (ime ho3 long it takes takes #or the ta*le tennis *all to reach reach the ground 3hen released released #rom rest at metres< (ake (ake re'eat readings readings and calculate the mean time taken, taken, t < Record your results in a ta*le and including a column o# t 2<
•
Re'eat this #or the di5erent heights you have chosen *et3een and C metres #rom the oor< Plot a gra'h o# distance travelled $ y axisN against t 2<
•
Dra3 a line o# *est ft and calculate the gradient<
•
Re'eat the 3hole 'rocedure #or the tennis *all and the 'a'er *all<
•
,fter the E!periment -hat 3as the inde'endent varia*le in i n your investigation> -hat did you use to measure this and 3hat 3as the 'recision o# this 'iece o# e&ui'ment> /o3 many di5erent values #or this varia*le did you use> -as this enough> !x'lain your ans3er< (a*le (a*le tennis *all -hat 3as the uncertainty in value o# t 3hen 3hen released #rom a height o# C metres> alculate this as a 'ercentage o# the mean value o# t < -hat does the gradient o# each gra'h re'resent> se your gradient o# your gra'h to 3rite do3n the value #or the acceleration< -hat is the di5erence *et3een this value and the acce'ted value o# G alculate this as a 'ercentage o# the acce'ted value< (ennis (ennis *all -hat 3as the uncertainty in value o# t 3hen 3hen released #rom a height o# C metres> alculate this as a 'ercentage o# the mean value o# t < se your gradient o# your gra'h to 3rite do3n the value #or the acceleration< -hat is the di5erence *et3een this value and the acce'ted value o# G alculate this as a 'ercentage o# the acce'ted value< Pa'er *all -hat 3as the uncertainty in value o# t 3hen 3hen released #rom a height o# C metres> alculate this as a 'ercentage o# the mean value o# t < se your gradient o# your gra'h to 3rite do3n the value #or the acceleration< -hat is the di5erence *et3een this value and the acce'ted value o# G alculate this as a 'ercentage o# the acce'ted value< -hat ty'e o# error is res'onsi*le #or the s'read o# results #or each measurement o# time and ho3 did it arise> -hich o# the *alls 3as a5ected most *y air resistance> /o3 could you use light gates and a data logger to im'rove your results> /o3 3ould this im'rove your results>
Practical 6< D-4!R
(ermin (erminal al )elocity )elocity
(ou are going to carry out an experiment to investigate how quic'ly di5erent siBed obCects reach terminal velocity. velocity.
E5uipment List $un ases various si@esN Sto' lock (a'e (a'e Measure
Rulers ;cm and BmN lam' Stand $oss and lam'
Tas* • •
•
hoose a *un case and measure its diameter< diameter< Dro' the *un case #rom a height o# 2
•
Re'eat the investigation 3ith *un cases o# di5erent diameters<
•
Record your results in a ta*le<
•
lam' the meter ruler vertically and 'osition it at the end o# the 3ork*ench<
•
•
•
AdQust its height so that the 3hen a *un case is released #rom a height o# 2
•
alculate the mean terminal velocity o# the *un case as it 'asses the ruler< ruler<
•
Re'eat the investigation 3ith *un cases o# di5erent diameters<
•
Record your results in a ta*le<
•
Plot a gra'h o# *un case diameter on the x axisN against time taken to reach terminal velocity< Plot a gra'h o# *un case diameter x axisN against terminal velocity< velocity<
•
Dra3 a line o# *est ft #or each gra'h<
•
,fter the E!periment -hat 3as the inde'endent varia*le in i n your investigation> -hat did you use to measure this and 3hat 3as the 'recision o# this 'iece o# e&ui'ment> -hat ty'e o# error is res'onsi*le #or the s'read o# results #or the time taken to reach terminal velocity> !x'lain ho3 this arose< For the largest *un case diameter calculate the uncertainty in the time taken< -hat is this as a 'ercentage o# the mean time taken> -hat does your frst gra'h tell you a*out the connection *et3een the t3o varia*les> -hat does the second gra'h tell you a*out the connection *et3een the t3o varia*les> "# you have dra3n a straight line o# *est ft calculate its gradient< "# you have dra3n a curve o# *est ft dra3 a tangent to the curve 3hen the x axis value is the middle o# the scale then calculate its gradient< -hat is the uncertainty in the terminal velocity o# the smallest *un case> alculate this as a 'ercentage o# the mean terminal velocity< velocity< -hat is the uncertainty in the terminal velocity o# the largest *un case> alculate this as a 'ercentage o# the smallest terminal velocity< velocity< hoose the data #rom any other *un case si@e< -hat is the uncertainty in the terminal velocity> alculate this as a 'ercentage o# the largest terminal velocity< velocity< /o3 can 3e descri*e the value 3ith the lo3est 'ercentage uncertainty>
Descri*e and ex'lain ho3 the use o# a motion sensor or light gate could lead to *etter results<
Practical
$ouncing $all
6< D-4!R
(ou are going to investigate how the height from which a table tennis ball is dropped a5ects how high it bounces.
E5uipment List (a*le (ennis $all Ruler BmN
$lu0(ack lam'
Tas* •
•
•
• •
•
se the ruler to measure the diameter, 2 , o# the ta*le tennis *all and record this result< %ive an estimate o# the uncertainty in this measurement Set u' the a''aratus as sho3n< (he metre ruler should *e held vertically in 'lace at the *ack o# the o'en clam' *y a 'iece o# $lu0(ack 3ith another 'iece o# $lu0(ack securing it to the *ench< (he ta*le tennis *all should *e gently clam'ed into 'osition in #ront o# the ruler 1'en the clam' and o*serve the motion o# the *all as it *ounces on the *ench Decide on a range o# heights, -, measured to the to' o# the *all, #rom 3hich you 3ill release the *all so that you can measure the height, $, o# its frst *ounce, also measured to the to' o# the *all Pre'are a single ta*le #or recording all o# your measurements, including re'eat readings #or $
•
arry out your ex'eriment and com'lete your ta*le
•
Dra3 a gra'h to sho3 ho3 $ 'lotted on the vertical axisN varies 3ith -3
,fter the E!periment "n your investigation 3hat 3as inde'endent varia*le> -hat 3as the de'endent varia*le> Descri*e the relationshi' i# there is oneN *et3een $ and -< -hat is the uncertainty in your measurement o# -> alculate the 'ercentage uncertainty in your largest value o# -< alculate the 'ercentage uncertainty in your smallest value o# -< !x'lain the source o# error res'onsi*le #or the variations in your measurements o# $ /o3 could you have made your measurements less 'recise> se data #rom your ta*le to estimate the uncertainty in your largest mean value o# $< !stimate the 'ercentage uncertainty in your largest mean value o# $< State and ex'lain your estimate #or the uncertainty in your measurement o# the diameter, 2 , o# the ta*le tennis *all<
(he loss in gravitational 'otential energy, Δ E P , o# a *ody #alling to the !arths sur#ace is given *y 3here mg is the 3eight o# the *all and 4 is the vertical distance through 3hich its centre o# mass #alls< "n your ex'eriment 47- 2 < alculate 4 #or your smallest value o# -< sing your uncertainty in $ and 2 , estimate the uncertainty in your value #or 4< alculate Δ E P #or your smallest value o# -< mg 7;<;2H T0;<;;B6 Determine the 'ercentage uncertainty in Δ E P <
Practical 6< D-4!R
-ork Done
(ou are going to carry out an experiment to investigate the wor' done when a mass is pulled up an inclined plane.
E5uipment List 2;;g mass 3ith hanger Forcemeter "nclined 'lane
Materials to cover 'lane Rulers Bm and ;cmN Protractor
Tas* •
se the 'rotractor to set the 'lane to an incline o# 2;Z<
•
Measure the height o# the 'lane and state the 'recision o# your reading<
•
(ake several measurements o# the length, $, o# the 'lane and calculate the mean value<
•
se the #orcemeter to drag the 2;;g mass across the ta*le and then u' the 'lane<
•
Record the #orce used to 'ull the mass u' the 'lane<
•
(ake re'eat readings and calculate the mean #orce a''lied, F <
•
For this angle calculate the 3ork done using
<
•
alculate the gain in gravitational 'otential energy using
•
alculate the di5erence in the 3ork done and the gravitational 'otential energy<
•
Re'eat this #or other angles o# incline<
•
Plot a gra'h on angle o# incline x axisN against di5erence *et3een W and E <
•
Dra3 a line o# *est fr #or your gra'h<
•
Re'eat the investigation 3ith di5erent materials covering the 'lane<
<
,fter the E!periment -hat 3as the inde'endent varia*le in the investigation> /o3 many di5erent values did you use #or this> -as this enough> !x'lain your ans3er< -hat 3as the 'recision o# the instrument you used to measure it> -hat 3as the de'endent varia*le in the investigation> -hat is the uncertainty in your measurements o# the height> alculate the 'ercentage uncertainty o# your largest height measurement< alculate the 'ercentage uncertainty o# your smallest height measurement< -hat 3ord descri*es the value 3ith the smaller 'ercentage uncertainty> -hat is the uncertainty in the #orce #or the largest angle on incline> alculate this as a 'ercentage o# the mean value #or the #orce -hat is the uncertainty in the #orce #or the second largest angle o# incline> alculate this as a 'ercentage o# the smallest value o# #orce at this angle< -hat is the uncertainty in the #orce #or the middle value #or the angle o# incline> alculate this as a 'ercentage o# the largest value o# #orce at this angle< -hich ty'e o# error is res'onsi*le #or the di5erences in the #orce a''lied to 'ull the mass u' the incline> (here 3as a di5erence *et3een the gravitational 'otential energy gained and the 3ork done< -hat 3as res'onsi*le #or this di5erence> -here did the energy go> "# you carried out the investigation #or other materials ho3 did they com'are to each other> -hat trend does your gra'h suggest a*out the relationshi' *et3een the angle o# incline and the di5erence> se your gra'h to comment on the relia*ility o# your results< /o3 could you increase the relia*ility o# your results>
Analysis 6< D-4!R
onservation o# !nergy
(ou will investigate the transfer of gravitational potential energy to 'inetic energy for a trolley rolling down a ramp. The trolley had a piece of card "< cm long attached to the top. The digital timer measures the time ta'en for the card to completely cut through the light gate. The trolley has a mass of #
E!perimental Data "eight= 6m7
t 1
t 2
t 3
;
;
;
;
;<2
;
;
;
;<
;
;<;G
;<;G
;
;<;H
;<;G
;<;K
;
;<;J
;<;J
;<;J
"eight= 6m7
Time Ta*en= t 6s7
Mean $elocity= v 6m9s7
$elocity= v 6m9s7 v1
E K 6A7
v2
E P 6A7
v3
E P 5 E K
6A7
;
,nalysis For each measurement o# time calculate the velocity o# the trolley< alculate the mean value o# the velocity #or each height that the trolley is released #rom< -hat is the uncertainty in the velocity #or a height o# ;<2 m> alculate this as a 'ercentage o# the mean velocity< -hat is the uncertainty in the velocity #or a height o# ;< m> alculate this as a 'ercentage o# the smallest velocity at this height< -hat is the uncertainty in the velocity #or a height o# ; alculate this as a 'ercentage o# the smallest velocity at this height< -hich ty'e o# error is res'onsi*le #or the di5erences in the time measurements> alculate the kinetic energy the trolley has gained as it 'asses through the light gate< -hat is the 'ercentage uncertainty in the kinetic energy #or a height o# ;<2 m> -hat is the 'ercentage uncertainty in the kinetic energy #or a height o# ;< m> -hat is the 'ercentage uncertainty in the kinetic energy #or a height o# ; alculate the gravitational 'otential energy that the trolley has lost as it 'asses through the light gate< Plot a gra'h o# kinetic energy gained against gravitational 'otential energy lost< Dra3 a line o# *est ft and calculate the gradient o# this line< !x'lain 3hat a gradient e&ual to B 3ould mean and ex'lain 3hy the gradient 3ill not *e e&ual to B< alculate the di5erence in kinetic and gravitational 'otential energy<
Practical 6< D-4!R
(he S'ring onstant
(ou are going to carry out an experiment to determine the total spring constant when two springs are connected in series and in then in parallel.
