Chapter 7 Kinetic energy and work
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1 Chpter 7 Kc energy nd wor I. Kc energy. II. or. III. or - Kc energy theorem. IV. or done by contnt orce - Grttonl orce V. or done by rble orce. VI. Power - Sprng orce. - Generl. D-Anly 3D-Anly or-kc Energy Theorem. Energy: clr quntty octed wth tte (or condton o one or more obect. I. Kc energy Energy octed wth the tte o moton o n obect. K m (7. Unt: Joule J gm / N m II. or Energy trnerred to or rom n obect by men o orce ctng on the obect. To + rom - - Contnt orce: m + d d ( ( m m md m d m( K K d d or done by the orce Energy trner due to the orce.
2 - To clculte the wor done on n obect by orce durng dplcement, we ue only the orce component long the obect dplcement. The orce component perpendculr to the dplcement doe zero wor. d co ϕ d d (7.3 coφ d - Aumpton: cte, Obect prtcle-le. Unt: Joule J gm / ϕ < > ϕ > 9 ϕ 9 A orce doe + when t h ector component n the me drecton the dplcement, nd when t h ector component n the oppote drecton. when t h no uch ector component. Net wor done by eerl orce Sum o wor done by nddul orce. Clculton: d II. or-kc Energy Theorem K K K (7.4 Chnge n the c energy o the prtcle Net wor done on the prtcle III. or done by contnt orce - Grttonl orce: d d coϕ (7.5 Rng obect: d co8º -d g trner d energy rom the obect c energy. llng obect: d co º +d g trner d energy to the obect c energy.
3 - Eternl ppled orce + Grttonl orce: K K K + g (7.6 Obect ttonry beore nd ter the lt: + g The ppled orce trner the me mount o energy to the obect the grttonl orce trner rom the obect. IV. or done by rble orce - Sprng orce: d (7.7 Hooe lw prng contnt meure prng tne. Unt: N/m Hooe lw D or done by prng orce: - Aumpton: Sprng mle m prng << m bloc Idel prng obey Hooe lw ectly. Contct between the bloc nd loor rctonle. Bloc prtcle-le. - Clculton: The bloc dplcement mut be dded nto mny egment o nnteml wdth,. ( cte wthn ech hort egment. 3
4 4 or done by n ppled orce + prng orce: d d ( I Bloc end up t. K K K + Bloc ttonry beore nd ter the dplcement: K - The wor done by the ppled orce dplcng the bloc the negte o the wor done by the prng orce. [ ] ( S d or done by generl rble orce: D-Anly (7. ( lm,,,, g g g d more ppromton better Geometrclly: or the re between the cure ( nd the -.
5 3D-Anly ˆ ˆ ˆ + y + z ; (, y ( y, z dr d ˆ + dy ˆ + dz ˆ d dr d + dy + dz or-kc Energy Theorem - Vrble orce ( d m d m d dt y d z m d d m d md d r ( z d d + ydy + zdz r y y z z d d d d dt d dt d m d m d m m K K K V. Power Tme rte t whch the ppled orce doe wor. - Aerge power: mount o wor done n n mount o tme t by orce. P g t (7. - Intntneou power: ntntneou tme rte o dong wor. d P dt (7.3 φ d coϕ d d P coϕ coϕ dt dt dt (7.4 Unt: tt J/ lowtt-hour h J 3.6 MJ 5
6 54. In the gure ( below N orce ppled to 4g bloc t downwrd ngle θ the bloc moe rghtwrd through m cro rctonle loor. nd n epreon or the peed t the end o tht dtnce the bloc ntl elocty : ( nd (b m/ to the rght. (c The tuton n (b mlr n tht the bloc ntlly mong t m/ to the rght, but now the N orce drected downwrd to the let. nd n epreon or the peed o the bloc t the end o the m dtnce. d ( coθ d N N K.5m( y y K.5m (N coθ.5(4g coθ m / ( b m / K.5m (N coθ.5(4g + coθ m / J.5 (4g (m / ( c m / K.5m (Ncoθ.5(4g coθ m / J J 8. In the gure below horzontl orce o mgntude N ppled to 3g pychology boo, the boo lde dtnce o d.5m up rctonle rmp. ( Durng the dplcement, wht the wor done on the boo by, the grttonl orce on the boo nd the norml orce on the boo? (b I the boo h zero c energy t the trt o the dplcement, wht the peed t the end o the dplcement? N d y g N gy Only g, g do wor g or (7.3 N 4.7N.5m.3J co3 n 3 d ( b K K K.3J.5m.93m / 6
7 55. A g lunchbo ent ldng oer rctonle urce, n the pote drecton o n long the urce. Begnnng t t, tedy wnd puhe on the lunchbo n the negte drecton o, g. below. Etmte the c energy o the lunchbo t ( t, (b t5. (c How much wor doe the orce rom the wnd do on the lunch bo rom t to t5? Moton conce downwrd t( t prbol d dt d dt t.m / cte m (g(.m / (.4N( t.t t K.8m /.5(g(.8m /.4N.64J ( b t 5 K J ( c K K (5 K.64.64J ( 74. ( nd the wor done on the prtcle by the orce repreented n the grph below the prtcle moe rom to 3m. (b The cure gen by /, wth 9Nm. Clculte the wor ung ntegrton Are under cure (.5qure(.5m( N 5.75J 3 9 ( b d 9 9( 6J An eletor h m o 45g nd cn crry mmum lod o 8g. I the cb mong upwrd t ull lod t 3.8m/, wht power requred o the orce mong the cb to mntn tht peed? mtotl 45g + 8g 63g + (63g(9.8m / g 6.74N P (6.74N(3.8m / P
8 A ngle orce ct on body tht moe long n -. The gure below how the elocty component eru tme or the body. or ech o the nterl AB, BC, CD, nd DE, ge the gn (plu or mnu o the wor done by the orce, or tte tht the wor zero. K K K m ( A B C D E t AB BC CD B C D > < B C A > < DE E <, > D 5. A 5g bloc dropped onto reled ertcl prng tht h prng contnt o.5n/cm. The bloc become ttched to the prng nd compree the prng cm beore momentrly toppng. hle the prng beng compreed, wht wor done on the bloc by ( the grttonl orce on t nd (b the prng orce? (c ht the peed o the bloc ut beore t ht the prng? (rcton neglgble (d I the peed t mpct doubled, wht the mmum compreon o the prng? d g g d d (.5g(9.8m / (.m. 9J ( b d.5 (5N / m(.m. 8J ( c K K.5m.5m K K.5m g +.9J.8J.5 (.5g 3.47m / ( d I ' 6.95m / Mmum prng compreo n? d '.5d ' d '.3m K.5m ' 8
9 6. In the gure below, cord run round two mle, rctonle pulley; cnter wth m mg hng rom one pulley; nd you eert orce on the ree end o the cord. ( ht mut be the mgntude o you re to lt the cnter t contnt peed? (b To lt the cnter by cm, how r mut you pull the ree end o the cord? Durng tht lt, wht the wor done on the cnter by (c your orce ( the cord nd (d the grttonl orce on the cnter? P T T T P Pulley : Hnd cord : cte T T 98N T 98N (b To re m.m, two egment o the cord mut be horten by tht mount. Thu, the mount o the trng pulled down t the let end :.4m ( c d (98N (.4m 3. 9J ( d g d (.m(g(9.8m / 3. 9J + g There no chnge n c energy. 9
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