UNIVERSITY OF MAURITIUS FACULTY OF ENGINEERING CIVIL ENGINEERING DEPARTMENT
STRUCTURES PRACTICALS STRUCTURAL MECHANICS MECHANIC S LABORAT LAB ORATORY ORY
BEng (HONS) CIVIL ENGINEERING P/T – E411 YEAR 1-SEMESTER 1 MODULE: INTRODUCTION TO STRUCTURES
REPORT OF E
SUBMITTED BY: GROUP 4 1 , 4
LUC!EENA LUC!EENARAIN RAIN Y" Y"g#$% !&' !&' (S*&+#n* (S*&+#n* ID:11 ID:111,.1) 1,.1) MATT MATTAPULL APULLUT UT M%#n+ M%#n+ !&' (S*&+#n* ID: 111 1110,) 0,) BHUN2UN BHUN2UN V Vn+n n+n (S*&+#n* (S*&+#n* ID:1 ID:11 11.33) 1.33) OLLITE OLLITE M"%''+ M"%''+ 2'5 2'5 A556 A556 (S*&+ (S*&+#n* #n* ID: 11, 11,) )
DATE OF SUBMISSION: 10 *% NOVEMBER 11
TABLE OF CON CONTEN TENTS TS
INTRODUCTION THEORY
1
-,
E
,
E
4
THEORETICAL THEORETIC AL RESULTS RESULTS TABULATION TABULATION OF THEORETICAL TH EORETICAL RESULT RE SULTS S COMP COMPA ARIS RISON OF OF THE THEOR ORE ETIC TICAL > E
3
PRECAUTIONS LIMITATIONS LIMITATIONS AND IMPROVEMENTS IMPRO VEMENTS CONCLUSION
1
REFERENCES
11
INTRODUCTION TO STRUCTURES | CIVE1105
.-0
INTRODUCTION A "9# is any influence that causes an object to une!"o a chan"e in s#ee$ a chan"e in i!ection$ o! a chan"e in sha#e% &o!ce can also be esc!ibe by intuiti'e conce#ts such as a #ush o! #ull that can cause an object (ith )ass to chan"e its 'elocity *(hich inclues to be"in )o'in" f!o) a state of !est+$ i%e%$ to accele!ate$ o! (hich can cause a fle,ible object to efo!)% A fo!ce has both )a"nitue an i!ection$ )a-in" it a 'ecto! .uantity% &o!ce is a .uantity that is )easu!e usin" the stana! )et!ic unit -no(n as the N#?*"n%
The!e a!e iffe!ent ty#es of fo!ces that act in iffe!ent (ays on st!uctu!es such as b!i"es$ chai!s$ builin"s$ in fact any st!uctu!e% The )ain e,a)#les of fo!ces a!e sho(n belo(% S**9 5"+- the effect of "!a'ity on an object o! st!uctu!e% D6n'9 5"+- the fo!ces that )o'e o! chan"e (hen actin" on a st!uctu!e% T#n$"n- the )a"nitue of the #ullin" fo!ce e,e!te by a st!in"$ cable$ chain$ o! si)ila!