E5uipment List S'rings 2N Rulers ;cm and BmN lam' Stand, $oss and lam' Masses B; x C;gN
Tas* •
Measure the lengths o# s'ring A and s'ring $< Record your readings<
•
Sus'end s'ring A #rom the clam' attached to the clam' stand< Attach a C;g mass to the *ottom o# the s'ring< Record the extension o# the s'ring #or C;g< Re'eat 3ith increasing mass u' to C;;g<
•
Dra3 a ta*le to include columns #or mass, #orce a''lied and extension<
•
•
Plot a gra'h o# #orce a''lied on the y0axisN against extension on the x0axisN< (his 3ill *e gra'h B alculate the gradient< (his is the s'ring constant #or s'ring A<
•
Re'eat this #or s'ring $<
•
•
6o3 that 3e have the s'ring constants o# s'ring A and $ you 3ill no3 fnd the total s'ring constant 3hen they are connected in series and in 'arallel< Re'eat the a*ove 'rocedure *ut 3ith the s'rings connected in series<
•
Plot a gra'h o# #orce a''lied against extension #or s'rings in series<
•
Re'eat the a*ove 'rocedure *ut 3ith the s'rings connected in 'arallel<
•
Plot a gra'h o# #orce a''lied against extension #or s'rings in 'arallel<
•
,fter the E!periment -hat 3ere the de'endent and inde'endent varia*les in your investigation> Look at your frst gra'h, are the results relia*le> -hy> Look at your second gra'h, are the results relia*le> -hy> /o3 could you have increased the relia*ility o# your results> /o3 could you have increased the 'recision o# your measurements #or the extension o# the s'rings>
For t3o s'rings in series the total s'ring constant, 6 T is given *y= < alculate this value #rom your gradients o# gra'hs B and 2< (his is the acce'ted value< alculate this value #rom the gradient o# the gra'h #or s'rings in series< -hat is the di5erence *et3een this value and the acce'ted value> alculate the 'ercentage di5erence #rom the acce'ted value< For t3o s'rings in 'arallel the total s'ring constant, 6 T is given *y= alculate this value #rom your gradients o# gra'hs B and 2< (his is the acce'ted value< alculate this value #rom the gradient o# the gra'h #or s'rings in series< -hat is the di5erence *et3een this value and the acce'ted value> alculate the 'ercentage di5erence #rom the acce'ted value< -hich is more relia*le, your value #or the s'rings in series or 'arallel> !x'lain your ans3er<
Practical
Findin the 4oun Modulus
(ou are going to carry out an experiment to determine the (oung odulus for copper.
E5uipment List % lam' (3o small 3ooden *locks $ench Pulley Metre Ruler 2
Tas* •
Set u' the e&ui'ment as sho3n in the diagram<
•
Position the marker ;cm #rom the 'ulley<
•
Measure the length, l , o# the 3ire #rom the 3ooden *lock to the marker<
•
• •
Measure the diameter o# the 3ire in several 'laces and calculate the mean radius, & , o# the 3ire< alculate the cross0sectional area, A, o# the 3ire using the e&uation
<
Add a B;;g mass to the hanger, measure the extension, , o# the 3ire, the mean radius and calculate the area<
•
alculate the tensile #orce using the e&uation
•
Re'eat this until B;;;g are on the hanger<
•
Record the results in a ta*le= F 6(7
l 6m7
6m7
& 6m7
3here g 7 G
A 6m.7
Stress= 7 6%a7
•
alculate the stress #or each #orce using the e&uation
•
Plot a gra'h o# tensile stress y axisN against tensile strain x axisN<
Strain= (
and the strain using
,fter the E!periment -hat 3as the inde'endent varia*le in the investigation> /o3 many values o# this varia*le did you use> -as this enough> !x'lain your ans3er< -hat is the 'recision o# your length measurements> -hat is the 'recision o# your diameter measurements> "# the 'ercentage uncertainty in the radius 3as C\ 3hat 3ould *e the 'ercentage uncertainty in the area> alculate the gradient o# the line o# *est ft o# your gra'h< (he gradient is e&ual to the 4oung modulus< (he acce'ted value #or the 4oung modulus is BBG %Pa ] J -hat is the di5erence *et3een your value and the acce'ted value o# BBG %Pa> alculate this as a 'ercentage o# the acce'ted value< se your gra'h to comment on the relia*ility o# your results< /o3 could you im'rove the relia*ility o# your results>
/o3 could you increase the 'recision o# your results> !x'lain 3hy the results cannot *e used 3hen the co''er is extended *eyond the elastic limit<
Analysis 6< D-4!R
Finding the 4oung Modulus
The load applied to a wire was varied and the length was recorded. (ou will use the data to nd the spring constant and the (oung modulus of the wire. The wire has a length of ".?<< m and diameter of ).# x "< ,@ m.
E!perimental Data Load= F 6(7 2<;
/ere are the lengths o# the 3ire 3hen di5erent loads are a''lied< Length= l E!tension= Stress= 7 Strain= ( 6m7 6m7 6%a7 BH;B<2
<;
BH;B
?<;
BH;2
C<;
BH;<;
H<;
BH;
J<;
BH;?<2
K<;
BH;?
G<;
BH;C
B;<;
BH;J<;
BB<;
BH;G<;
,nalysis -hat -hat -hat -hat
is is is is
the the the the
inde'endent varia*le in this investigation> de'endent varia*le in this investigation> 'recision o# the load measurements> 'recision o# the length measurements>
alculate the uncertainty in the length measurement 3hen the load is J<; 6< -hat is this as a 'ercentage o# the measurement> alculate the uncertainty in the load measurement 3hen the length is BH;2 alculate the change in length extensionN #or each load< alculate the cross0sectional area o# the 3ire using
alculate the stress #or each #orce using the e&uation
< and the strain using
<
Plot a gra'h o# F against x axisN and dra3 a line o# *est ft< Does the line 'ass through the origin> Should it> !x'lain your ans3er< "# F and are connected *y the e&uation se the gradient to fnd the s'ring constant<
F and are also linked *y the e&uation
3hat does the gradient re'resent>
, in this case 3hat does the gradient o# your
line re'resent> se the gradient to calculate the 4oung Modulus o# the 3ire< (he acce'ted value o# the 4oung Modulus is <C x B; B;, 3hat is the di5erence *et3een this value and yours>
alculate this as a 'ercentage o# the actual value<
Practical 6< D-4!R
Loading and nloading
In this experiment you will determine the force,extension graph for a rubber sample as it is loaded and unloaded.
E5uipment List Ru**er$and Ruler ;cmN lam' Stand
$oss and lam' Masses B;;g x B;N Mass /anger
Tas* •
/ang the ru**er *and #rom the clam'<
•
Attach the mass hanger B;;gN to the *ottom o# the ru**er *and and determine the extension this causes< Add a B;;g mass to the mass hanger ensuring the tension in the *and is not allo3ed to decrease< Record the extension< ontinue to add the masses and record the extension u' to B;;;g< Remove the masses one at a time and determine the extension as the tensile #orce is reduced< Re'eat the ex'eriment t3ice more<
•
Record all your results in a ta*le<
•
•
•
•
•
•
alculate the mean values o# the extension #or the di5erent masses *oth loading and unloading< Plot a gra'h o# Force on the y0axisN against extension<
,fter the E!periment -hat -hat -hat -hat
3as the inde'endent varia*le in your investigation> 3as the de'endent varia*le in your investigation> did you use to measure this> 3as the 'recision o# this 'iece o# e&ui'ment>
-hat is the uncertainty in the extension 3hen the load is ?;;g loadingN> alculate this as a 'ercentage o# the mean extension< -hat is the uncertainty in the extension 3hen the load is ?;;g unloadingN> alculate this as a 'ercentage o# the mean extension< -hich is the greater source o# uncertainty> /o3 can you descri*e the lo3er source o# uncertainty> -hat is the uncertainty in the extension 3hen the load is J;;g loadingN> alculate this as a 'ercentage o# the lo3est extension reading 3ith this load< -hat is the uncertainty in the extension 3hen the load is J;;g unloadingN> alculate this as a 'ercentage o# the greatest extension reading 3ith this load< Does the ru**er *and o*ey /ookes La3> Uusti#y your ans3er< "# your gra'h suggests a ^loo' rather than a straight line 3hat is the signifcance o# the area o# the loo' *et3een the loading and unloading sections o# the gra'h>
!x'lain 3hat 3ould ha''en to the results o# the re'eat ex'eriment i# the ru**er *and had extended *eyond the elastic limit during the frst run< /o3 could you increase the 'recision o# your results> /o3 could you increase the relia*ility o# your results>
Practical 6< D-4!R
(he S'eed o# -aves in -ater
(ou are going to carry out an experiment to determine the speed of a wave as it crosses a shallow tray of water
E5uipment List Standard tray Sto' clock Rulers ;cm and BmN
Tas* •
Fill the tray 3ith 3ater to a de'th o# a*out Bcm<
•
Measure the de'th o# 3ater in a num*er o# 'laces and also the length o# the tray< Record your readings< 4ou are going to time the 3ave travelling *ack3ards and #or3ards across the sur#ace o# the 3ater< Dra3 a ta*le to include columns #or distance travelled and time taken, and include columns #or re'eat readings< Raise one end o# the tray a*out Bcm and allo3 to dro' so that a ri''le is sent across the sur#ace o# the 3ater and is reected *ack3ards and #or3ards *y the ends o# the tray< (ime ho3 long the 3ave takes to cross the tray once<
•
(ime ho3 long the 3ave takes to cross the tray t3ice ie, there and *eckN<
•
•
•
•
•
• •
(ake #urther times #or , ?, C, H etc more crossings until the 3ave is too #aint to see, u' to a maximum o# eight crossings< (ake re'eat readings #or each distance< Plot a gra'h o# distance travelled *y the 3aveN on the y0axis against time on the x0axis< se it to determine the average s'eed on the 3ave<
,fter the E!periment -hat 3as the inde'endent varia*le in your investigation> -hat did you use to measure this> -hat 3as the 'recision o# this 'iece o# e&ui'ment> -hat 3as the de'endent varia*le in your investigation> -hat did you use to measure this> -hat 3as the 'recision o# this 'iece o# e&ui'ment> se the 'recision o# your e&ui'ment to calculate the 'ercentage uncertainty o# your smallest measurement o# the time taken< se the 'recision o# your e&ui'ment to calculate the 'ercentage uncertainty o# your largest measurement o# the time taken< se your ra3 data to calculate the uncertainty in your smallest measurement o# the time taken< 6o3 calculate the 'ercentage uncertainty in this measurement< se your ra3 data to calculate the uncertainty in your largest measurement o# the time taken< 6o3 calculate the 'ercentage uncertainty in this measurement<
-hat caused the s'read in your measurements o# the de'th o# the 3ater> se your gra'h to comment on the relia*ility o# your results< /o3 could you increase the relia*ility o# your results> /o3 could you increase the 'recision o# your results>
Analysis
!lectromagnetic S'eed
6< D-4!R
The frequencies of di5erent coloured light were recorded. Dnowing the wavelengths you will analyse the data below to nd the speed of light in a vacuum8 c.
E!perimental Data Light &olour
/ere are the #re&uencies recorded #or light o# seven di5erent colours< Wavelengt Mean -9 ! Fre5uency= f ?-0 h= ! 6nm7 6m 7 6! -> "87 Fre5uency= f 6! ->-0 "87
)iolet
?BC
J<22
J<2B
J<2H
$lue
?H
H
H
H
yan
?KG
H
H
H<;G
%reen
C2
C
C
C
4ello3
CK;
C
C<2?
C
1range
H;K
?
?
?
Red
HKC
?<K
?<K
?<K
,nalysis alculate the mean #re&uency o# each coloured light< alculate the uncertainty in the #re&uency o# *lue light< -hat is this as a 'ercentage o# the mean #re&uency> alculate the uncertainty in the #re&uency o# *lue light< -hat is this as a 'ercentage o# the mean #re&uency> alculate the uncertainty in the #re&uency o# red light< -hat is this as a 'ercentage o# the mean #re&uency> -hat is the 'recision o# the 3avelength measurements> alculate the 'ercentage uncertainty in the value o# 3avelength #or cyan light< alculate the 'ercentage uncertainty in the value o# 3avelength #or yello3 light< alculate the value o# BO ! #or each coloured light< !nsure your units are 'er metre m0BN< Plot a gra'h o# f on the y axisN against on the x axisN< alculate the gradient o# your line o# *est ft< (he gradient should *e e&ual to c, x B;K< -hat is the di5erence *et3een your gradient and the acce'ted value> alculate the 'ercentage di5erence #rom the acce'ted value< Does your line 'ass through the origin> Should it>
se these calculations and your gra'h to comment on the relia*ility, 'recision and accuracy o# the ex'eriment< se the e&uation to calculate the value o# c #or each coloured light< alculate your mean value #or the 3ave s'eed c< -hat is the uncertainty in the 3ave s'eed> alculate the 'ercentage di5erence *et3een your mean value and the acce'ted value<
Practical 6< D-4!R
Phase Di5erence o# Pendulums
(ou are going to carry out an experiment to investigate how the time between two pendulum moving in phase depends on their relative lengths.
