Chapter 6 - Work and Energy

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Caper 6 - Work ad Eergy Rosedo Pysics 1-B Eploraory Aciviy Usig your book or e iere aswer e ollowig quesios: How is work doe? Deie work, joule, eergy, poeial ad kieic eergy.

Objecives: Aer compleig is module, you sould be able o: Deie kieic eergy ad poeial eergy, alog wi e appropriae uis i eac sysem.

1 Caper 6 - Work ad Eergy Rosedo Pysics 1-B Eploraory Aciviy Usig your book or e iere aswer e ollowig quesios: How is work doe? Deie work, joule, eergy, poeial ad kieic eergy. How does e work doe o a objec aec is kieic eergy. Wa deermies ow muc poeial eergy a objec as? Deie ad eplai coservaio o eergy. How is power relaed o orce ad speed? Objecives: Aer compleig is module, you sould be able o: Deie kieic eergy ad poeial eergy, alog wi e appropriae uis i eac sysem. Te Nija, a roller coaser a Si Flags over Georgia, as a eig o 1 ad a speed o 5 mi/. Te poeial eergy due o is eig cages io kieic eergy o moio. Describe e relaiosip bewee work ad kieic eergy, ad apply e WORK- ENERGY THEOREM. Deie ad apply e cocep o POWER, alog wi e appropriae uis. 1

A suspeded weig A sreced bow Eample Problem: Wa is e poeial eergy o a 5-kg perso i a skyscraper i e is 48 m above e sree below?

2 Eergy Eergy is ayig a ca be covered io work; i.e., ayig a ca eer a orce roug a disace. Poeial Eergy Poeial Eergy: Abiliy o do work by virue o posiio or codiio. Eergy is e capabiliy or doig work. A suspeded weig A sreced bow Eample Problem: Wa is e poeial eergy o a 5-kg perso i a skyscraper i e is 48 m above e sree below? Graviaioal Poeial Eergy Wa is e P.E. o a 5-kg perso a a eig o 48 m? U = = (5 kg)(9.8 m/s )(48 m) Kieic Eergy Kieic Eergy: Abiliy o do work by virue o moio. (Mass wi velociy) A speedig car or a space rocke U = 35 kj

Eamples o Kieic Eergy Wa is e kieic eergy o a 5-g bulle 5 g ravelig a m/s? K 1 mv 1(.5 kg)( m/s) m/s K = 1 J Wa is e kieic eergy o a 1-kg car ravelig a 14.1 m/s? K 1 mv 1 (1 kg)(14.1 m/s) K = 99.

3 Eamples o Kieic Eergy Wa is e kieic eergy o a 5-g bulle 5 g ravelig a m/s? K 1 mv 1(.5 kg)( m/s) m/s K = 1 J Wa is e kieic eergy o a 1-kg car ravelig a 14.1 m/s? K 1 mv 1 (1 kg)(14.1 m/s) K = 99.4 J Work ad Kieic Eergy A resula orce cages e velociy o a objec ad does work o a objec. v o m F Work F ( ma) ; v m v a Work mv mv 1 1 v F Te Work-Eergy Teorem Work is orce imes disace bu! Work is equal o e cage i ½mv Work mv mv 1 1 I we deie kieic eergy as ½mv e we ca sae a very impora pysical priciple: Te Work-Eergy Teorem: Te work doe by a resula orce is equal o e cage i kieic eergy a i produces. Oly e orce compoe i e direcio o moio cous! Uis o work: Joule 3

4 Force i direcio o moio is wa maers F F = F cosq I ve go work o do. F = Mg Tis is e work doe by e perso liig e bo. D W = D * F cosq F = Mg Dy W=F*Dy=MgH How abou e reverse?. F = Mg W=F*Dy = - MgH Posiive or Negaive? Work doe by graviy. H F = Mg Work ca be posiive or egaive. Liig a bo is posiive work. Lowerig e bo is egaive work. Dy = - H F g = - Mg Work doe by orce o graviy is posiive we a objec is dropped. 4

5 Eample 1: A -g projecile srikes a mud bak, peeraig a disace o 6 cm beore soppig. Fid e soppig orce F i e erace velociy is 8 m/s. 6 cm 8 m/s Work = ½ mv - ½ mv o F = - ½ mv o F =? F (.6 m) cos 18 = - ½ (. kg)(8 m/s) Eample : A bus slams o brakes o avoid a accide. Te read marks o e ires are 8 m log. I m k =.7, wa was e speed beore applyig brakes? Work = DK Work = F(cos q) = m k. = m k Work = - m k 5 m DK = ½ mv - ½ mv o F (.6 m)(-1) = -64 J F = 167 N -½DK mv o = Work = -m k v o = m k g Work o sop bulle = cage i K.E. or bulle v o = (.7)(9.8 m/s )(5 m) v o = 59.9 /s Eample 3: A 4-kg block slides rom res a op o boom o e 3 iclied plae. Fid velociy a boom. ( = m ad m k =.) 3 Pla: We mus calculae bo e resula work ad e e displaceme. Te e velociy ca be oud rom e ac a Work = DK. Resula work = (Resula orce dow e plae) (e displaceme dow e plae) Eample 3 (Co.): We irs id e e displaceme dow e plae: 3 From rig, we kow a e Si 3 = / ad: si 3 3 m 4 m si 3 5

