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Descripción: Investigues lab 8
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Name: Jivan Raghoo Date: 23/03/12
Young’s Modulus Mod ulus Title: Young’s Aim:
1. To invest investigate igate how the peiod peiod o! os"illat os"illations ions o! a loaded loaded steel #lade #lade vaies with with the length o! the #lade. 2. To detem detemine ine a value !o the the You Young ng Modulus Modulus o! steel using using the esults esults o! the the e$peiment. Materials & Apparatus: • • • • • •
This e$peiment shows simple hamoni" motion whi"h a #od- e$peien"es when its a""eleation is die"ted towads a !i$ed point in its path and is die"tl- popotional to its distan"e !om that point. n this "ase the #lade des"i#es simple hamoni" motion a#out its euili#ium position os"illating #a"& and !oth until its eneg- is dispesed and it etuns to est. The longe the steel #lade is the longe the peiod *time !o one "omplete os"illation+ and the euation that e$pesses this: T =k d
n
hee T is the peiod o! os"illation d is the distan"e !om the "ente o! the masses to the edge o! the #lo"&s & and n ae "onstants
Name: Jivan Raghoo The Young’s modulus *+ o! a mateial is the atio o! the tensile stess to the tensile stain the mateial e$peien"es povided that the stess is not so high that the limit o! popotionalit- has #een e$"eeded. tess *4+ is de!ined as the ,o"e pe unit aea and stain ∈ is the atio o! e$tension podu"ed and the oiginal length o! the mateial. 5 theoeti"al teatment o! the os"illato suggests that
√
k =
2
16 π M 3
Eb t
hee: 6 Young modulus M6 the mass atta"hed to end o! the #lade &6 "onstant !om os"illation euation #6 width o! #lade t6 thi"&ness o! #lade Method:
1
The appaatus was setup as shown in the diagam.
2
The distan"e d !om the "ente o! the mass to the edge o! the #lo"&s o! wood was e"oded.
3
The end o! the #lade was displa"ed !om its euili#ium position and eleased so that small os"illations o""ued in a veti"al plane.
7
The time ta&en !o 20 os"illations to o""u was e"oded twi"e and the peiod *T+ was detemined.
)
The po"edue was epeated ) additional times with di!!eent values !o d anging !om 0.13m to 0.2)m #eing used. 5ll esults wee e"oded.
Name: Jivan Raghoo 8
The width o! the #lade # and the thi"&ness o! the #lade t wee #oth measued using a mi"omete s"ew gauge and e"oded.
Variables:
Manipulated: length o! #lade Responding: peiod o! os"illation 9onstant: mass atta"hed to end o! #lade Results:
Ta#le 1 showing values o! time peiod distan"e #etween "ente o! masses and the edges o! the #lo"&s lg T and lg d. d/m
Time !o 20
Time !o 20
5veage
T/s
lg T
lg d
0.27 0.22 0.20 0.1 0.18 0.17
os"illations1/s 11.7 10.2 .<1 ;.) 8.; ).1
os"illations2/s 11.77 10.3; .<0 ;.;2 8.)< ).3;
time/s 11.87 10.33 .<1 ;.8) 8.8< ).)<
0.) 0.)2 0.7) 0.3 0.33 0.2
(0.27 (0.2 (0.3) (0.72 (0.7 (0.))
(0.82 (0.88 (0.;0 (0.;7 (0.0 (0.)
Ta#le 2 showing values o#tained !o the width and thi"&ness o! the #lade. idth o! #lade *#+ /m Thi"&ness o! #lade *t+ /m
Treatment of results:
'adient 6
y 2− y 1 x 2− x 1
0.0128 0.0008)
Name: Jivan Raghoo
−0.2125 −(−0.5775 ) 6 −0.60 −(−0.87 ) 6 1.3) T =k d
n
Ta&e log o! #oth sides: lgT =lgk d
n
lgT =lgk + lg d
n
lgT =nlgd + lgk y =mx + c
Thee!oe using gaph 'adient 6 n
=1.35
∴n
-(inte"ept 6
lgk
hee n 61.3) and using pt. *(0.;) (0.71)+
− 0.415=1.35 (−0.75 )+ lgk 0.598
=lgk
=
∴ k 3.96
To !ind we use the !omula
Name: Jivan Raghoo k =
√
2
16 π M 3
Eb t
=
3.96
√
2
( 0.1) E ( 0.0126 ) ( 0.00065 ) 16 π
3
2
15.6816
E 6
=
16 π
( 0.1) − 12
E ( 3.460275 x 10
2.<1 $ 1011 =a
o 9al"ulations: T =k d
n
δk δT nδd = + k T d
δk 3.96
=
0.005 0.58
+
(
1.35 0.0005 0.24
δk =± 0.0453
,om euation:
k =
√
2
16 π M 3
Eb t
2
2
k =
16 π M 3
Ebt
δE δb 3 δt 2 δk = + + E b t k
)
)
Name: Jivan Raghoo δE δb 3 δt 2 δk = + + E b t k
δE = E (
δb 3 δt 2 δk + + ) b t k
11
δE =2.91 x 10
(
0.0005 0.012 6
+
(
−6 3 1 × 10
0.0006 5
)
+
(
2 0.0453 3.96
)
)
10
δE =1.95 × 10
=a
Precautions:
1. The stop(wat"h was stated a!te thee !ull os"illations in ode to edu"e eo due to ea"tion time. 2. hen measuing d the #lade was held hoi>ontall- to get a""uate measuements. Sources of error:
1. ?ue to the ui"& movements o! the #lade it was possi#le to ma&e eos when ta&ing values !o time ta&en !o 20 os"illations. Conclusion:
1. The peiod o! the os"illation was !ound to de"ease as the length o! the #lade de"eased. 11