E5uipment List Pendulum *o* x2N String 2 x B
lam' Stands, $osses and lam's Sto' clock Plasticine
Tas* •
•
•
lam' a ruler *et3een t3o clam' stands and sus'end t3o 'endulums o# e&ual length a''roximately B<;; m< Attach a second clam' to one o# the clam' stands so that it o*structs the s3ing o# the second 'endulum< Set the initial value o# 8 to *y ;<2;m<
•
Measure the lengths L and 8 and state the 'recision o# your readings< Dis'lace and release the 'endulums so they oscillate 3ith a small am'litude 'arallel to the edge o# the *ench< Start the timer 3hen the t3o 'endulum motions are seen to *e exactly in 'hase< Measure and record the time until the 'endulums are next seen to *e in 'hase, T <
•
Re'eat this reading three times<
•
Measure and record #urther values o# T 3hich corres'ond to #our larger values o# y <
•
Record your results in a ta*le 3ith a column
•
•
•
<
,fter the E!periment -hat 3ere the de'endent and inde'endent varia*les in your investigation> Look at your gra'h, are the results relia*le> -hy> 1ther than taking re'eat readings ho3 else could you increase the relia*ility o# your ex'eriment>
Plot a gra'h o# on the y0axisN against Dra3 a line o# *est ft #or your gra'h< alculate the gradient o# this line< alculate alculate alculate alculate
on the x0axisN
the uncertainty in the measurement #or the value o# T 3hen 8 has a value o# ;<2; m< this as a 'ercentage uncertainty o# the mean value o# T #or this value o# 8. the uncertainty in the measurement #or the value o# T #or your largest value o# 8< this as a 'ercentage uncertainty o# the mean value o# T #or this value o# 8<
A student suggests that in order to extend the investigation additional measurements o# ( should *e made using values o# y that 3ere much smaller than ;<2; m and much *igger than ;
Analysis 6< D-4!R
Sound -aves in a olumn o# Air
A spea'er was attached to the top of an open ended glass cylinder. The other end was placed in a trough of water so that the column of air between the spea'er and the water is " cm. The spea'er is attached to a signal generator which is adCusted until each harmonic is heard
E!perimental Data "armonic
/ere are the #re&uencies recorded #or the frst fve harmonics< Fre5uency= f 6"87 Wavelength= ! 6m7
First
BB?
BBB
BB2C
Second
22KK
22K2
22GB
(hird
KJ
?;J
?;H
Forth
?KK
?K?B
?KC;
Fi#th
CHG
CHHH
CH?C
"armonic
Mean Fre5uency= f 6"87
Wavelength= ! 6m7
6m?-7
First Second (hird Forth Fi#th
,nalysis alculate the mean #re&uency #or each harmonic< alculate the uncertainty in the #re&uency o# the frst harmonic< -hat is this as a 'ercentage o# the mean #re&uency> alculate the uncertainty in the #re&uency o# the third harmonic< -hat is this as a 'ercentage o# the mean #re&uency> alculate the uncertainty in the #re&uency o# the f#th harmonic<
Wave Speed= v 6m9s7
-hat is this as a 'ercentage o# the mean #re&uency> alculate the 3avelength o# the standing 3ave #or each harmonic< om'lete the column in the ta*le la*elled
:
Plot a gra'h o# f on the y axis against on the x axis< Dra3 a line o# *est ft and calculate the gradient< alculate the 'ercentage di5erence *et3een the gradient and the acce'ted value o# ? mOs< se the e&uation to com'lete the last column o# the ta*le< alculate your mean value #or the 3ave s'eed v< -hat is the uncertainty in the 3ave s'eed> alculate the 'ercentage di5erence *et3een your mean value and the acce'ted value< "s the gradient value or the ta*le value o# v more accurate> -hat ty'e o# error is res'onsi*le #or the s'read o# #re&uencies #or each harmonic>
Practical 6< D-4!R
Finding the Re#ractive "ndex
(ou are going to carry out an experiment to determine the refractive index of a Perspex bloc'.
E5uipment List Po3er Pack Ray $ox Pers'ex $lock Protractor
A? -hite Pa'er x Red Filter Ruler Shar' Pencil
Tas* • •
•
•
•
•
•
Place the *lock on the 'a'er and dra3 around its outline< Set u' the a''aratus so that a narro3 *eam o# coloured light 'asses through the *lock< Dra3 the 'ath o# the *eam through the *lock as sho3n in the diagram< sing a 'rotractor, measure the angle o# incidence, * 1, and the angle o# re#raction, * 2, at the frst sur#ace< (ake a set o# readings #or various values o# the angle o# incidence 3ithin the range 2;Z to H;Z< sing the other t3o sheets o# 'a'er, re'eat the measurements #or the same angles o# incidence< (a*ulate all your results in a single ta*le<
•
Record the 'recision o# your 'rotractor<
•
alculate sin* 1 and sin* 2 #or each angle o# incidence and include these values in your ta*le<
•
Plot sin* 1 on the y axis against sin* 2 and dra3 a straight line o# *est ft<
,fter the E!periment -hat is the uncertainty in your measurements o# the inde'endent varia*le> /o3 many values did you use #or the inde'endent varia*le> -as this enough values> !x'lain your ans3er< -hat 3ould increasing the num*er o# values used do to your results> -hat is the uncertainty in the value o# * 2 3hen * 1 7 H;Z> alculate this as a 'ercentage o# the mean value o# * 2 at this value o# * 1<
-hat is the uncertainty in the value o# * 2 3hen * 1 7 2;Z> alculate this as a 'ercentage o# your smallest value o# * 2< se your gra'h to comment on the relia*ility o# your results< alculate the gradient o# the line o# *est ft<
(he re#ractive indices o# material B and 2 are linked *y the e&uation Rearrange this to sho3 the e&uation o# your line o# *est ft< "# material B is air 11 7 BN 3hat does the gradient re'resent> se your gradient to fnd the re#ractive index o# Pers'ex< -hat is the di5erence *et3een your value and the acce'ted value o# B alculate this as a 'ercentage o# the acce'ted value< -hat does this 'ercentage tell you a*out your results> sing a shar' 'encil rather than a *lunt 'encil did 3hat to your results> %ive some o# the advantages o# using a laser instead o# a flament *ul*<
Analysis 6< D-4!R
<
Finding the Re#ractive "ndex
(ou are going to use experimental data on light being shone through a Perspex bloc' to nd its refractive index. The incident angle is measured from the normal in the Perspex bloc' and the refracted angle is measured from the normal out of the bloc' in the air.
E!perimental Data (he 'rotractor used to measure the incident and re#racted angle had a 'recision o# ;
B?
BC
BC<;
BC<;
22<;
2<;
2<;
2;<;
B<;
;<;
B<;
2C<;
K<;
G<;
G
;<;
?J
?J
?J
C<;
CJ
CJ
CK
?;<;
JB
JB
J<;
,nalysis alculate the mean values #or the re#racted angle #or each incident angle< -hat ty'e o# error is res'onsi*le #or the variation in readings #or the re#racted angle> alculate the uncertainty in the mean re#racted angle #or an incident angle o# BCZ< -hat is this as a 'ercentage o# the mean re#racted angle> alculate the uncertainty in the mean re#racted angle #or an incident angle o# ;Z< -hat is this as a 'ercentage o# the mean re#racted angle> -hich measurement is more 'recise> om'lete the columns la*elled sin * 1and sin * 2 and state your values to decimal 'laces< Plot a gra'h o# sin * 1 on the y axis and sin * 2 on the x axis< Dra3 a line o# *est ft #or the gra'h<
(he e&uation #or the line is , 3hat does the gradient re'resent> alculate the gradient o# your line< -hat value #or the re#ractive index, 1, does your gra'h 'roduce> (he acce'ted re#ractive index o# Pers'ex is B -ork out this out as a 'ercentage o# the acce'ted value<
se the e&uation to calculate the critical angle o# Pers'ex< (he acce'ted critical angle is ?2 alculate this as a 'ercentage o# the acce'ted value< /o3 could you 'rove that this 3as the critical angle> Descri*e ho3 you 3ould go a*out doing this<
Analysis
"nter#erence o# Sound
6< D-4!R
Five spea'ers are set into a box in the formation as shown in the diagram below. ;y measuring the separation of the loud interference fringes at di5erent distance from the spea'er box it is possible to deduce which spea'ers are emitting a sound of wavelength 3 ! 4 <."2 m.
alues in cm
E!perimental Data /ere are the se'arations o# the #ringes at di5erent distances #rom the s'eaker *ox< Distance to Fringe Separation= Mean Spea*er Spea*er= Separation= % % 6m7 6m7 D $ 6m7 6m7 B<;; ;<2; ;<2B ;<2B B
;<
;<
;<2G
2<;;
;
;
;
2
;
;
;
<;;
;
;
H
;
;
;
?<;;
;
;
;
?
;
;
;
,nalysis "n this ex'eriment 3hat 3ere the inde'endent and de'endent varia*les> -hat 3as the 'recision in the 3avelength value and distances #rom the s'eaker> alculate the mean values o# the #ringe se'aration #or each distance to the s'eaker< -hat is the uncertainty in the #ringe se'aration #or a distance o# 2<;;m> alculate this as a 'ercentage o# the mean<
-hat is the uncertainty in the #ringe se'aration #or a distance o# alculate this as a 'ercentage o# the largest value at this distance< -hat is the uncertainty in the #ringe se'aration #or a distance o# ? alculate this as a 'ercentage o# the smallest value at this distance< -hat is the name given to the error res'onsi*le #or the s'read in the #ringe se'arations>
se the e&uation to calculate the s'eaker se'aration #or each distance to the s'eaker< -hat is a 'ercentage uncertainty in the value o# $ #or 3hen D 7 2 alculate the mean value o# the s'eaker se'aration< !ither= 'lot a gra'h o# D on the y axis against % on the x axis and use your gradient to calculate $< or
'lot a gra'h o# D against
the values o#
and your gradient 3ill e&ual $< A column has *een le#t #or
<
Does your gra'h su''ort the value o# $ o*tained #rom the ta*le> -hich s'eakers does this suggest are emitting the sound>
Practical 6< D-4!R
Laser Di5raction
(ou are going to carry out an experiment to determine the wavelength of light emitted from a laser then use this value to calculate the slit separation of a di5raction grating.
E5uipment List Laser Rulers ;cm and BmN (a'e Measure at least CmN
Di5raction %ratings ;; lines 'er mm and ourse N
Tas* •
Aim the laser at a screenO3all a''roximately ? metres a3ay<
•
Place the ;;lines 'er mm grating a''roximately Ccm in #ront o# the laser<
•
Measure the distance #rom the grating to the screenO3all< State the 'recision o# your instrument< Measure the distance #rom the central s'ot to the frst order *right s'ot to the right and to the le#t< State the 'recision o# your instrument<
•
Re'eat this #or the second, third and #orth order maxima<
•
Record your results in a ta*le including columns #or sin* and 3avelength !N<
•
•
Tas* . •
9ee'ing the laser in the same 'osition, re'lace the grating 3ith the course grating<
•
Measure the distance #rom the grating to the screenO3all< State the 'recision o# your instrument< Measure the distance #rom the central s'ot to the frst order *right s'ot to the right and to the le#t< State the 'recision o# your instrument<
•
Re'eat this #or the second, third and #orth order maxima<
•
Record your results in a ta*le including columns #or sin* and 3avelength !N<
•
•
,fter the E!periment For each order maxima calculate the value o# sin* *y dividing the distance #rom the central maxima *y the distance to the screen< "# there are ;; lines 'er mm calculate the slit se'aration 2 < sing the e&uation calculate the value o# ! #or each maxima 1N< alculate the mean value o# !< -hat is the uncertainty in this value>-hat is this as a 'ercentage o# the mean> "# the acce'ted value is HH; nm 3hat is the di5erence o# your value #rom the acce'ted value> alculate this as a 'ercentage o# the acce'ted value< Plot a gra'h o# sin* on the y0axis against 1 on the x0axis< Dra3 a line o# *est ft and calculate the gradient o# this line< se the gradient to calculate the value o# !< Look at your data #or the frst order maxima
,fter the E!periment . For each order maxima calculate the value o# sin* *y dividing the distance #rom the central maxima *y the distance to the screen< sing the e&uation calculate the value o# 2 #or each order maxima 1N< alculate the mean value o# 2 < -hat is the uncertainty in this value> -hat is this as a 'ercentage o# the mean> Plot a gra'h o# sin* on the y0axis against 1 on the x0axis< Dra3 a line o# *est ft and calculate the gradient o# this line< se the gradient to calculate the value o# 2 <
Analysis 6< D-4!R
$raking Force
(ou are going to use information from the 9ighway $ode to calculate the bra'ing force exerted on a car performing an emergency stop.
