Work and Energy. A Force F will do work on a particle only when the particle undergoes a displacement in the direction of the force.

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1 The wok of a oce Wok and Enegy A oce wll do wok on a patcle only when the patcle undegoe a dplacement n the decton of the foce. d d coθ d d nt of wok: N m o Joule (J) oce Dplacement Wok xed pont (zeo dp.) Potve Negatve 0 0

2 Wok of a Vaable oce The wok of a oce d coθ d Wok of a Contant oce Movng Along a Staght Lne c coθ c coθ ( d )

3 The wok of a oce Wok of a Weght ( ˆ) ( ˆ ˆ d mg j dx + dyj + dzkˆ) mg dy mg( y y ) mg y The wok ndependent of the path Depend on t vetcal dplacement

4 Wok of a Spng oce The wok of a oce The wok done on the png d k k k d potve The wok done on a patcle attached to a png oce exeted on the patcle oppote to that exeted on the png k k negatve

5 The wok of a oce p Hll Downhll oce Wok (Potve/ Negatve) oce Wok (Potve/ Negatve) Towng foce T Towng foce T Weght W Weght W Nomal foce N Nomal foce N cton cton

6 Pncple of Wok and Enegy t n R + + t n R d d d d ma d d t t t a d vdv t mv mv mvdv Reultant Wok done by eultant (all foce) om ) (, 0 n

7 Pncple of Wok and Enegy Knetc enegy om mvdv mv mv If v 0, v v mv Knetc Enegy (T) Knetc enegy: The total wok whch mut be done on the patcle to bng t fom a tate of et to a velocty v.

8 Pncple of Wok and Enegy Wok done by eultant (all foce) om mvdv mv mv T T T o T + T The patcle ntal knetc enegy plu the wok done by all the foce equal to the patcle fnal knetc enegy

9 Wok and Enegy fo a Sytem of Patcle R f + Reultant of patcle Ext. foce + Int. foce T T + om ) ( ) ( t t v m d f d m v + + Wok and enegy equaton fo the ytem + + ) ( ) ( t t v m d f d m v Int. foce on adjacent patcle ae equal and oppote, but the wok done wll not cancel out nce the path wll be dffeent. Note

10 Wok and Enegy fo a Sytem of Patcle o the connecton among the patcle whch fctonle and ncapable of any defomaton Ex. Tanlatng gd body Patcle connected by nextenble cable The wok of ntenal foce cancel. Wok and enegy equaton fo the ytem m + v ( ) t d m v

11 Powe Powe and Effcency The amount of wok pefomed pe unt of tme. om Effcency P d P dt d d d P v dt dt dt ε Powe output Powe nput Enegy output Enegy nput The effcency alway le than.

12 Sample poblem 3/ The flatbed tuck, whch cae an 80-kg cate, tat fom et and attan a peed of 7 km/h n a dtance of 75 m on a level oad wth contant acceleaton. Calculate the wok done by the fcton foce actng on the cate dung th nteval f the tatc and knetc coeffcent of fcton between the cate and the tuck bed ae (a) 0.30 and 0.8, epectvely, o (b) 0.5 and 0. epectvely.

13 Sample poblem 3/3 The 50-kg block at A mounted on olle o that t move along the fxed hozontal al wth neglgble fcton unde the acton of the contant 300-N foce n the cable. The block eleaed fom et at A, wth the png to whch t attached extended an ntal amount x 0.33 m. The png ha a tffne k 80 N/m. Calculate the velocty v of the block a t eache poton B.

14 Sample poblem 3/4 The powe wnch A hot the 360-kg log up the 30 nclne at a contant peed of. m/. If the powe output of the wnch 4 kw, compute the coeffcent of knetc fcton µ k between the log and the nclne. If the powe uddenly nceaed to 6 kw, what the coepondng ntantaneou acceleaton a of the log.

15 Sample poblem 4.4 The platfom P ha neglgble ma and ted down o that the 0.4- m-long cod keep a -m-long png compeed 0.6 m when nothng on the platfom. If a -kg block placed on the platfom and eleaed fom et afte the platfom puhed down 0. m, detemne the maxmum heght h the block e n the a, meaued fom the gound.

16 Sample poblem 4.5 Package havng a ma of kg ae delveed fom a conveyo to a mooth ccula amp wth a velocty of v 0 m/. If the adu of the amp 0.5 m, detemne the angle θ θ max at whch each package begn to leave the uface.

17 Sample poblem 4.6 The block A and B have a ma of 0 kg and 00 kg, epectvely. Detemne the dtance B tavel fom the pont whee t eleaed fom et to the pont whee t peed become m/.

18 Conevatve oce and Potental Enegy Conevatve foce The wok done by a conevatve foce ndependent of the path. Weght and png ae conevatve foce (depend on poton) ctonal foce ae nonconevatve foce (The longe path, the geate the wok.) Potental enegy Enegy: the capacty fo dong wok. Potental enegy : meaue of the amount of wok of a conevatve foce wll do when t move fom a gven poton to the datum.

19 Potental Enegy Gavtatonal P.E. Elatc P.E. V g Wy mgy Ve k (alway potve) PE the wok of a foce wll do when t move fom a gven poton to the datum. P.E. (the wok of a weght) (the wok of a png foce exeted on the patcle)

20 Conevaton of Enegy Wok-Enegy Equaton om T T T the wok of all extenal foce othe than gavtatonal foce and png foce + ( V ) + ( V ) g T e + V g + V e T o T + Vg + Ve + T + Vg + Ve

21 Conevaton of Enegy T T T All foce mut be condeed N path wok 0 T + V g + V e and ae condeed V g and V e ae added n calculaton

22 Conevaton of Enegy om T + V g + V e E whee E T + V g + V e The total mechancal enegy of the patcle o poblem whee the only foce ae gavtatonal, elatc, and nonwokng contant foce, E 0 o E contant Conevaton of Enegy The um of patcle K.E. and P.E. eman cont. K.E. mut be tanfomed nto P.E. and vce vea.

23 Sample poblem 3/6 The 0-kg lde A move wth neglgble fcton up the nclned gude. The attached png ha a tffne of 60 N/m and tetched 0.6 m n poton A, whee the lde eleaed fom et. The 50-N foce contant and the pulley offe neglgble etance to the moton of the cod. Calculate the velocty v of the lde a t pae pont C.

24 Sample poblem 3/7 The 3-kg lde eleaed fom et at pont A and lde wth neglgble fcton n a vetcal plane along the ccula od. The attached png ha a tffne of 350 N/m and ha an untetched length of 0.6 m. Detemne the velocty of the lde a t pae poton B.

25 Sample poblem 4. A mooth -kg colla C ft looely on the vetcal haft. If the png untetched when the colla n the poton A, detemne the peed at whch the colla movng when y m, f (a) t eleaed fom et at A, and (b) t eleaed at A wth an upwad velocty v a m/.

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