Forms of Energy. Mass = Energy. Page 1. SPH4U: Introduction to Work. Work & Energy. Particle Physics:


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1 SPH4U: Inroducion o ork ork & Energy ork & Energy Discussion Definiion Do Produc ork of consn force ork/kineic energy heore ork of uliple consn forces Coens One of he os iporn conceps in physics Alernive pproch o echnics Mny pplicions beyond echnics Therodynics (oveen of he) Qunu echnics... Very useful ools You will lern new (soeies uch esier) wys o solve probles ors of Energy Mss = Energy Kineic: Energy of oion. A cr on he highwy hs kineic energy. Pricle Physics: E = ev () e e+ + 5,000,000,000 V  5,000,000,000 V e hve o reove his energy o sop i. The brkes of cr ge HOT! This is n exple of urning one for of energy ino noher (herl energy). (b) (c) M E = MC 2 ( poof! ) Pge 1
2 Energy Conservion Energy cnno be desroyed or creed. Jus chnged fro one for o noher. Definiion of ork: Ingrediens: orce (), displceen (r) e sy energy is conserved! True for ny closed syse. i.e. when we pu on he brkes, he kineic energy of he cr is urned ino he using fricion in he brkes. The ol energy of he crbrkesrodosphere syse is he se. The energy of he cr lone is no conserved... I is reduced by he brking. Doing work on n isoled syse will chnge is energy... ork,, of consn force cing hrough displceen r is: = r = r cos = r r Do Produc r r The do produc llows us o uliply wo vecors, bu jus he coponens h re going in he se direcion (usully long he second vecor) Definiion of ork... Only he coponen of long he displceen is doing work. Exple: Trin on rck. r cos Aside: Do Produc (or Sclr Produc) Definiion:. b = b cos = [b cos ] = b = b[ cos ] = b b Soe properies: b = b q(b) = (qb) = b(q) (b + c) = (b) + (c) b b (q is sclr) (c is vecor) b b The do produc of perpendiculr vecors is 0!! Pge 2
3 Soluion ork & Energy Undersnding A box is pulled up rough ( > 0) incline by ropepulleyweigh rrngeen s shown below. Drw BD of box: T v How ny forces re doing work on he box? Consider direcion of oion of he box () 2 (b) 3 (c) 4 Any force no perpendiculr o he oion will do work: does no work (perp. o v) T does posiive work f f does negive work g does negive work 3 forces do work g ork: Exple (consn force) A force = 10 pushes box cross fricionless floor for disnce x = 5. Unis of ork: orce x Disnce = ork ewon x [M][L] / [T] 2 Meer = Joule [L] [M][L] 2 / [T] 2 ks cgs oher x ork done by on box is: = x = x (since is prllel o x)  (Joule) Dynec (erg) = 107 J BTU = 1054 J clorie = J foolb = J ev = 1.6x1019 J = (10 ) x (5 ) = 50 Joules (J) Pge 3
4 ork & Kineic Energy: A force = 10 pushes box cross fricionless floor for disnce x = 5. The speed of he box is v 1 before he push nd v 2 fer he push. ork & Kineic Energy... Since he force is consn, ccelerion will be consn. e hve shown h for consn : v v 2 1 = 2(x 2 x 1 ) = 2x. uliply by 1 / 2 : 1 / 2 v / 2 v 2 1 = x Bu = 1 / 2 v / 2 v 2 1 = x v 1 v 2 v 1 v 2 x x ork & Kineic Energy... So we find h 1 / 2 v / 2 v 1 2 = x = Define Kineic Energy K: K = 1 / 2 v 2 K 2  K 1 = = K v 1 (ork/kineic energy heore) v 2 ork/kineic Energy Theore: {e ork done on objec} = {chnge in kineic energy of objec} ne K K f K 1 1 v f v 2 2 i 2 2 i x Universiy will prove his for vrible force ler. Pge 4
5 ice o Know B ork & Energy Quesion B dx A B dx A B dv dx A d B dv vd A d B v vdv v A vb The 1work in 2 going fro v A o 2 B. va 1 1 v v B A KE KE B A KE A Two blocks hve sses 1 nd 2, where 1 > 2. They re sliding on fricionless floor nd hve he se kineic energy when hey encouner long rough srech (i.e. > 0) which slows he down o sop. hich one will go frher before sopping? () 1 (b) (c) hey will go he se disnce Soluion Soluion The workenergy heore sys h for ny objec ET = K In his exple he only force h does work is fricion (since boh nd g re perpendiculr o he block s oion). The workenergy heore sys h for ny objec ET = K In his exple he only force h does work is fricion (since boh nd g re perpendiculr o he blocks oion). The ne work done o sop he box is  fd = gd. This work reoves he kineic energy h he box hd: ET = K 2  K 1 = 0  K 1 f g D Pge 5
6 Soluion The ne work done o sop box is  fd = gd. This work reoves he kineic energy h he box hd: ET = K 2  K 1 = 0  K 1 This is he se for boh boxes (se sring kineic energy). A Siple Applicion: ork done by grviy on flling objec h is he speed of n objec fer flling disnce H, ssuing i srs res? g = r = g r cos(0) = gh v 0 = 0 2 gd 2 1 gd 1 2 D 2 1 D 1 Since 1 > 2 we cn see h D 2 > D 1 g = gh ork/kineic Energy Theore: H r g j g = gh = 1 / 2 v v 2gH v D 1 D 2 h bou uliple forces? Coens: Suppose ET = nd he displceen is r. The work done by ech force is: Tie inervl no relevn Run up he sirs quickly or slowly...se ork 1 = 1 r 2 = 2 r TOT = = 1 r + 2 r = ( ) r 1 ET r 2 Since = r o work is done if: = 0 or r = 0 or = 90 o TOT = TOT r I s he ol force h ers!! Pge 6
7 Coens... ork & Energy Quesion = r o work done if = 90 o. o work done by T. T v An inclined plne is ccelering wih consn ccelerion. A box resing on he plne is held in plce by sic fricion. How ny forces re doing work on he block? o work done by. v () 1 (b) 2 (c) 3 Soluion Soluion irs, drw ll he forces in he syse: Recll h = Δr so only forces h hve coponen long he direcion of he displceen re doing work. S S g g The nswer is (b) 2. Pge 7
8 POER Siply pu, power is he re which work ges done (or energy ges rnsferred). Suppose you nd I ech do 1000J of work, bu I do he work in 2 inues while you do i in 1 inue. e boh did he se oun of work, bu you did i ore quickly (you were ore powerful) ork Power ie Power Power is lso needed for ccelerion nd for oving gins he force of grviy. The verge power cn be wrien in ers of he force nd he verge velociy: d P v v v () P J s Undersnding Undersnding A over pushes lrge cre (= 75 kg) fro one side of ruck o he oher side ( disnce of 6 ), exering sedy push of 300. If she oves he cre in 20 s, wh is he power oupu during his ove? h us he power oupu of n elevor oor be such h i cn lif ol ss of 1000 kg, while inining consn speed of 8.0 /s? P d s 90 P d v gv 1000kg kg s 78,000 78k Pge 8
9 lsh Pge 9
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