E!perimental Data Speed 6mph7
/ere are the *raking distances #or vehicles travelling at di5erent s'eeds< nitial Bra*ing Time Bra*ing Speed Speed= distance= $ ta*en= Force= 6*m9h7 v t F 6m7 6m9s7 6s7 6(7
2;
H
;
B?
?;
2?
C;
K
H;
CC
J;
JC
,nalysis onvert the s'eeds #rom miles 'er hour to kilometres 'er hour using the conversion Bmile 7 B
se the e&uation
to com'lete the column #or the time taken to sto'<
"# a car has a mass mN o# GC; kg calculate the &uantity mΔv #or each o# the initial s'eeds< -rite your values in the em'ty column o# the ta*le including a heading and a''ro'riate units< Plot a gra'h o# mΔv on the y axis against t on the x axis< Dra3 a line o# *est ft #or the 'oints< (he gradient o# the line o# *est ft is e&ual to the $raking Force F N o# the car< alculate this value<
se the e&uation to com'lete the last column o# the ta*le< alculate the mean *raking #orce on the car #rom the ta*le< -hat is the di5erence *et3een this value and the gradient o# your gra'h> alculate this as a 'ercentage o# the gradient< -hat is the uncertainty in the *raking #orce #rom the ta*le> alculate this as a 'ercentage o# the mean *raking #orce you o*tained #rom the ta*le< Does the gradient #all 3ithin the uncertainty> (he /igh3ay ode states that these are the average *raking distances, 3hat might cause a variation in the *raking distances> (he /igh3ay ode also gives the overall sto''ing distances 3hich are larger than the *raking distances, 3hy> -hy didnt 3e use the overall sto''ing distances> Descri*e the #orces acting u'on the car *e#ore the *rakes are a''lied<
Analysis
"m'ulse
6< D-4!R
A device for ring toy cars was used to investigate the concept of impulse. The ring force could be adCusted and the velocity of a car of un'nown mass was recorded.
E!perimental Data /ere are the velocities the car travelled at a#ter the #orce 3as a''lied #or ;<;J seconds< Force= $elocity= Mean $elocity= Mass= F
v
v
m
6(7 ;
6m9s7
6*g7
;<2J
6m9s7 ;<2K
;<2K
B
;
;
;
2
B
B<J
B<H
2<;
B
B
?
2
2
2
C
2
<;G
H
,nalysis alculate the mean velocity #or each o# the #orces< -hat is the uncertainty in the measurement o# v 3hen F is B alculate this as a 'ercentage o# the mean v< -hat is the uncertainty in the measurement o# v 3hen F is 2
alculate this as a 'ercentage o# the mean v< -hat is the uncertainty in the measurement o# v 3hen F is ? alculate this as a 'ercentage o# the mean v< -hich ty'e o# error is res'onsi*le #or the variation in value o# v> Plot a gra'h o# F against v on the x axisN and dra3 a line o# *est ft< Does your line o# *est ft 'ass through the origin> Should it> !x'lain your ans3er< "# F and v are connected *y the e&uation , 3hat does the gradient o# your line re'resent> alculate the gradient o# your line o# *est ft< se the gradient to calculate the mass o# the toy car< se the a*ove e&uation to calculate a value o# m #or each value o# F , 3rite these values in the ta*le a*ove< alculate the mean value o# m #rom the ta*le< -hat is the uncertainty in this value> (he mass o# the toy 3as measured to *e B2Cg< alculate the di5erence *et3een the actual value and the gradient ans3er< -hat is this as a 'ercentage o# the actual ans3er> alculate the di5erence *et3een the actual value and the ta*le ans3er< -hat is this as a 'ercentage o# the actual ans3er> -hich 3ord descri*es the ans3er that is closer to the true ans3er> "# the velocity 3as calculated *y measuring ho3 #ar the toy car moved in B second, ho3 could you increase the 'recision o# the value o# velocity>
Practical 6< D-4!R
ircular Motion
(ou are going to carry out an experiment to investigate the relationship between the centripetal force and the mass of a bung on a string system. (ou will then use your data to calculate the mass of the bung.
E5uipment List Plastic tu*e String B<;mN Ru**er *ung 3ith hole Rulers ;cm and BmN
Sto' clock Masses ? x B;;g, B x C;gN Digital *alance
Tas* •
•
•
•
•
(ie one end o# the string to the ru**er *ung and make a mark on the string at a distance o# ?Ccm #rom the *ung< (hread the string through the 'lastic tu*e and attach BC;g to the other end o# the string< -hirl the ru**er *ung in a hori@ontal circle as sho3n in the diagram< AdQust the s'eed o# the *ung so that the radiusr o# the circle is e&ual to ?Ccm< Measure the time t #or 2; revolutions o# the *ung<(ake re'eat readings and calculate a mean value<
•
alculate the centri'etal #orce using
•
alculate the s'eed v o# the *ung using
•
Re'eat the ex'eriment #or masses e&ual to 2;;, 2C;, ;;, C;, ?;; and ?C;g<
•
Plot a gra'h o# F on the y0axis against v 2< Dra3 a line o# *est ft and calculate the gradient<
•
se the digital *alance to fnd the mass o# the *ung< Record this measurement as the ^actual mass<
,fter the E!periment -hat 3ere the de'endent and inde'endent varia*les in your investigation> -hat is the uncertainty in your value #or the radius> alculate the 'ercentage uncertainty in your reading< -hat is the uncertainty in your mean value o# the t 3hen the mass 3as 2;;g> alculate the 'ercentage uncertainty in the mean value< se the mean value o# t to calculate the time taken #or a single revolution< -hat is the uncertainty o# this value> -hat is the uncertainty in your mean value o# the t 3hen the mass 3as ;;g> alculate the 'ercentage uncertainty in the mean value< se the mean value o# t to calculate the time taken #or a single revolution< -hat is the uncertainty o# this value> -hich o# the t3o 'roduced a more 'recise value> sing the results you o*tained #or a mass o# ;;g calculate the 'ercentage uncertainty in the value o# v< -hat 3ould *e the 'ercentage uncertainty in the corres'onding value o# v 2>
(he e&uation o# your line o# *est ft is given *y < se your value o# the gradient to calculate m< -hat is the di5erence *et3een your value and the actual mass> alculate the 'ercentage di5erence o# your value # rom the actual mass<
Practical 6< D-4!R
Finding g 3ith a Sim'le Pendulum
(ou are going to carry out an experiment to investigate the relationship between the time period of a pendulum8 its length and the gravitational eld strength8 g .
E5uipment List Pendulum *o* String B
lam' Stand, $oss and lam' Sto' clock Plasticine
Tas* •
• •
•
Sus'end the 'endulum *o* #rom the clam' attached to the clam' stand so that the 'endulum length is ;<;m< -rite do3n the 'recision o# the ruler< Dis'lace the 'endulum *y less than B;Z #rom the vertical to set it in sim'le harmonic motion< Measure the time taken #or the 'endulum to com'lete B; s3ings< Record this in a ta*le along 3ith the time 'eriod #or B s3ing<
•
-rite do3n the 'recision o# the sto' clock<
•
Re'eat this ex'eriment t3ice more and take an average #or the tim e taken #or B s3ing, T <
•
"nclude a column in your ta*le o# T 2, 3here T is the time 'eriod o# B s3ing<
•
1*tain mean values o# T #or 'endulums o# length= ;
•
"nclude a column la*elled g < Plot a gra'h o# time 'eriod s&uared, T 2 on the y0axisN against 'endulum length, l on the x0 axisN< Plot a line o# *est ft and calculate its gradient<
•
•
,fter the E!periment -hat 3ere the de'endent and inde'endent varia*les in your investigation> -hy do you think you 3ere asked to dis'lace the 'endulum *y less than B;Z> Look at your gra'h, are the results relia*le> -hy> 1ther than taking re'eat readings ho3 else could you increase the relia*ility o# your ex'eriment> se the value o# l and T 2 #or each value o# l to fll in the column you la*elled g < alculate the mean value o# g #rom this column< -hat is the di5erence *et3een your value and the acce'ted value o# G alculate the 'ercentage di5erence o# your value # rom the acce'ted value<
(he e&uation o# your line o# *est ft is given *y < se your value o# the gradient to calculate g < -hat is the di5erence *et3een your value and the acce'ted value o# G alculate the 'ercentage di5erence o# your value # rom the acce'ted value< -hich o# your t3o values o# g is more accurate> Look at the column la*elled g and the largest value< se your ra3 data to calculate the uncertainty in the mean value o# T < 6o3 calculate the 'ercentage uncertainty in this measurement< -hat is the 'ercentage uncertainty in the corres'onding value o# T 2> se the 'recision o# your e&ui'ment to calculate the 'ercentage uncertainty in your measurement o# the corres'onding length< "#
calculate the overall uncertainty in this value o# g <
Practical 6< D-4!R
Finding 6 3ith a Mass and S'ring
(ou are going to carry out an experiment to investigate the relationship between the time period of a mass and spring system8 the mass applied and the spring constant8 6 .