object on anothe! object% C"'8#$$"n- the e"!ee to (hich a substance has ec!ease in si/e *in 'olu)e$ len"th$ o! so)e othe! i)ension+ afte! bein" o! (hile bein" subject to st!ess that is (hen a fo!ce is a##lie to it% S%# F"9#- an inte!nal fo!ce in any )ate!ial (hich is usually cause by any e,te!nal fo!ce actin" #e!#enicula! to the )ate!ial$ o! a fo!ce (hich has a co)#onent actin" tan"ent to the )ate!ial% T"$"n- The st!ess o! efo!)ation cause (hen one en of an object is t(iste in one i!ection an the othe! en is hel )otionless o! t(iste in the o##osite i!ection%
Shea! fo!ce is an inte!nal fo!ce in any )ate!ial (hich is usually cause by any fo!ce actin" #e!#enicula! to the )ate!ial$ o! a fo!ce (hich has a co)#onent actin" tan"ent to the )ate!ial%
INTRODUCTION TO STRUCTURES | CIVE1105
1
A shea! fo!ce ia"!a) is si)#ly const!ucte by )o'in" a section alon" the bea) f!o) *say+ the left o!i"in an su))in" the fo!ces to the left of the section% The e.uilib!iu) conition states that the fo!ces on eithe! sie of a section balance an the!efo!e the !esistin" shea! fo!ce of the section is obtaine by this si)#le o#e!ation%
The benin" )o)ent ia"!a) is obtaine in the sa)e (ay e,ce#t that the )o)ent is the su) of the #!ouct of each fo!ce an its istance*,+ f!o) the section% Dist!ibute loas a!e calculate buy su))in" the #!ouct of the total fo!ce *to the left of the section+ an the istance*,+ of the cent!oi of the ist!ibute loa%
The s-etches belo( sho( si)#ly su##o!te bea)s (ith on concent!ate fo!ce%
INTRODUCTION TO STRUCTURES | CIVE1105
2
INTRODUCTION TO STRUCTURES | CIVE1105
2
THEORY In this e,#e!i)ent$ (e (ill eal (ith the shea!in" fo!ces that e,ist in a s#lit bea) in t(o$ #a!t *A+ an #a!t *+$ joine by a ball bea!in" !olls at the no!)al section% S#!in" balances a!e #lace onto the syste) fi!stly to !esist an a'oi benin" )o)ents an seconly to #!o'ie 'e!tical shea!in" fo!ce%
The ens of the bea) a!e su##o!te by bea!in" stans$ an to int!ouce the fo!ces sha#e loas an han"e!s can be #lace to the bea) at iffe!ent istance f!o) the section% &o! the fi!st #a!t of the e,#e!i)ent$ (e (oul 'a!y the a##lie loas only at the iffe!ent #osition on the bea) -ee#in" the istance bet(een the han"e!s fi,e% An fo! the secon #a!t$ the han"e!s an su##o!t (oul be )o'e at iffe!ent #osition on the bea)% The s#!in"s use to hol the s#lit bea) to"ethe! )ust #!ouce a syste) of fo!ces e.ui'alent to those (hich (oul e,ist inte!nally in the bea) at that section as if it (as not s#lit% Since the fo!ces in #a!t *A+ actin" on #a!t *+ is e.ual but o##osite to those in *+ actin" on *A+$ the sa)e 'alues (ill be obtaine by (o!-in" eithe! on the !i"ht o! left of the section #lane% i'en a ho!i/ontal bea) (ith 'e!tical loain"$ the inte!nal fo!ces (ill be2 • •
