cture13
Work Le and the Work/Kine Ene The m tic rgy ore
Motivation to go be yond Ne wton's laws
N Loop theloop
m g N Thenorm forcehas diffe nt dire al re ction and m agnitudeat e ry point on the ve track!! m g m g
N
R
Writing and solving Ne wton's laws can bea nasty e rie ... (se appe xpe nce e ndix of le cture15)
nd
Playing around with Ne wton's 2 law
C onside them r otion of a be of m mon a straight wirepushe by a constant ne ad ass d t forceFx paralle to thewire along a displace e x: l , m nt x m
ne t,x
vi
Forceproduce s acce ration: le Acce ration produce changein le s spe d: e
vf F Fx = max 2ax x = vf2 - vi 2
Fx x = vf - vi m
WORK (W )
doneby forceF ove r displace e x m nt
1 1 2 Fnet ,x x = mvf - mvi 2 2 2
C hangein KI NETIC ENERGY (K)
of thebe ad
This is an e ssion of the"e ctive ss" of theforce xpre ffe ne .
1 1 2 Fnet ,x x = mvf - mvi 2 2 2 Work/Kine Ene tic rgy Wnet = K The m ore
Of how a forceapplie ove a d r distance ... ...change som thing in thesyste s e m
Work
An "e rnal age that change the xte nt" s am ount of kine e rgy (thestate in tic ne ) thesyste m
Kine e rgy tic ne
An "inte rnal" quantity (state of the ) syste m
W = Fx x
1 2 K = mv 2
Units for work and e rgy: ne
S: I Joule Othe com on units: r m Kilowatt-hour calorie
Not to beconfuse with: d
1J= 1N m
KWh 1 cal = 4.184 J 1 C = 1000 cal al
C alorie(or food calorie )
What is work?
Thede finition of work W =F x corre sponds to theintuitiveide of a e ffort:
Wnet
1 2 1 2 = Fnet , x x = mv f - mvi = K 2 2
assiveobje will re ct quirem work to ge to thesam spe d (fromre ore t e e st) Morem n ass, tting to a highe spe d (fromre re r e st) quire m work s ore For a give m ge r , ore I f wepush for a longe distance it's m work. s e le ct ft I t take thesam work to acce ratetheobje to theright as to thele (both displace e and forcere rse m nt ve )
Work is e rgy be transfe d ne ing rre
x m
ne t,x
Ene source rgy
F
Positivework W > 0
I nitial kine e rgy K tic ne
Final kine e rgy K > K tic ne
Now, theforcepoints in theoppositedire ction: x m
ne t,x
Fnet ,x x =
1 1 mvf2 - mvi 2 2 2
<0
vi F
vf
Ne gativework W < 0 I nitial kine tic e rgy K ne Final kine e rgy K < K tic ne
Othe typeof r e rgy ne
Ene rgy
Many type of e rgy: s ne kine e rgy tic ne e ctric e rgy le ne inte the al- e rgy rnal rm ne e lastic e rgy ne che ical e rgy m ne Etc.
Ene is transfe d and transformed fromonetypeto rgy rre anothe but is ne r de r, ve stroye nor cre d ("C rvation of d ate onse e rgy"). ne
Exam : Pushing a box with friction ple
Paul pushe a box along 10 macross thefloor at a constant ve s locity by e rting a force xe of 200N.
Paul
Work by Paul on thebox: W = (200 N)(10 m = 2000 J ) f (e rgy com fromthebioche ical re ne ing m actions in his m s) uscle Work by friction on thebox: W = (-200 N)(10 m = -2000 J ) Paul f f i (re ase as the al e rgy into theair and thefloor) le d rm ne WKE the m W ore : +W =0
Paul
K K =0
FPaul - f k = ma = 0 (const ant speed) f k = FPaul
k
F
f
Exam : Fre fall with WKE ple e
A ball is droppe and hits theground 50 mbe d low. I f theinitial spe d is 0 and e weignoreair re sistance what is thespe d of theball as it hits theground? , e
Wecan usekine atics or... theWKE the m m ore .
A. 50 m /s B. 42 m /s C. 31 m /s D. 23 m /s E. 10 m /s
r m g C hangein K:
W = K mgh = 1 mv 2 2
K = Kf inal - Kinit ial = 1 mv 2 - 0 2
Work doneby gravity: m gh
v = 2 gh = 2(9.8 m/ s2 )(50 m) = 31 m/ s
AC : Two blocks pushe by e T d qual force s
AC : blocks Two pushe by e T d qual force s
Two blocks (m =2m ) arepushe by ide d ntical force e s, ach 1 2 starting at re at theblueve st rtical line(start). Which obje has thegre r kine e rgy whe it re s ct ate tic ne n ache thegre n ve e rtical line(finish)? A. Box 1 Sameforce, samedistance S ework am B. Box 2 C. The both havethesam kine Samechangein kinetic energy y e tic e rgy. ne
What if theforcedoe not point in thedire s ction of m otion?
2a r = vf2 - vi 2
Re thev e call quation in m ulti-dim nsions: e
1 a r = F r m
Work by a constant forcealong a straight path:
W = F r = Fr cos = F// r
For work, only thepart of theforcethat is in thedire ction of displace e m nt "m rs" (= can changespe d) atte e (= can changekine e rgy) tic ne
Exam s of Non-Work ple
This pe is not doing any work on therock sincethe rson ce ntripe forceis pe ndicular to thedire tal rpe ction that the stoneis m oving.
T
Exam s of Non-Work ple
Thewe of thebox that Paul pushe along a horizontal surfacedoe ight s s no work sincethewe is pe ndicular to them ight rpe otion Thenorm by thefloor doe no work e r. al s ithe
N
x
Paul k
F f m g
ACT: Ram p
A pe pulls a 10-kg block up a ram of he h = 10 mand angle = 10 at constant rson p ight spe d. Theropem s an angle = 15 with theram and has a te e ake p nsion of 50 N. How m force aredoing work on thebox? any s
T
A. 2 B. 3 C. 4
x
Wf > 0 N Wg < 0 WN < 0
k
h
T
W =0
Ne t
f mg
W
=0
A pe pulls a 10-kg block up a ram of he h = 10 mand angle = 10 at constant rson p ight spe d. Theropem s an angle = 15 with theram and has a te e ake p nsion of 50 N. Find thework doneby all theforce s.
1. Work by thete nsion:
x
T
WT =T x cos = (50 N)(57.6 m)cos15
= 2780 J
h 10 m x = = = 57.6 m sin sin10
x
N T
k
h mg
f
A pe pulls a 10-kg block up a ram of he h = 10 mand angle = 10 at constant rson p ight spe d. Theropem s an angle = 15 with theram and has a te e ake p nsion of 50 N. Find the work doneby all theforce s.
2. Work by gravity:
x
+ W g = mg x cos 2 = -mg x sin
= -mgh = -980 J
Of course ! h h is thecom nt of the pone displace e in thedire...