E5uipment List S'ring Masses B; x C;gN Ruler ;cmN
lam' Stand, $oss and lam' Sto' clock Plasticine
Tas* Part B
•
Measure the length o# the s'ring<
•
Sus'end the s'ring #rom the clam' attached to the clam' stand< Attach a C;g mass to the *ottom o# the s'ring< Record the extension o# the s'ring #or C;g< Re'eat 3ith increasing mass u' to C;;g<
•
Dra3 a ta*le to include columns #or mass, #orce a''lied and extension<
•
Plot a gra'h o# #orce a''lied on the y0axisN against extension on the x0axisN<
•
alculate the gradient< (his is the s'ring constant #or the s'ring and 3ill *e called the acce'ted value< Part 2 /ang a C;g mass #rom the s'ring< Dis'lace the mass to set it into sim'le harmonic motion<
•
•
•
Measure the time taken #or the 'endulum to com'lete B; cycles< Record this in a ta*le along 3ith the time 'eriod #or B cycle< -rite do3n the 'recision o# the sto' clock<
•
Re'eat this ex'eriment t3ice more and take an average #or the tim e taken #or B cycle, T <
•
"nclude a column in your ta*le o# T 2, 3here T is the time 'eriod o# B cycle<
•
1*tain mean values o# T #or masses= B;;, BC;, 2;;, 2C;, ;;, C;, ?;;, ?C; and C;;g
•
"nclude a column la*elled 6 <
•
Plot a gra'h o# time 'eriod s&uared, T 2 on the y0axisN against mass, m on the x0axisN<
•
Plot a line o# *est ft and calculate its gradient<
•
,fter the E!periment se the value o# m and T 2 #or each value o# m to fll in the column you la*elled 6 < alculate the mean value o# 6 #rom this column< -hat is the di5erence *et3een the mean value #rom the ta*le and the acce'ted value> alculate the 'ercentage di5erence o# the mean value #rom the acce'ted value< (he e&uation o# your line o# *est ft is given *y calculate 6 <
< se your value o# the gradient to
-hat is the di5erence *et3een the gradient and the acce'ted value> alculate the 'ercentage di5erence o# the gradient #rom the acce'ted value< -hich o# your t3o values o# 6 is more accurate> -hat 3ere the de'endent and inde'endent varia*les in Part 2 o# your investigation> se your gra'h to comment on the relia*ility o# your results< /o3 could you have increased the relia*ility o# your results> /o3 could you have increased the 'recision o# your results> alculate the 'ercentage uncertainty in your largest time measurement< -hat is the 'ercentage uncertainty in the corres'onding T 2 value>
Practical 6< D-4!R
S/M 1scillations o# a S'ring
(ou are going to investigate how the time period of the oscillations of a ruler8 which is supported by a spring8 varies when di5erent masses are suspended from the ruler
E5uipment List S'ring Masses B; x C;gN 3ith hanger Ruler BmN lam'ing *locks
lam' Stand, $oss and lam' x2N Sto' clock $lu0(ack and Pin S'irit level
Tas* •
•
•
• • •
• •
Set u' the a''aratus as sho3n in Figure -< (he threads ta'ed to the ruler should *e held frmly *et3een the t3o 3ooden *locks so the ruler is #ree to 'ivot a*out this end< (he s'ring should su''ort the ruler B;<; cm #rom its #ree end< AdQust each clam' so that the ruler is hori@ontal and the s'ring is vertical< (he mass, m, should initially *e the B;; g slotted mass holder and *e su''orted at x 7 C;<; cm< 9ee' *oth Land 4constant throughout the ex'eriment< De'ress the #ree end o# the ruler slightly and release it so that it oscillates vertically< (ake suita*le readings to determine the time 'eriod, T , o# the oscillation
,fter the E!periment "n your investigation 3hat 3as the de'endent varia*le> /o3 did you ensure that the ruler 3as hori@ontal and the s'ring 3as vertical> Descri*e and ex'lain t3o techni&ues you used to ensure accurate timings< Descri*e 3hat your gra'h suggests a*out the relationshi' *et3een T 2 and m< !valuate the relia*ility o# your results< Descri*e the e5ect on your gra'h o# using a ruler 3ith greater mass< Determine the uncertainty in the largest value o# T3 -hat is the 'ercentage uncertainty in the largest value o# T9 -hat is the 'ercentage uncertainty in the corres'onding o# T 2> Determine the uncertainty in the smallest value o# T3 -hat is the 'ercentage uncertainty in the smallest value o# T9 -hat is the 'ercentage uncertainty in the corres'onding o# T 2> State one likely source o# this uncertainty< State the name given to this ty'e o# error< -hat does the gradient o# your gra'h re'resent> alculate the gradient o# your line<
Practical 6< D-4!R
) Sha'ed Pendulum
(ou are going to investigate how the time period of a ,shaped pendulum varies with distance 2
E5uipment List Ruler BmN lam' Stand, $oss and lam' x2N Pendulum $o* (hin String or (hread
Sto' lock $lu0(ack and Pin S'irit Level
Tas* • • •
•
•
• •
4ou are 'rovided 3ith a )0sha'ed 'endulum set u' as sho3n in Figure (he length $ should remain constant throughout the ex'eriment< "nitially set distance 2 to B;<;cm -hen the 'endulum *o* is dis'laced and released in the direction sho3n in Figure ., it oscillates 3ith S/M, 'rovided the am'litude is small< Make suita*le measurements to determine accurately the time 'eriod, T , o# the oscillations< (he mounted 'in is availa*le as a re#erence marker sometimes called a fducial markerN #or use in timing the oscillations< Re'eat the time measurements #or a range o# values o# distance 2 se your results to 'lot a gra'h o# T against 2 .
,fter the E!periment "n your investigation 3hat 3as the de'endent varia*le> State and ex'lain the *est 'osition to 'lace the re#erence marker or fducial markerN #or timing the oscillations< State and ex'lain one 'rocedure, other than using the fducial m arker, that you used to reduce the uncertainty in the measurement o# the time 'eriod o# the oscillations< (he e5ective length, Lo# a )0sha'ed 'endulum, is given *y=
the time 'eriod, T , o# the 'endulum is given *y= strength<
< (heory sho3s that
3here g is the gravitational feld
Sho3 that $y com'aring the a*ove e&uation 3ith the general e&uation o# a straight line, 8 = m4 + c, state 3hat should *e 'lotted to o*tain a straight gra'h< /o3 could a value #or g *e o*tained #rom this gra'h> alculate the gradient o# your gra'h< se your gra'h to evaluate the relia*ility o# your results< -hat is your uncertainty in the measurement o# 2 > alculate the 'ercentage uncertainty #or your smallest value o# 2 < alculate the 'ercentage uncertainty #or your largest value o# 2 <
Analysis 6< D-4!R
Dam'ing
A mass and spring system was set up with three masses of "<
E!perimental Data
Radius of card 6cm7
Time ta*en for oscillator to come to rest 6s7
;<;
2CG
2?K
2C?
H<;
B?
BB
B?
J<;
BBH
BBC
BBB
K<;
G2
K
K
G<;
HC
HK
HK
B;<;
CK
CJ
C
Mean time 6s7
,rea of #scillator 6m.7
,dditional ,rea 6m.7
4 of 3ndamped time to come to rest
000
000
,nalysis alculate mean value #or the time taken #or the oscillator to come to rest #or each radius o# card< -hat is the uncertainty in the time taken to sto' 3hen the radius is H cm> alculate this as a 'ercentage o# the mean value< -hat is the uncertainty in the time taken to sto' 3hen the radius is K cm> alculate this as a 'ercentage o# the shortest time measurement at this radius< -hat is the uncertainty in the time taken to sto' 3hen the radius is B; cm> alculate this as a 'ercentage o# the longest time measurement at this radius< -hat ty'e o# error is res'onsi*le #or the di5erence in the value o# the time taken to come to rest> alculate the area o# the oscillator using < -rite these values in the column 'rovided< -hat is the 'recision in the radius i# card measurements> alculate the 'ercentage uncertainty in the J<; cm measurement< -hat 3ill *e the 'ercentage uncertainty in the value o# the Area> -rite do3n the u''er and lo3er limits o# the Area< Plot a gra'h o# Radius o# 1scillator on the y axisN against time taken to come to rest< Descri*e the gra'h you have 'lotted< -hat does your gra'h suggest a*out the relationshi' *et3een the t3o varia*les> Plot a gra'h o# Area o# 1scillator on the y axisN against time taken to come to rest< Descri*e the gra'h you have 'lotted< -hat does your gra'h suggest a*out the relationshi' *et3een these t3o varia*les> om'lete the fnal columns o# the ta*le *y calculating the additional area each card adds to the oscillator and the time 'eriod as a 'ercentage o# the undam'ed time taken to come to rest< Do you notice any 'atterns or trends> Plot a gra'h o# Additional Area y axisN against 'ercentage o# undam'ed time taken to come to rest< /o3 are these varia*les linked> (heory states that dam'ing 3ill not a5ect the time 'eriod o# the S/M system< /o3 could you 'rove this using the ex'erimental set u' descri*ed at the to' o# the 'age>
Analysis 6< D-4!R
(he %ravitational onstant
(ou are going to use experimental data on the six closest planets to the *un to determine the gravitational constant G.
E!perimental Data
%lanet Mercury )enus !arth Mars Uu'iter Saturn
%lanet Mercury )enus !arth Mars Uu'iter Saturn
/ere is the 'lanetary data #or the six closest 'lanets to the Sun Radius= & 6m7 Surface 2eld strength= g 6( *g?-7 2
Mean radius= & 6m7
Mass= M 6*g7 <; ?
x x x x x x
Mean surface 2eld strength= g 6( *g?-7
G
6( m. *g?.7
B;2 B;2? B;2? B;2 B;2J B;2H
,nalysis alculate the mean values o# the radius #or each 'lanet alculate the mean values o# sur#ace feld strength #or each 'lanet< -hat is the name given to the error res'onsi*le #or the s'read in the values o# radius and sur#ace feld strength> alculate the uncertainty in the radius o# Mercury< alculate the 'ercentage uncertainty in the largest value o# the radius o# Mercury< alculate the uncertainty in the sur#ace feld strength o# Uu'iter< alculate the 'ercentage uncertainty in the smallest value o# the sur#ace feld strength o# Uu'iter<
se the e&uation to com'lete the last column o# the ta*le< alculate your mean value #or the gravitational constant G< alculate the 'ercentage di5erence o# your mean value #rom the acce'ted value o# H 4ou may ignore any uncertainty in the measurement o# the mass M <
Plot a gra'h o# sur#ace feld strength g on the y0axisN against on the x0axisN< alculate the gradient o# the line o# *est ft< alculate the di5erence *et3een the gradient and your mean value o# G< alculate the 'ercentage di5erence *et3een the gradient and your mean value o# G< alculate the di5erence *et3een the gradient and the acce'ted value o# G< alculate the 'ercentage di5erence *et3een the gradient and the acce'ted value o# G3
Analysis A< /DS16
%ravitational Potential
An experiment was carried out to nd the relationship between the distance from the centre of the earth and the gravitational potential. The raw data are shown below-
E!perimental Data Distance= & = from the centre of the Earth to test mass 6m7
+ravitational potential= V 6AGg?-7 BO& 6m?-7
Trial -
Trial .
Trial /
H<JxB;H
0J<;; x B;J
0H
0C
K<JxB;H
0?
0?
0?
B<;? xB;J
0
0
0
B<2? xB;J
0
0<C x B;J
0<;; x B;J
B
02
02
02
B
02
02
02
B
02<B x B;J
02<2H x B;J
02<;K x B;J
2<;? xB;J
0B
0B
02
2<2? xB;J
02<;B x B;J
0B
0B
Mean
,nalysis alculate the mean gravitational 'otential #or each distance and the values #or BO & < -hat error is res'onsi*le #or the s'read in the values o# gravitational 'otential> alculate the uncertainty in the measurement o# gravitational 'otential #or the largest distance measured< alculate the 'ercentage uncertainty in this measurement o# gravitational 'otential< alculate the uncertainty in the measurement o# gravitational 'otential #or the smallest distance measured< alculate the 'ercentage uncertainty in this measurement o# gravitational 'otential< Plot a gra'h o# gravitational 'otential y0axisN against distance #rom the centre o# the earth x0 axisN< Descri*e any 'attern or trend sho3n *y your gra'h< se your gra'h to fnd the gravitational 'otential at distances o# B<;xB; Jm #rom the centre o# the earth and 2<;xB;Jm #rom the centre o# the earth< alculate the 3ork done in moving a 2Ckg mass #rom B<;xB; Jm #rom the centre o# the earth to 2<;xB;Jm #rom the centre o# the earth< (he gradient o# the line at any 'oint on the gra'h gives the gravitational feld strength at that distance #rom the centre o# the 'lanet< se your gra'h to calculate the gravitational feld strength at a distance o# B
(his value can *e used in the e&uation
<
Plot a gra'h o# V y0axisN against BO & x0axisN< -hat does the gradient o# this line re'resent> se your gra'h to calculate a value #or the gravitational constant, G< alculate the 'ercentage di5erence *et3een your value o# G and the acce'ted value o# H
Analysis
6< D-4!R
9e'lers (hird La3
(ou are going to use experimental data on the six closest planets to the *un and Depler7s Third 6aw to determine the ass of the *un .
E!perimental Data %lanet Mercury )enus !arth Mars Uu'iter Saturn ranus 6e'tune
%lanet
/ere is the 'lanetary data #or the six closest 'lanets to the Sun Minimum radius Ma!imum radius #r'it time= T 6days7 of or'it 6->@ m7 of or'it 6->@ m7 ?C
Mean radius= & 6m7
Mean radius cu'ed=& 3 6->/. m/7
Mean or'it time= 6s7 T
#r'it time s5uared= T 2 6->-/ s.7
Mean radius= & 6 m7
Mean radius cu'ed= & 3 6->/1 m/7
Mean or'it time= T 6s7
#r'it time s5uared= T 2 6->-H s.7
Mercury )enus !arth Mars
%lanet Uu'iter Saturn ranus 6e'tune
,nalysis alculate the mean radius o# or*it #or each o# the 'lanets< om'lete the column #or the radius o# or*it cu*ed< State your results in the #orm given in the heading o# the column< alculate the mean or*it time #or each 'lanet in seconds< om'lete the column #or the or*it time s&uared< State your results in the #orm given in the heading o# the column< Plot a gra'h o# T 2 on the y axis and & 3 on the x axis #or the ? inner 'lanets and a second gra'h #or the ? outer 'lanets< Dra3 a line o# *est ft on each gra'h< (he e&uation #or your line o# *est ft is given *y constant H
3here G is the gravitational
alculate the gradient #or the ? inner 'lanets gra'h< se this to calculate M < -hat is the di5erence *et3een this value and the acce'ted value o# B -ork this out as a 'ercentage o# the acce'ted value< alculate the gradient #or the ? outer 'lanets gra'h< se this to calculate M < -hat is the di5erence *et3een this value and the acce'ted value> -ork this out as a 'ercentage o# the acce'ted value< -hich o# the gra'hs gave you a value o# closest to the true value>-hat 3ord descri*es this>
Analysis
!lectric Potential
6< D-4!R
(ou are going to analyse the data obtained in an investigation into the electric potential at di5erent distances from a an de 1raa5 generator whose dome has a diameter of @< cm.