&o! 'e!tical e.uilib!iu)$ a shea!in" fo!ce in the section #lane% &o! e.uilib!iu) of )o)ents$ a )o)ent of !esistance ue to co)#!ession in the to# half of bea) section an tension in the botto) half%
INTRODUCTION TO STRUCTURES | CIVE1105
3
OB2ECTIVES
To une!stan the action of the shea! in the bea) an to )easu!e the shea!in" fo!ce of a no!)al section of a loae bea) an to co)#a!e (ith the theo!y% E@&8'#n*$
Shea! fo!ce a##a!atus (ith su##o!ts$ 3 han"e!s$ (ei"hts *10%0N 4 0%0N+ an a s#i!it le'el% S#* U8
The a##a!atus is set u# sho(n as belo(
INTRODUCTION TO STRUCTURES | CIVE1105
4
E
The bea) is set u# so that the face of the no!)al section is 300))$ labele as *A+ f!o) the left han su##o!t an 600)) f!o) the !i"ht han su##o!t$ labele as *+%
One loa han"e! is #ositione on the )ile of the s)alle! #a!t *A+ of the bea)$ one in the )ile of the #a!t *+
7lace a thi! han"e! on the "!oo'e just to the !i"ht of the no!)al section$ (hich is on the
sta!t of section *+% 8easu!e the istance bet(een the han"e!s an the su##o!ts an label the) , an y fo! the
s)alle! section an lon"e! section$ !es#ecti'ely% 8a-e the necessa!y ajust)ent to the une! han" an s#!in" balance so that the t(o #a!ts of the syste) a!e ali"ne an le'el$ an the !eain" on the s#!in" balance is note%*Note2
A s#i!it le'el is use fo! the le'elin" #!ocess+ A loa of 10N is han"e on the #a!t *+$ the bea) is !e9ali"ne an the ne( !eain"
inicate on the s#!in" balance is note% The iffe!ence bet(een the t(o !eain"s is the effect of a##lyin" the 1N (ei"ht on the
bea)% Reco! the istance f!o) this (ei"ht to the !i"ht han su##o!t%
The #!oceu!e is !e#eate usin" the han"e! just to the !i"ht of the no!)al section%
The han"e! is then )o'e just to the left of the no!)al section an both the s#!in" balance an istance f!o) left han su##o!t (e!e note%
The 10N loa is t!ansfe!!e to the han"e! at the )ile of #a!t *A+ an the !eain" is a"ain note%
&inally the #!oceu!es abo'e a!e !e#eate no( usin" the loa 0N an the iffe!ences in the s#!in" balance !eain"s is a"ain calculate%
PART
Re)o'e all loas an !eali"n an le'el the bea) a"ain% Retu!n all the han"e!s to the initial #osition%
&o! the secon #a!t of this e,#e!i)ent$ all the 3 han"e!s )ust be loae$ an the bea) syste) )ust be !eali"ne an le'ele% The s#!in" balance !eain"$ the a##lie loas$ an the len"th bet(een the han"e! an the su##o!ts a!e note fo! the ne( confi"u!ation of the loas%
The #!oceu!e is !e#eate (ith iffe!ent istance bet(een su##o!ts (ith the loa han"e!s in iffe!ent #osition an (ith iffe!ent s#ans%
TABULATION OF RESULTS PART 1 N"*#: M++5# %ng# "n *%# g%* 8"$*"n " *%# $85* B#g#/S85*
A
B
C
<
D$*n9# ;#*?##n $8n$
Y
S8ng B5n9#
L"+ 885#+ "n %ng#
#+ng
E78 N" <('')
Y('') A(N)
1
300
600
, 4 .
300 300 300 300 300
600 600 600 600 600
=
300
600
B(N)
C(N)
In*5(N)
Fn5(N)
(*%"&*
(*%
L"+)
L"+)
10 10 10 10
10
10 0
0 0
S%#ng F"9# (N)
%5
3%0
0%5
%5 %5 %5 %5 %5
6%0 9%5 1 6%0 90%:
%5
No !eain"
3%5 91%5 :%5 3%5 93%; No !eain"
N"*#: S%# F"9# M#$&#+ 5&# ?*% 5"+ – In*5 M#$&#+ 5&# ?*%"&* 5"+
PART N"*#: M++5# %ng# "n *%# 5#* 8"$*"n " *%# $85* B#g#/S85*
A
B <
C Y
E78 D$*n9# ;#*?##n L"+ 885#+ "n N"
$8n$ <('') Y('')
%ng# A(N) B(N)
1 ,
300 300 300
500 500 500
10
4
300 300
500 500
10 0
S8ng B5n9# #+ng S%#ng F"9# (N) C(N) In*5(N) Fn5(N)
10 10
10 0
10 0
(*%"&*
(*%
L"+) 1%0 1%0 1%0
L"+) %0 %3 No !eain"
1%0 1%0
6%0 1%0
1.0 1.3 No reading 5.0 11.0
N"*#: S%# F"9# M#$&#+ 5&# ?*% 5"+ – In*5 M#$&#+ 5&# ?*%"&* 5"+
THEORETICAL RESULTS
To allo( ete!)ination of all of the e,te!nal loas a f!ee9boy ia"!a) is const!uction (ith all of the loas an su##o!ts !e#lace by thei! e.ui'alent fo!ces% A ty#ical f!ee9boy ia"!a) is sho(n belo(%
The un-no(n fo!ces *"ene!ally the su##o!t !eactions+ a!e then ete!)ine usin" the e.uations fo! #lane static e.uilib!iu)%
&o! e,a)#le consie!in" the si)#le bea) abo'e the !eaction R is ete!)ine by Su))in" the )o)ents about R 1 to /e!o R % < 9 =%a > 0 The!efo!e R > =%a ? < R 1 is ete!)ine by su))in" the 'e!tical fo!ces to 0 = 9 R 1 9 R > 0 The!efo!e R 1 > = 9 R
P* 1
10N
() A B
RA
300 mm
600 mm
RB
0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *10 @ 600+ > *R @ :00+ R > 6%6N
V >0
R A R > 10N R A > 10 4 6%6 > 3%33N S%# F"9# Dg'
S.F
3.33 +ve 0
300
600
:00
X/mm
9'e
96%6
The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ > 3%33 FN
()
10N A B
RA
300 mm
600 mm
RB
Usin" E.uation of statics &o! e.uilib!iu) of the bea) at any #oint$ 8 >0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *10 @ 300+ > *R @ :00+ R > 3%33N V >0 R A R >10N R A > 10 4 3%33 > 6%6N
S.F
S%# F"9# Dg'
6.67
+ve 0
300
9'e
:00
X/mm
3%33
The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ > 0%0 FN
()
10N A B
RA
300 mm
600 mm
RB
0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *10 @ 150+ > *R @ :00+ R > 1%6N
V >0 R A R >10N R A > 10 4 1%6 > G%33N
S.F
S%# F"9# Dg'
8.3
+ve 0
150
300
9'e
:00
X/mm
1.67
The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ > 91%6 FN
()
10N
10N
10N
A B
RA
300 mm
600 mm
RB
0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *10 @ 150+ *10 @ 300+ *10 @ 600+ > *R @ :00+ R > 11%6N
V >0 R A R >30N R A > 30 4 11%6 > 1G%33N
S.F
18.33
8.33
S%# F"9# Dg'
+ve 0
150
300
9'e
:00
X/mm
1.67 11.67 The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ > G%33 FN
(v)
20N A B
RA
300 mm
600 mm
RB
0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *0 @ 600+ > *R @ :00+ R > 13%3N
V >0 R A R > 0N R A > 0 4 13%3 > 6%N S%# F"9# Dg'
S.F
6.7 +ve 0
300
600
:00
X/mm
9'e
913%3
The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ > 6% FN ()
20N A B
RA
300 mm
600 mm
RB 0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *0 @ 300+ > *R @ :00+ R > 6%6N
V >0 R A R >0N R A > 0 4 6%6 > 13%3N
S%# F"9# Dg'
S.F
13.3
+ve 0
6.67
300
9'e
:00
X/mm
