Work and Energy (Work Done by a Varying Force)

Transcription

1 Lecture 1 Chpter 7 Physcs I ork nd Energy (ork Done y Vryng Force) Course weste: Lecture Cpture: , Sprng 14, Lecture 1

2 Outlne Chpter 7 Vrle forces ork s re under force-dstnce grph Sprng force Prolem solvng , Sprng 14, Lecture 1

3 ork nd Energy (lst clss revew) K F = const d K f ork done y constnt force long dsplcement d: F d Fd cos , Sprng 14, Lecture 1

4 Lst clss we derved: Knetc energy ork-knetc Energy Prncple 1 mv f K 1 mv f 1 mv F( ) d ork-knetc Energy Prncple K f K K net The work done s equl to the chnge n the knetc energy (very powerful prncple). ork done f F( ) d K F K f , Sprng 14, Lecture 1

5 Trnsltonl Knetc Energy Knetc energy (K) s the energy of moton Trnsltonl knetc energy s the energy of moton n lne or trjectory Knetc energy K 1 mv Knetc energy s the energy possessed y n oject ecuse of ts moton , Sprng 14, Lecture 1

6 Emple Net ork requred to ccelerte 1kg cr from v v f () from m/s to 4 m/s? m K [ v f v ] 1 [4 ] 6,J 6kJ () from 4 m/s to zero? m 1 K [ v f v ] [ 4 ] 8,J 8kJ , Sprng 14, Lecture 1 ork-knetc Energy Prncple K f K K net If the net work s postve, the knetc energy ncreses. If the net work s negtve, the knetc energy decreses.

7 ork Done By Vryng Force A stellte fllng towrds the erth GmM F rˆ r Oject osclltng on sprng F k Generl cse: oth force nd dsplcement vectors vry n oth mgntude nd drecton e need to fgure out how to del wth these cses , Sprng 14, Lecture 1

8 ork Done By Vryng Force y F F Dvde pth nto nfntesmlly short segments Sum up works to get totl work ork done y F over ech l: 1 F1 cos1 1 ; F cos ; etc Totl work done y F s sum: l 1 l Dstnce l , Sprng 14, Lecture lm F cosd 7 F 1 F cos cos By defnton, ths s n ntegrl: F d

9 ork done y force =Are under the curve F d Dstnce l , Sprng 14, Lecture 1

10 ork Integrl n component form d F F d F ˆ F y ˆj F kˆ ( d)ˆ ( dy) ˆj Let s wrte t n component form: z ( dz) kˆ F d y y F y dy z z F z dz , Sprng 14, Lecture 1

11 The Sprng Force vrle force The vrle force eerted y sprng s gven y Hooke s Lw: F sprng k k sprng constnt F S F s F s k F s k( ) The force s to the left The force s to the rght , Sprng 14, Lecture 1 Restorng force

12 ork done y person to compress sprng Appled force: ork done y F: kd k F 1 k , Sprng 14, Lecture 1 k F d (Method I) The sprng s compressed wthout ccelerton (v=const), so ( ) k F p k Fpˆ k(ˆ) Dsplcement: d d(ˆ) k(ˆ) d ˆ kdˆ ˆ Stretched Ths ws used to ntegrte: n î d F sprng k 1 d n1 n 1 F p

13 ork done y person to compress sprng (Method II) ork done y force =Are under the curve Generl cse F d Dstnce l Our cse F p k ; Cos 1 k Are under the curve ( 1 )( se)( lttude) ( 1 )( )( k) 1 k , Sprng 14, Lecture 1

14 Emple: Crt s speed provded y the Sprng ht s the knetc energy (nd velocty) cqured y the.-kg mss when t seprtes from the relesed sprng t =? k=8n/m; sprng compresson=.1m. Intl stuton (compressed). 1m m Fnl stuton (relesed) v mv K m 1 v f K f 1 mv f Fnlly, speed of the crt ork-knetc Energy Prncple net K ork done to compress the sprng (found n the prevous slde) wll e converted to KE of the mss 1 K f K mv f 1 1 k (8 N m)(.1m).4 J 1.4 J (. kg) v f v f 4 m/s m/s , Sprng 14, Lecture 1

15 Summry ork done y constnt force: ork done y vrle force: Knetc energy s energy of moton: Net work done on n oject corresponds to ts chnge n knetc energy: , Sprng 14, Lecture 1 ork-knetc Energy Prncple net K

16 Thnk you See you on Mondy , Sprng 14, Lecture 1

17 Let s dd Frcton If constnt frctonl force (5N) cts on the mss s t s pushed y the sprng, re-clculte the knetc energy nd velocty on relese. Intl stuton (compressed) F fr Fnl stuton = -1cm m dsplcement F sp m , Sprng 14, Lecture 1 v f K f 1 mv f thout frcton we hd v f m/s ork-knetc Energy Prncple net K sprng frcton K f K frcton Frcton does negtve work. J (.5J ) K f 1.5 J 1 ( kg)v f v f F fr d cos18 frcton ( 5N)(.1m )( 1). 5J 1.5 m/s 1. m/s