E!perimental Data Distance from the $an de +raa 6m7 ;<;
r
6m7
m0BN
Electric %otential= V 6A &?-7 H2;;
HBC;;
HB;;
;
H;;
HB;;
C;;
B<;
2CB;;
2C;;;
2HB;;
B
2;;;
BG2;;
BG;;
2<;
BH;;
BCG;;
BCC;;
2
BH;;
BH;;
B;;
<;
BB?;;
BBH;;
BBK;;
B;;;
B;;;
B;;;
?<;
G2C;
G;H;
G2;
?
KBG;
KJ;
KB;
Mean V 6A &?-7
,nalysis alculate the distance #rom the centre & N #or each distance #rom the )an de %raa5 generator< -hat is the 'recision o# the distance measurements> alculate BO& #or each distance #rom the )an de %raa5 generator< alculate the mean electric 'otential V N #or each distance< -hat is the uncertainty in V #or a distance o# ; alculate this as a 'ercentage o# the mean value o# V at this distance< -hat is the uncertainty in V #or a distance o# B alculate this as a 'ercentage o# the smallest value o# V at this distance< -hat is the uncertainty in V #or a distance o# <; m> alculate this as a 'ercentage o# the largest value o# V at this distance< -hat is the uncertainty in V #or a distance on ?<; m> alculate this as a 'ercentage o# the middle value o# V at this distance< -hat error is res'onsi*le #or the s'read in values o# the electric feld strength at 2 Plot a gra'h o# V against BO& and dra3 a line o# *est ft<
"# the e&uation o# the line is 3hat does the gradient 'resent> se your gradient to calculate the charge, Q, on the )an de %raa5< Plot a gra'h o# V against & and dra3 a line o# *est ft< Dra3 a tangent to the line o# *est ft 3hen & 7 2
se the e&uation to calculate the theoretical value o# E 3hen & is 2 alculate this di5erence as a 'ercentage o# the theoretical value<
Analysis
Finding :;
6< D-4!R
(ou are going to analyse the data obtained in an investigation into the electric potential at di5erent distances from a an de 1raa5 generator that has a charge of ") $ stored on its surface. This will lead to you finding a value for E <.
E!perimental Data Distance from &entre= & 6m7 2<;
Electric Field Strength=
2G
2K
2G
2
BG<;
BK
BK
<;
B<;K
B2
B
G
G
G
?<;
J<H
J<2G
J<2K
?
C
C
C
C<;
?
?
?
C
H<;
<2K
<2K
H
2
2
2
Mean E 6! ->@ (9&7
E
6! ->@ (9&7
& #
. / & #
6m.7
6m?.7
,nalysis -hat is the inde'endent varia*le in this investigation> -hat is the de'endent varia*le in this investigation> -hat is the 'recision o# the distance measurements> alculate the mean values o# electric feld strength #or each value o# & < alculate the values o# & # and . / & #< alculate the uncertainty in the value o# E 3hen & is 2 alculate the uncertainty in the value o# E 3hen & is ?<; -hat is this as a 'ercentage o# the mean value o# E > alculate the uncertainty in the value o# E 3hen & is C<; -hat is this as a 'ercentage o# the mean value o# E > alculate the uncertainty in the value o# E 3hen & is H
m> m> m> m>
Plot a gra'h o# E against . / & # on the x axisN Dra3 a line o# *est ft and calculate its gradient<
"# the e&uation linking E and . / & # is se the gradient to calculate a value o# (0<
, 3hat does the gradient o# your line re'resent>
(he acce'ted value o# (0 is K alculate this as a 'ercentage o# the actual value>
Analysis
a'acitance
6< D-4!R
(ou are going to use experimental data to nd the capacitance of a capacitor .
E!perimental Data /ere is the charge stored on the ca'acitor 3hen di5erent voltages are a''lied across it &harge Stored= Q Mean &harge Stored= $oltage= V 0H Q 6x B; &7 6$7 6 &7 2<;2
G
G
G
G
?
BG<2
BG<2
BG<2
BG<2
H<;?
2K
2K<J
2K<2
2K
J
J
J
BB
J
B;<;
?J
?H
?J<2C
?J<2?
,nalysis alculate the mean charge stored *y the ca'acitor at each o# the voltages< -hat is the 'recision o# the voltage readings> alculate the 'ercentage uncertainty in the middle voltage reading< -hat is the uncertainty in the charge stored reading 3hen the voltage 3as 2<;2 )< alculate this as a 'ercentage o# the mean charge stored< -hat is the uncertainty in the charge stored reading 3hen the voltage 3as ? (he ca'acitance &uoted on the ca'acitor is ? alculate this as a 'ercentage o# the &uoted value<
4ou can calculate the ca'acitance using the e&uation
<
se the readings #rom the J -hat is the maximum the ca'acitance could *e> -hat is the minimum the ca'acitance could *e> Does the &uoted value #all 3ith0in these limits> /o3 can 3e descri*e this>
Practical 6< D-4!R
Discharging a'acitors
(ou are going to carry out an experiment to determine the capacitance of an unmar'ed commercial capacitor.
E5uipment List Po3er 'ack rocodile cli's and Leads a'acitors various valuesN a'acitor unkno3n valueN
Resistors various valuesN )oltmeter SPD( s3itch Sto' clock
Tas* Part B Set u' a circuit like the one sho3n in the diagram< (he resistor should have a value o# 22; kX and the ca'acitor should have a value o# B;;; IF< !nsure the ca'acitor is connected 3ith the correct 'olarity< !nsure the Single Pole, Dou*le (hro3 SPD(N s3itch is s3itched to charge the ca'acitor #rom the 'o3er 'ack< Set the 'o3er 'ack to a '
•
•
•
•
•
• •
Plot a gra'h o# 'otential di5erencey axisN against time<
Dra3 a curve o# *est ft< Part 2 Ask your su'ervisor #or an unmarked ca'acitor and set u' a similar circuit as *e#ore<
•
• •
• • •
•
Discharge the ca'acitor and determine the time : taken #or the 'otential di5erence across the ca'acitor to decrease to J\ o# its initial value< (ake re'eat readings< Re'eat this measurement #or di5erent values o# R, *oth larger and smaller< Record your results in a ta*le including a *lank column at the end to *e used in the analysis< Plot a gra'h : y axisN against R and dra3 a line o# *est ft<
,fter the E!periment se your #irst gra'h to calculate the time constant _ o# the ca'acitor< (ake several readings and clearly la*el these on your gra'h< (he theoretical value is 22; seconds< -hat is the di5erence *et3een this and your mean value #or : > alculate this as a 'ercentage o# the theoretical value< Ask your su'ervisor #or the actual ca'acitance stated on the ca'acitor in the second 'art o# the ex'eriment< (he gradient o# your line o# *est ft is e&ual to C < -hat is the di5erence *et3een your gradient and the actual value> alculate this as a 'ercentage o# the actual value<
"n the *lank column o# your ta*le calculate C #or each value o# R using the e&uation < alculate the mean value o# C #rom the ta*le< -hat is the di5erence *et3een this value and the actual value> alculate this as a 'ercentage o# the actual value< "s the gradient value or the ta*le value more 'recise> !x'lain ho3 using a voltmeter connected to a data logger 3ould im'rove your ex'eriment<
Analysis 6< D-4!R
a'acitor (ime onstant
A circuit was set up to initially charge a @2< F capacitor from a 2.# battery and then discharge through a resistor of un'nown resistance. (ou are going to use the data of how the potential di5erence changes over time to nd the resistance of the resistor.
E!perimental Data /ere are the 'otential di5erences #or di5erent times #rom the start o# discharge< Time= %otential Dierence= V Mean V t V / V 0 ln(V / V 0) 6$7 6$7 6s7 C
C
C
C
B;
?
?
?
BC
2;
2
2
2
2C
2
2
2
;
B
B
B
C
B<;
B<2
B<B
?;
B<;2
;
;
?C
;
;
;
C;
;
;
;
,nalysis 6ame one control varia*le on the investigation< -hat is the inde'endent varia*le in this investigation and ho3 3as it measured> -hat is the de'endent varia*le in this investigation and ho3 3as it measured> -hat 3as the 'recision o# the voltmeter> alculate the mean values o# each 'otential di5erence< alculate the value o# V / V 0 #or each time< alculate the value o# ln(V / V 0) #or each time< alculate the uncertainty in the ' alculate the uncertainty in the ' Plot a gra'h o# ln(V / V 0) against t x axisN and dra3 a line o# *est ft< "# V and V 0 are connected *y the e&uation 3hat does the gradient o# your line o# *est ft re'resent> alculate the gradient o# your line< se your gradient to calculate the resistance, R, o# the resistor< (he resistance given #or the resistor is ?2 kX, 3hat is the di##erence *et3een the acce'ted value and your value> -ork this out as a 'ercentage o# the acce'ted value<
Plot a gra'h o# V against t x axisN< se your gra'h to fnd the time constant< se the time constant to fnd the resistance, R, o# the resistor< -hat is the di5erence *et3een this value o# R and the acce'ted value> -ork this out as a 'ercentage o# the acce'ted value<
Practical 6< D-4!R
a'acitor Discharge
(ou are going to investigate the discharge of a capacitor through di5erent resistors
E5uipment List Po3er 'ackO$attery rocodile li's and Leads a'acitors ?J;`FN
Resistors various valuesN )oltmeter Sto' clock
Tas* •
•
•
•
•
•
•
•
Set u' the circuit as sho3n in the diagram< 4ou should ensure that the negative terminal o# the su''ly is connected to the negative terminal o# the ca'acitor< "# in dou*t, ask your su'ervisor< 4ou 3ill not lose marks #or this sa#ety check< onnect the resistor 3ith the least resistance in the circuit as R, and record its value< onnect the ying lead to 'oint A to charge the ca'acitor< Record the '
Dra3 a gra'h to sho3 ho3
'lotted in the vertical axisN varies 3ith
<
,fter the E!periment State the control varia*le in your ex'eriment se your data calculate the uncertainty in your smallest mean 'd, V 10< alculate the 'ercentage uncertainty in your smallest mean 'd, V 10< se your data calculate the uncertainty in your largest mean 'd, V 10< alculate the 'ercentage uncertainty in your largest mean 'd, V 10< State and ex'lain t3o #actors that determined the accuracy o# the measurement o# V 10< State and ex'lain t3o 3ays in 3hich a data logger instead o# a voltmeter and sto'clock, 3ould im'rove the accuracy in the measurement o# V 10<
For a ca'acitor o# ca'acitance C discharging through a resistor o# resistance R the 'otential di5erence across the ca'acitor is given *y the e&uation 3here V is the 'd across the ca'acitor at time, t , and V 0 is the 'd across the ca'acitor at time t 7 ;< se this e&uation to
sho3 that -hat does the gradient o# your gra'h re'resent> se your gradient to calculate the ca'acitance o# the ca'acitor< alculate the di5erence *et3een your value o# the ca'acitance and the given value on the ca'acitor -hat is the 'ercentage di5erence *et3een your value and the given value>
Analysis 6< D-4!R
Mass S'ectrometer
(ou are going to use experimental data to nd the charge to mass ratio of a proton and an electron.