The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ > 0 FN ()
20N A B
RA
300 mm
600 mm
RB
0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *0 @ 150+ > *R @ :00+ R > 3%33N
V >0 R A R >0N R A > 0 4 3%33 > 16%6N S%# F"9# Dg'
S.F
16.67
+ve 0
150
300
9'e
:00
X/mm
3.33 The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ > 93%33 FN
P*
(i)
10N A B
RA
300 mm
500 mm
RB 0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *10 @ 550+ > *R @ G00+ R > 6%G5N
V >0 R A R > 10N R A > 10 4 6%G5 > 3%15N S%# F"9# Dg'
S.F
3.13 +ve 0
300
550
G00
X/m
9'e
96%GG
The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ > 3%13 FN% ()
10N A B
RA
300 mm
500 mm
RB 0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *10 @ 300+ > *R @ G00+ R > 3%5N
V > 0 R A R >10N R A > 10 4 3%5 > 6%5N S%# F"9# Dg'
S.F
6.25
+ve 0
300
9'e
G00
X/mm
3.75
The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ >0%0 FN ()
10N
A B
RA
300 mm
500 mm
RB
0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *10 @ 150+ > *R @ G00+ R > 1%GGN
V > 0 R A R >10N R A > 10 4 1%GG > G%1N S%# F"9# Dg'
S.F
8.12
+ve 0
150
300
9'e
G00
X/mm
1.88 The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ > 91%GG FN ()
10N A B
10N
10N
RA
300 mm
500 mm
RB
0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *10 @ 150+ *10 @ 300+ *10 @ 550+ > *R @ G00+ R > 1%5N V > 0 R A R >30N R A > 30 4 1%5 > 1%5N S%# F"9# Dg'
S.F
17.5
7.5 +ve 0
150
300
9'e
G00
X/mm
2.5
12.5 The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ > %5 FN (v)
20N A B
20N
20N
RA
300 mm
500 mm
RB
0$ V > 0 B >0
Ta-in" #oint A as )o)ent cent!e 8 at A >0 *R A @ 0+ *0 @ 150+ *0 @ 300+ *0 @ 550+ > *R @ G00+ R > 5N
V > 0 R A R >60N R A > 60 4 5 > 35N S%# F"9# Dg'
S.F
35
15
150
5
300
550
G00
X/mm
9'e
25 The!efo!e$ f!o) the shea! fo!ce ia"!a)$ Shea! fo!ce at s#lit *300 )) f!o) #oint A+ > 15%0 FN
TABULATION OF THEORETICAL RESULTS P* 1 E78 D$*n9# ;#*?##n L"+ 885#+ "n %ng# N" $8n$
V#*95 R#9*"n
S%#ng F"9# (A* $85*) (N)
<('') Y('') 1 3 ; 5 6
300 300 300 300 300 300 300
600 600 600 600 600 600 600
A(N)
B(N)
C(N)
10 10 10 10
10
10 0
0 0
RA
R B
3%33 6%6 G%33 1G%3 6% 13%3 16%
6%6 3%33 1%6 11% 13%3 6%0 3%33
3%33 0%00 91%6 G%33 6%0 0%00 93%33
P* E78 D$*n9# ;#*?##n L"+ 885#+ "n %ng# V#*95 R#9*"n N"
$8n$ <('') Y('')
1 , 4
300 300 300 300 300
A(N) B(N)
500 500 500 500 500
C(N)
RA
R B
10
3%13 6%5 G%1 1%5 35
6%GG 3%5 1%GG 1%5 5
10 10 10 0
10 0
10 0
S%#ng F"9#(A* S85*) (N)
3.13 0.00 1.88 7.5 15.0
COMPARISON OF THEORETICAL > E
300 300 300 300 300 300 300
600 600 600 600 600 600 600
L"+ 885#+ "n %ng# S%#ng F"9# (N) A(N)
B(N)
C(N) E78#'#n*5 T%#"#*95
10 10 10 10
10 0
0
10 0
0.5 3.5 1.5 !.5 3.5 3.4 No reading
3.33 0.00 1.67 8.33 6.70 0.00 3.33
PART E78 N"
D$*n9#
L"+ 885#+ "n
;#*?##n $8n$ %ng# <('') Y('') A(N) B(N) C(N)
S%#ng F"9# (N) E78#'#n* 5
T%#"#*95 3%13 0%00 91%GG %50 15%0