6 Eample 3(Co.): Ne we id e resula work o 4-kg block. ( = 4 m ad m k =.) Draw ree-body diagram o id e resula orce: = 4 m 3 W y = (4 kg)(9.8 m/s )(cos 3 ) = 33.9 N cos 3 si 3 y 3 W = (4 kg)(9.8 m/s )(si 3 ) = 19.6 N Eample 3(Co.): Fid e resula orce o 4-kg block. ( = 4 m ad m k =.) 33.9 N y 19.6 N 3 Resula orce dow plae: 19.6 N - Recall a k = m k SF y = or = 33.9 N Resula Force = 19.6 N m k ; ad m k =. Resula Force = 19.6 N (.)(33.9 N) = 1.8 N Resula Force Dow Plae = 1.8 N Eample 3 (Co.): Te resula work o 4-kg block. ( = 4 m ad F R = 1.8 N) F R 3 (Work) R = F R Ne Work = (1.8 N)(4 m) Ne Work = 51 J Fially, we are able o apply e work-eergy eorem o id e ial velociy: Work mv mv 1 1 Eample 3 (Co.): A 4-kg block slides rom res a op o boom o e 3 plae. Fid velociy a boom. ( = m ad m k =.) 3 ½ mv - ½ mv o = Work Resula Work = 51 J Work doe o block equals e cage i K. E. o block. ½ mv = 51 J ½(4 kg)v = 51 J v = 16 m/s 6

1 W = 1 J/s ad 1 kw = 1 W Oe lb/s is a older (USCS) ui o power. Oe orsepower is work doe a e rae o 55 lb/s.

7 4 s m Power Power is deied as e rae a wic work is doe: (P = dw/d ) F m 1 kg Work F r Power ime r P (1kg)(9.8m/s )(m) 4 s P 49J/s or 49 was (W) Power o 1 W is work doe a rae o 1 J/s Uis o Power Oe wa (W) is work doe a e rae o oe joule per secod. 1 W = 1 J/s ad 1 kw = 1 W Oe lb/s is a older (USCS) ui o power. Oe orsepower is work doe a e rae o 55 lb/s. ( 1 p = 55 lb/s ) Eample o Power Wa power is cosumed i liig a 7-kg robber 1.6 m i.5 s? F P (7 kg)(9.8 m/s )(1.6 m) P.5 s Power Cosumed: P = W Eample 4: A 1-kg ceea moves rom res o 3 m/s i 4 s. Wa is e power? Recogize a work is equal o e cage i kieic eergy: 1 1 Work Work mv mv P P mv 1 1 (1 kg)(3 m/s) 4 s Power Cosumed: P = 1. kw m = 1 kg 7

3 kw v = 4 m/s Eample 6: Wa work is doe by a 4-p mower i oe our? Te coversio acor is eeded: 1 p = 55 lb/s.

8 Power ad Velociy Recall a average or cosa velociy is disace covered per ui o ime v = /. F P = = F P Fv I power varies wi ime, e calculus is eeded o iegrae over ime. (Opioal) Sice P = dw/d: Work P() d Eample 5: Wa power is required o li a 9-kg elevaor a a cosa speed o 4 m/s? P = F v = v P = (9 kg)(9.8 m/s )(4 m/s) P = 35.3 kw v = 4 m/s Eample 6: Wa work is doe by a 4-p mower i oe our? Te coversio acor is eeded: 1 p = 55 lb/s. 55 lb/s 4p lb/s 1p Work P ; Work P Work ( lb/s)(6s) Work = 13, lb Summary Poeial Eergy: Abiliy o do work by virue o posiio or codiio. U Kieic Eergy: Abiliy o do work by K virue o moio. (Mass wi velociy) Te Work-Eergy Teorem: Te work doe by a resula orce is equal o e cage i kieic eergy a i produces. Work = ½ mv - ½ mv o 1 mv 8

9 Summary (Co.) Power is deied as e rae a wic work is doe: (P = dw/d ) Work P CONCLUSION: Caper 6 Work ad Eergy Work F r Power ime P= F v Power o 1 W is work doe a rae o 1 J/s 9

2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i)

2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i) Mah PracTes Be sure o review Lab (ad all labs) There are los of good quesios o i a) Sae he Mea Value Theorem ad draw a graph ha illusraes b) Name a impora heorem where he Mea Value Theorem was used i he