%roton E!perimental Data Radius= & 6m7 ;<;2 ;<;? ;<;H ;<;K ;
(he magnetic ux density o# the feld is B1 m9s7 6m9s7 BK
vO B
6m9sT7
Electron E!perimental Data Radius= & 6! ->?I m7 2<; ?<; H<; K<; B;<;
(he magnetic ux density o# the feld is B<2K( Mean Speed= v speed= v 6! ->1 m9s7 6m9s7 ?
vO B
6m9sT7
%roton ,nalysis alculate the mean s'eed #or each radius< For the smallest radius calculate the uncertainty in the mean s'eed< alculate the 'ercentage uncertainty in the mean s'eed< -hat is the 'ercentage uncertainty in the corres'onding value o# vO B> Plot a gra'h o# radius on the y axis against vO B on the x axis< Dra3 a line o# *est ft and calculate the gradient o# this line< (he e&uation #or this line is given *y , 3hat does the gradient re'resent> se the gradient to calculate the charge to mass ratio #or the 'roton< -hat is the di5erence *et3een your value and the acce'ted value o# G -hat is this as a 'ercentage o# the acce'ted value>
Electron ,nalysis alculate the mean s'eed #or each radius< For the largest radius calculate the uncertainty in the mean s'eed< alculate the 'ercentage uncertainty in the mean s'eed< -hat is the 'ercentage uncertainty in the corres'onding value o# vO B> Plot a gra'h o# radius on the y axis against vO B on the x axis< Dra3 a line o# *est ft and calculate the gradient o# this line< se the gradient to calculate the charge to mass ratio #or the electron< -hat is the di5erence *et3een your value and the acce'ted value o# B -hat is this as a 'ercentage o# the acce'ted value>
Analysis
Magnetic Flux Density
6< D-4!R
An experiment was conducted to nd the magnetic Gux density between the poles of a magnet using the apparatus as shown in the diagram. The current,carrying wire experiences an upwards force so the magnet experiences and equal and opposite force. The current Gowing through the wire was varied and the reading on the top pan balance recorded. The length of wire in the magnetic eld can be ta'en as "< cm.
E!perimental Data &urrent I
Reading on Top %an Balance
Mean mass
Force
m
F
Magnetic Flu! Density
m
6g7
6(7
B
6,7
6g7
6T7
B<;
;B<2
;B<;
;B<J
2<;
;2
;2
;2
<;
;?<;B
;
;
?<;
;C<2J
;C<2?
;C<2G
C<;
;H
;H
;H
H<;
;J
;J
;J
,nalysis -hat is the inde'endent varia*le and its 'recision> alculate the mean values o# the mass reading #or each o# the currents< -hat is the uncertainty in the mass reading #or a current o# B<; A> alculate this as a 'ercentage o# the mean< -hat is the uncertainty in the mass reading #or a current o# ?<; A> alculate this as a 'ercentage o# the smallest mass reading at this current< -hat is the uncertainty in the mass reading #or a current o# H<; A> alculate this as a 'ercentage o# the largest mass reading at this current< -hat ty'e o# error is res'onsi*le #or the variation in the mass readings> se the e&uation
to calculate the Force #or each o# the currents< (ake g to *e G
se the e&uation to com'lete the last column o# the ta*le< se the gra'h to comment on the relia*ility o# the results<
alculate your mean value #or the magnetic ux density B< Plot a gra'h o# current y axisN against Force< Dra3 a straight line o# *est ft and calculate the gradient< -hat is the e&uation o# your line o# *est ft> se the gradient to fnd the value #or the magnetic ux density< alculate the di5erence *et3een the value o# B #rom the gra'h and the value #rom the ta*le< alculate this as a 'ercentage o# the ta*le value< "# the reading on the *alance 3as ;;<;H 3hen no current o3s 3hat ty'e o# error 3ould that *e> /o3 3ould this have e5ected your mass measurements>
Analysis
(rans#ormers
6< D-4!R
An investigation was carried out on a simple transformer. The primary coil was xed with @#< turns but un'nown potential di5erence. The number of turns on the secondary coil was varied and the potential di5erence measured. %ith this information it should be possible to nd the potential di5erence of the primary coil.
E!perimental Data /ere is the data #ound 3hen the num*er o# coils on the secondary coil 3as varied Turns on the %otential Dierence across the Secondary Secondary Mean=V S &oil= V S &oil= 6$7 6$7 N S
B;
J
J
J
J
BC
BB<;K
BB
BB<2K
BB<?
2C
BK
BK
BG<;H
BK
?;
2G
;
2G
;<2?
H;
?C
??
??<J
?C
KC
HC<2
H
H?
H2
BBC
KK<;
KC
KH
KJ
,nalysis om'lete the ta*le *y calculating the mean value o# V S #or each value o# N S < Did you ignore any o# the values *ecause they 3ere anomalous> "denti#y them and Qusti#y their exclusion< -hich ty'e o# error is res'onsi*le #or the variation o# values o# V S 3hen N S is BBC> /o3 are these errors reduced> -hat is the 'recision o# the voltmeter used> -hat is the uncertainty in the value o# V S 3hen N S is alculate this as a 'ercentage o# the mean value o# -hat is the uncertainty in the value o# V S 3hen N S is alculate this as a 'ercentage o# the mean value o# -hat is the uncertainty in the value o# V S 3hen N S is alculate this as a 'ercentage o# the mean value o#
BC> V S< ?;> V S< KC> V S<
Plot a gra'h o# V S on the y axisN against N S on the x axisN< Dra3 a line o# *est ft< Does your line o# *est fr 'ass through the origin> Should it> !x'lain your ans3er<
"# V S and N S are linking *y the e&uation , 3hat does the gradient o# your line o# *est ft re'resent> alculate the gradient o# your line o# *est ft< se your gradient to fnd a value o# V P , the 'otential across the 'rimary coil< (he 'otential 3as measured to *e 2;;), 3hat is the di5erence *et3een this and the value #rom the gradient> alculate this as a 'ercentage o# the measured value< se this to comment on the accuracy o# the investigation< "denti#y and ex'lain 2 3ays in 3hich a trans#ormer loses energy< For each 3ay ex'lain ho3 to reduce these losses<
Analysis 6< D-4!R
(he 6uclear Radius onstant
(ou are going to use experimental data on the nuclear radius of ten elements to nd the nuclear radius constant r <.
E!perimental Data Element
A
A
⅓
Radius 6fm7
Mean Radius 6fm7
/elium
?<;;
2<;G
2<;C
2<;?
$eryllium
G<;B
2
2
2
<;H
<;H
<;G
?
?
?
C
C
C
H
H
H
J<2G
J
J
K<;B
K<;J
K<;G
1xygen Aluminium alcium 8inc 6io*ium (ellerium !r*ium ranium
BH<; ; 2H
r >
,nalysis alculate the value o# A⅓ #or each o# the elements< alculate the mean value o# the nuclear radius #or each element< -hat is the name given to the error res'onsi*le #or the s'read in the values o# nuclear radius> alculate the uncertainty in the radius o# each element< -hich has the largest uncertainty> alculate the 'ercentage uncertainty in each value o# mean radius< -hich has the largest 'ercentage uncertainty> se the e&uation to com'lete the last column o# the ta*le< -rite the a''ro'riate units in the heading o# this column<
alculate the mean value #or the nuclear radius constant & 0< Plot a gra'h o# nuclear radius R on the y0axisN against the cu*e root o# the num*er o# nucleons A⅓ on the x0axisN< Dra3 a line o# *est ft and use it to calculate the gradient< "# the acce'ted value o# & 0 3as B<2J #m <<<< alculate the di5erence *et3een this value and the value you calculated #rom the ta*le< alculate the 'ercentage di5erence this gives< alculate the di5erence *et3een this value and the gradient o# your gra'h< alculate the 'ercentage di5erence this gives< -hich o# these values is more accurate> -hy> se your gra'h to comment on the relia*ility o# the data you 3ere given #or this ex'eriment< -hat 3ould increasing the num*er o# re'eat readings #or each radius do to our mean value o# radius> -hat 3ould kee'ing the same num*er o# re'eats *ut measuring to radius to a smaller scale eg< decimal 'lacesN do to our mean value o# radius>
Practical 6< D-4!R
Radioactive Decay
(ou are going to carry out an experiment to determine the half,life of a sample of yellow cubes which will represent radioactive nuclei and from this the decay constant.
E5uipment List C2C yello3 cu*es 3ith one side coloured *lack The cubes will represent radioactive nuclei. All the cubes with their blac' side facing up will represent nuclei which have decayed to safety and the cubes with their yellow side facing up will represent nuclei which are still radioactive.
Tas* •
• •
•
ount the num*er o# cu*es at the start o# the ex'eriment< (his 3ill *e kno3n as the initial num*er, N 0< (he decay constant should *e < sing
calculate the ex'ected activity, AE<
Place the cu*es into their container, shake and then 'our them onto the desk< ount the cu*es 3hich have decayed and 'lace them to one side< Record this value as actual activity, AA< Record the remaining num*er o# radioactive nuclei, N <
•
alculate the ex'ected activity #or roll num*er t3o<
•
ontinue until all the nuclei have decayed<
•
Record your results in a ta*le 3hich has the #ollo3ing columns= 6um*er o# Rolls t
!x'ected Activity
6um*er Remaining N
Actual Activity
Decay onstant
AA
!
AE
,fter the E!periment alculate the di5erence *et3een the !x'ected Activity AEN and Actual Activity AAN #or each num*er o# rolls< alculate these di5erences as 'ercentages o# the Actual Activity< -hich is the most accurate roll>
alculate the decay constant #or each roll< 4ou should use the num*er remaining *e#ore the roll and the actual activity< -hich is the most accurate> alculate the mean value #or the decay constant< -hat is the uncertainty> alculate this as a 'ercentage o# the value< Plot a gra'h o# Actual Activity AAN against num*er o# rollst N< (ake #our values #rom your gra'h #or the hal# li#e o# the sam'le< alculate the mean value #or the hal#0li#e, T b< -hat is the uncertainty in your mean> -hat is the 'ercentage uncertainty o# the mean> se the e&uation to calculate the value o# the decay constant< (he 'ercentage uncertainty is the same as that in your value #or the hal#0li#e< reate a second ta*le 3ith columns #or t , N O N 0 and ln N O N 0) se your data #rom the ex'eriment to com'lete this ta*le< Plot a gra'h o# ln N O N 0) on the y0axis against t on the x0axis and dra3 a line o# *est ft< alculate the gradient o# your line< (his is e&ual to the decay constant< "s the decay constant calculated #rom the ta*le, #rom the hal#0li#e or #rom the last gra'h the most accurate>
Analysis
/al#0Li#e and the Decay onstant
6< D-4!R
A radioactive sample of 2<< nuclei was observed over a period of time and the remaining radioactive nuclei were counted. (ou are going to use experimental data to nd the decay constant and half,life of a radioactive substance. The bac'ground radiation was measured to be "" counts per second.
E!perimental Data Time= t 6s7
,ctivity= A
6B57
C
BJB
B;
BB2?
BC
G22
2;
JCJ
2C
H22
;
CBB
C
?2B
?;
?H
?C
2KC
C;
2H
&orrected A 6B57
(um'er of (uclei= N
N / N 0
ln ( N / N 0)
,nalysis (ake the *ackground radiation into account to fnd the corrected activity< alculate the num*er o# radioactive nuclei remaining, N , #or each time measurement< alculate N/N 0 #or each time interval< alculate ln N/N 0N #or each time interval< Plot a gra'h o# N against t on the x axisN and dra3 a line o# *est ft< (ake at least measurements #rom your gra'h o# the hal# li#e< se the e&uation
to fnd the decay constant !<
Plot a gra'h o# ln N/N 0N against t on the x axisN and dra3 a line o# *est ft< "# ln N/N 0N and t are linked *y the e&uation 3hat does the gradient # your line re'resent> alculate the gradient o# your line o# *est ft< se your gradient to calculate the decay constant !< (he decay constant 3as given to *e ;<;?< alculate the di5erence *et3een this value and your value #ound #rom the hal#0li#e< -hat is this as a 'ercentage o# the actual value> alculate the di5erence *et3een the actual value and your value #ound #rom the gradient< -hat is this as a 'ercentage o# the actual value> -hich ans3er is more accurate>
Analysis 6< D-4!R
(he "nverse S&uare La3
(ou are going to use experimental data obtained to investigate the inverse square law of H radiation.
E!perimental Data A %0M tu*e 3as 'laced at various distances #rom a gamma source< A#ter a set time the reading on the counter 3as recorded<(he *ackground radiation 3as measured over a minute time 'eriod 3hich resulted in a count o# HB< Distan &oun Time &ount &ou Time &ount rate &oun Time &ount ?t 6s7 rate nt 6s7 6s 7 t 6s7 rate ce 2 ?6s 7 6s?-7 6m7
>:-1
2BJ?
2;
?2?
?;
HHB2
H;
>:/>
CHH
2;
BB2K
?;
BHC;
H;
>:01
2CK
2;
C2
?;
JJ?
H;
>:I>
BHH
2;
B2
?;
?J?
H;
>:H1
B;?