1 , 4
300 300 300 300
500 500 500 500
10 10
10
10
1%0 1%3 No !eain" 5%0
300
500
0
0
0
11%0
10 10
DISCUSSION =hen co)#a!in" the theo!etical 'alues of shea! fo!ce (ith e,#e!i)ental 'alues f!o) the tables abo'e$ the !atio of e,#e!i)ental shea! fo!ce to theo!etical shea! fo!ce is )o!e o! less e.ual
to
1%
This
inicates
the
e,#e!i)ental
!esults
a!e
co)#atible
(ith
the
theo!etical?calculate !esults%
PRECAUTIONS
1% &o! each conition of loain"$ (e shoul ensu!e that the bea) is ho!i/ontal by usin" the s#i!it le'el% % E,cessi'e loas nee to be a'oie% 3% The foot of the t!i#os is hel (ith t(o bo,es so as to a'oi the bea) f!o) sliin" (hen ain" an ajustin" the loa% ;% The sc!e( abo'e the s#!in" balance is ajuste ca!efully to ensu!e the bea) is ho!i/ontal% 5% The sc!e( in the une! slun" s#!in" is ajuste to !e)o'e any benin" effect because if the!e is a benin" effect$ the !eaction obtaine on the s#!in" balance (ill be iffe!ent% 6% Ca!e shoul be ta-en all th!ou"hout the e,#e!i)ent as it eals (ith sufficiently la!"e loas (hich a!e able to cause inju!ies *fo! e,a)#le$ if it falls on the foot+% % =e shoul a'oi #a!alla, e!!o! (hen !eain" the s#!in" balance%
LIMITATIONS AND IMPROVEMENTS
•
The s#!in" balance (as not so accu!ateH instea a Di"ital &o!ce Dis#lay )ete! coul
•
has been use instea to obtain )o!e #!ecise 'alues% At the no!)al section (he!e the!e is a #ai! of ball bea!in" !olle!s #inne in $ !unnin" on a flat 'e!tical t!ac- fi,e in A$ f!iction coul has e,iste an hence affectin" the 'alues note% The ball bea!in" shoul be lub!icate continuously u!in" the e,#e!i)ent%
CONCLUSION
The!e is a sli"ht iffe!ence bet(een the e,#e!i)ental !esults an theo!etical 'alues$ (hich (e!e #e!ha#s ue to the labo!ato!y e.ui#)ents$ es#ecially the s#!in" balance$ an ue to f!iction (hich (e ne"lecte (hile oin" this e,#e!i)ent% The e,#e!i)ent (as a ti)e consu)in" one an !e.ui!in" )a,i)u) attention%
This e,#e!i)ent hel#e us to une!stan the action of shea! fo!ce in a bea)% =hen the loa (as ouble in #a!t 1 of the e,#e!i)ent$ the shea! fo!ce (as also ouble as sho(n in both e,#e!i)ental an theo!etical 'alues% This is because shea! fo!ce oes not 'a!y (ith the istance f!o) the #oint of a##lication of the fo!ce but it e#ens on the )a"nitue of the fo!ce on the a##lication% The shea! fo!ce is al(ays )a,i)u) at su##o!ts an it c!eates a shea!in" effect the!e%
REFERENCES T#7*;"" RS!URMI SCHAND S*#ng*% " '*#5$ (M#9%n9$ " $"5+$) (Pg#$ ,-,=) ER!R8&* *% E+*"n 1 R#8n* 11 (Pg#$ .-14)
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D"&g5$ R R''# - Unite States De#a!t)ent of A"!icultu!e 9 Resea!ch 7a#e!
&7<9R75 htt#2??(((%f#l%fs%fe%us?ocu)nts?f#l!#?f#l!#5%#f Accesse on2 1;?11?11J
F"9#$ - V% Ryan K 00 4 010
htt#2??(((%technolo"ystuent%co)?fo!c)o)?fo!ce1%ht) Accesse on2 1;?11?11J
The #hysics class!oo)9Ne(tonLs la(9
