Chapter 07: Kinetic Energy and Work


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1 Chapter 07: Knetc Energy and Work Conservaton o Energy s one o Nature s undamental laws that s not volated. Energy can take on derent orms n a gven system. Ths chapter we wll dscuss work and knetc energy. Net chapter we wll dscuss potental energy. I we put energy nto the system by dong work, ths addtonal energy has to go somewhere. That s, the knetc energy ncreases or as n net chapter, the potental energy ncreases. The opposte s also true when we take energy out o a system
2 Workdone on the object by the orce Postve work: object receves energy Negatve work: object loses energy
3 Chapter 07: Knetc Energy and Work Knetc Energy s the energy assocated wth the moton o an object K (1/) mv m: mass and v: speed Ths orm o K.E. holds only or speeds v << c. SI unt o energy: 1 joule 1 J 1 kg.m /s Other useul unt o energy s the electron volt (ev) 1 ev J
4 Work Work s energy transerred to or rom an object by means o a orce actng on the object Work done by a constant orce: W ( F cos φ) d F d cos φ In general, W v F ds v
5 W F d cosφ F. d SI Unt or Work 1 N. m 1 kg. m/s. m 1 kg. m /s 1 J Net work done by several orces Σ W F net. d ( F 1 + F + F 3 ). d F 1. d + F. d + F 3. d W 1 + W + W 3
6 Consder 1D moton. W v v F d m dv d mvdv ( m a) d d dt 1 mv v v d mv 1 mv m dv d dv dt d 1 mv d So, knetc energy s mathematcally connected to work!!
7 WorkKnetc Energy Theorem The change n the knetc energy o a partcle s equal the net work done on the partcle K K K... or n other words, W net 1 mv 1 mv nal knetc energy ntal knetc energy + net work 1 1 K mv K + Wnet mv + W net
8 A partcle moves along the as. Does the knetc energy o the partcle ncrease, decrease, or reman the same the partcle s velocty changes: (a) rom 3 m/s to m/s? (b) rom m/s to m/s? m/s 0m/s: work negatve 0 m/s +m/s: work postve Together they add to zero work. v < v means K < K, so work s negatve (c) In each stuaton, s the work done postve, negatve or zero?
9 Work done by Gravtaton Force W g mg d cos φ throw a ball upwards: durng the rse, W g mg d cos180 o mgd negatve work, K, v decrease mg d durng the all, W g mgd cos0 o mgd postve work, K, v ncrease mg d
10 Sample problem 75: An ntally statonary 15.0 kg crate s pulled a dstance L 5.70 m up a rctonless ramp, to a heght H o.5 m, where t stops. (a) How much work W g s done on the crate by the gravtatonal orce F g durng the lt? F g s constant n ths problem, so we can use W F g. d mgd cos φ, where φ 90 o + θ
11 F g s constant n ths problem, so we can use W F g. d mgd cos φ, where φ 90 o + θ Notce the trangle that s set up: d h d snθ θ d cosθ W F g. d mgd cos(90o + θ) mgd snθ mgh 368 J Work done aganst orce o gravty, thereore negatve. Ths work s just the negatve o the change n potental energy.
12 How much work W t s done on the crate by the orce T rom the cable durng the lt? v v 0 means K0 and the net work must equal zero. W g 368 J + W N 0 J + W T 0 because N d W T +368 J
13 Work done by a varable orce W j F j, avg W Σ W j ΣF j, avg lm 0 ΣF j, avg W F()d Three dmensonal analyss W r r F d v v F dr + y y F dy y + z z F dz z
14 Work done by a sprng orce The sprng orce s gven by F k ( Hooke s law) k: sprng (or orce) constant k relates to stness o sprng; unt or k: N/m. Sprng orce s a varable orce. 0 at the ree end o the relaed sprng.
15 Work done by a sprng orce The sprng orce tres to restore the system to ts equlbrum state (poston). Eamples: sprngs molecules pendulum Moton results n Smple Harmonc Moton
16 Work done by Sprng Force Work done by the sprng orce W s Fd ( k)d I > (urther away rom 0); W < 0 k I < (closer to 0); W > k I 0, then W s ½ k Ths work went nto potental energy, snce the speeds are zero beore and ater.
17 The work done by an appled orce (.e., us). I the block s statonary both beore and ater the dsplacement: v v 0 then K K 0 workknetc energy theorem: W a + W s K 0 thereore: W a W s
18 Power The tme rate at whch work s done by a orce Average power P avg W/ t Instantaneous power P dw/dt (Fcosφ d)/dt F v cosφ F. v Unt: watt 1 watt 1 W 1 J / s 1 horsepower 1 hp 550 t lb/s 746 W klowatthour s a unt or energy or work: 1 kw h 3.6 M J
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