2;
BGH
?;
2G?
H;
Distance 2 6m7 >:-1 >:/> >:01 >:I>
Mean count rate C 6s?-7
&orrected count?rate C 6s?-7
>:H1
,nalysis alculate the count rate #or each trail at every distance #rom the gamma source< alculate the mean count rate at every distance #rom the gamma source< -hat is the uncertainty in the mean count rate at a distance on ;<;m> alculate this as a 'ercentage o# the mean count rate< -hat is the uncertainty o# the distance measurement o# ;<;m> alculate this as a 'ercentage o# the actual measurement< -hich o# the &uantities is the greater source o# uncertainty> -hat is the *ackground count rate> om'lete the column #or the corrected count rate #or every distance #rom the gamma source< "# 3e did not su*tract the *ackground radiation #rom our readings 3hich ty'e o# error 3ould this *e>
Plot a gra'h o#= AN against C and $N against 2 Dra3 lines o# *est ft 3hich continue to cut the axes< Does either o# your gra'hs su''ort the inverse s&uare la3> !x'lain 3hich #eatures do< (he count rate at 'oint A and $ can *e com'ared using the e&uation= se this e&uation and data #rom the ex'eriment to calculate the count rate at ;<Cm #rom the gamma source< se gra'h A to calculate the count rate at ;<Cm #rom the gamma source< se gra'h $ to calculate the count rate at ;<Cm #rom the gamma source< "# the calculate ans3er is the actual value 3hich o# your gra'hs gave the most accurate result> "# 3e had not su*tracted the *ackground radiation ho3 3ould it have a5ected the gradient o# gra'h A>
Analysis 6< D-4!R
$inding !nergy
$omplete this table and plot a graph of binding energy per nucleon 3y,axis4 against nucleon number 3x,axis4 Mass o# Proton 7 B<;;J2Ku Mass o# 6eutron 7 B<;;KHJu Bu 7 GB< Me) !leme 8 6 A Mass o# Mass o# Mass De#ect $inding $!OA Me)N nt se'arate 6ucleus uN !nergy nucleons uN uN Me)N / B ; B B<;;J2K /e 2 2 ? ?<;;BC; Li ? J J<;B?C $e ? C G G<;;GGK $ C H BB BB<;;HCH H H B2 BB
9 a Sc (i ) r Mn Fe 6i o u 8n %a %e As $r Se 9r R* Sr 4 8r 6* Mo
BG 2; 2B 22 2 2? 2C 2H 2J 2K 2G ; B 2 ? C H J K G ?; ?B ?2
2; 2; 2? 2C 2K 2K ; ; ; 2 ? ? K ?2 ?2 ?? ?H ?H ?K C; C; C; C2 CH
2G ?; ?C ?J CB C2 CC CH CK CG H H? HG J? JC JG K; K2 KC KK KG G; G GK
K
Analysis
!7mc2
6< D-4!R
(ou are going to use experimental data and +instein7s mass,energy equation to c alculate the speed of light.
E!perimental Data (he energy released 3as measured and recorded #or di5erent mass de#ects< Energy Released= Mean Speed of Speed of Mass Energy Light Light= c E Defect= ?-. 6! -> A7 Released= S5uared= c 6m9s7 m E 6m9s7. 6! ->?.J*g7 6A7 ?
?<;J
?<;H
G
K
K
K
B?
B2
B2<
B2
BG
BH
BH
BH<
2?
2;
2;
2;<2
2G<2
2
2
2?
?
2G
;
;
,nalysis alculate the mean energy released #or each mass de#ect< -hat is the 'recision o# the mass de#ect> alculate the 'ercentage uncertainty in the middle mass de#ect> -hat is the uncertainty in the energy released #or a mass de#ect o# ? alculate this as a 'ercentage o# the mean energy released<
-hat is the uncertainty in the energy released #or a mass de#ect o# B? alculate this as a 'ercentage o# the smallest energy released #or this mass de#ect -hat is the uncertainty in the energy released #or a mass de#ect o# 2? alculate this as a 'ercentage o# the largest energy released #or this mass de#ect< -hat is the uncertainty in the energy released #or a mass de#ect o# ? alculate this as a 'ercentage o# the middle energy released #or this mass de#ect< se the e&uation to com'lete the last columns o# the ta*le la*elled c2 and c< alculate your mean value #or the s'eed o# light c< -hat is the di5erence *et3een your mean value and the acce'ted value <; x B; K mOs> alculate this as a 'ercentage o# the acce'ted value< Plot a gra'h o# mean energy released E on the y0axisN against mass de#ect m on the x0axisN< Dra3 a line o# *est ft and descri*e any 'attern or trend sho3n *y your gra'h< alculate the gradient o# the line o# *est ft< (he s&uare root o# the gradient gives us a value #or c< -hat value does the gradient yield> -hat is the di5erence *et3een your gradient value #or c and the acce'ted value> alculate this as a 'ercentage o# the acce'ted value< -hat does accurate mean> -hich o# your values is more accurate> -hat does relia*le mean> /o3 could the results *e made more relia*le>
Analysis 6< D-4!R
"deal %ases
(ou are going to analyse two experiments which were carried out to nd the molar gas constant8 0. The accepted value of 0 is .)"
&onstant $olume E!perimental Data BC moles o# a gas 3ere ke't in a container o# volume 2
&onstant %ressure E!perimental Data BC moles o# the same gas 3ere ke't at a constant 'ressure o# B
,nalysis - &onstant $olume alculate the mean 'ressures and fll in the ta*le<
se the e&uation to fll in the last column o# the ta*le< alculate the mean value o# R< -hat is the 'ercentage di5erence o# your value #rom the acce'ted value> Plot a gra'h o# 'ressure on the y0axisN against tem'erature on the x0axisN and dra3 a line o# *est ft< alculate the gradient o# your line and use it to fnd the value o# R< -hat is the 'ercentage di5erence o# this value #rom the acce'ted value> -hich o# your values in more accurate>
,nalysis . &onstant %ressure alculate the mean volumes and fll in the ta*le< se the e&uation to fll in the last column o# the ta*le< alculate the mean value o# R< -hat is the 'ercentage di5erence o# your value #rom the acce'ted value> Plot a gra'h o# volume on the y0axisN against tem'erature on the x0axisN and dra3 a line o# *est ft< alculate the gradient o# your line and use it to fnd the value o# R< -hat is the 'ercentage di5erence o# this value #rom the acce'ted value> -hich o# your values in more accurate>
,nalysis / ? &omparison -ith re#erence to the 'ercentage di5erences ex'lain 3hich o# the ex'eriments 3as more accurate< -ith re#erence to the gra'hs you have dra3n ex'lain 3hich o# the ex'eriments 3as more relia*le< (he third run o# ex'eriment B and the #ourth run o# ex'eriment 2 should have given you the same value o# R< se the 'ercentage uncertainties #or the 'ressure, tem'erature and volume in each ex'eriment to calculate the 'ercentage uncertainty in the values o# R< -hat 3ord can 3e use to descri*e the value o# R 3ith the lo3er 'ercentage uncertainty>
Practical 6< D-4!R
Finding A*solute 8ero
(ou are going to carry out an experiment to investigate the how the volume a gas occupies varies with temperature. (ou will then use this data to predict the absolute Bero temperature.
E5uipment List Sim'le %as (hermometer Ruler ;cmN $eakers
"ce 9ettle ali*rated (hermometer
Tas* •
A sim'le gas thermometer consists o# a ca'illary tu*e sealed at one end 3ith a thread o# sul'huric acid tra''ing a column o# air< Measure the room tem'erature<
•
Place the ice, thermometer and ca'illary tu*e into the *eaker<
•
Record the tem'erature and the length l o# the column o# tra''ed air<
•
Record values o# l #or various tem'eratures as the ice 3ater a''roaches room tem'erature<
•
•
!m'ty the *eaker, *oil the kettle and fll the *eaker< Place the thermometer and ca'illary tu*e into the *eaker< Record values o# l #or various tem'eratures as the 3ater a''roaches room tem'erature<
•
Re'eat the ex'eriment t3o more times<
•
•
•
Produce a ta*le o# the three sets o# ra3 data and the mean values o# l #or di5erent tem'eratures Plot a gra'h o# length l on the y0axis and the tem'erature on the x0axis<
• •
4our x0axis should have a range o# 0;;Z to B;;Z< Dra3 a straight line o# *est ft #or your results and extra'olate it until it crosses the x0axis<
,fter the E!periment -hat 3ere the inde'endent and de'endent varia*les in your ex'eriment> Look at your gra'h, 3hat is the relationshi' *et3een the t3o varia*les you have investigated> -hat 3as the 'recision o# the thermometer you used during the investigation> alculate the 'ercentage uncertainty in your largest reading o# the tem'erature< -hat 3as the 'recision o# the ruler you used during the investigation> alculate the 'ercentage uncertainty in your largest reading o# the length o# the column o# air< For this reading 3hich o# the t3o instruments is more 'recise> hoose any reading #rom the middle o# the range o# tem'eratures you used in the investigation< alculate the uncertainty in the value o# the mean length< -hat is this as a 'ercentage uncertainty o# the mean length> -here does your gra'h cut the x0axis> (his is your value #or the a*solute @ero tem'erature< (he acce'ted value is given as 02J9, 3hat is the di5erence *et3een your value and the acce'ted value> alculate the 'ercentage di5erence o# your value # rom the acce'ted value< omment on the relia*ility o# your results including a re#erence to your gra'h< !x'lain ho3 taking #e3er readings 3ould a5ect the relia*ility o# your results and 3hy< !x'lain ho3 taking more readings 3ould a5ect the relia*ility o# your results and 3hy< "denti#y 3hat you *elieve is the *iggest cause o# error in your investigation< /o3 could you reduce this>
Analysis
Finding A*solute 8ero
6< D-4!R
"#.2 m) of gas was heated to @< J$ and then cooled. The pressure was measured every "< J$ as it was cooled. :sing this we can nd the absolute Bero temperature and the number of moles of gas.
E!perimental Data (he energy released 3as measured and recorded #or di5erent mass de#ects< Temperatur %ressure= ; Mean %ressure= ; Temperature= T e= T 6%a7 6%a7 6G7 6K&7 ?;
BKJ
BK;
BK2
;
BKK
BG
BKG
2;
2;;
BGJ
2;;
B;
2;J
2;K
2;H
;
2BB
2BH
2BC
0B;
22;
222
22J
02;
22K
2B
2B
0;
2?2
2H
2H
0?;
2?;
2CB
2?J
,nalysis -hat 3as the inde'endent varia*le in the investigation> 6ame one o# the control varia*les in the investigation< -hat 3as the de'endent varia*le in the investigation> -hat is the 'recision o# the tem'erature measurement> -hat is the 'recision o# the volume measurement> alculate the mean 'ressure #or each tem'erature< onvert the tem'eratures into kelvins< -hat is the uncertainty in the 'ressure measurement at ; Z> alculate this as a 'ercentage o# the mean 'ressure at this tem'erature< -hat is the uncertainty in the 'ressure measurement at B; Z> alculate this as a 'ercentage o# the mean 'ressure at this tem'erature< -hat is the uncertainty in the 'ressure measurement at 0B; Z> alculate this as a 'ercentage o# the mean 'ressure at this tem'erature< -hat is the uncertainty in the 'ressure measurement at 0; Z> alculate this as a 'ercentage o# the mean 'ressure at this tem'erature< Plot a gra'h o# P against T x axisN and dra3 a line o# *est ft< -here does the line cut the x axis> (his should *e 02J Z, 3hat is the di5erence *et3een your value and the acce'ted value> alculate this as a 'ercentage o# the acce'ted value< Pressure and tem'erature are linked *y the e&uation ;V < 1RT , 3hat does the gradient o# your line re'resent> alculate the gradient o# your line< se the gradient to calculate the num*er o# moles o# gas in the container< (he acce'ted num*er o# moles is B<2, 3hat is the di5erence *et3een this value and your value #rom the gradient> alculate this as a 'ercentage o# the acce'ted value<
Practical 6< D-4!R
S'ecifc /eat a'acity
(ou are going to carry out an experiment to calculate the specic heat capacity of di5erent materials and compare your values to the accepted values.
E5uipment List Po3er 'ack Ammeter )oltmeter "mmersion /eater Leads
ali*rated (hermometer Sto' lock (est Metals $eaker and $alance u' to BkgN /eat Proo# Mat and Lagging
