CHAPTER 8 Potential Energy and Conservation of Energy


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1 CHAPTER 8 Potental Energy and Conservaton o Energy One orm o energy can be converted nto another orm o energy. Conservatve and nonconservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated wth moton Energy assocated wth poston Potental energy U: Can be thought o as stored energy that can ether do work or be converted to knetc energy. When work gets done on an object, ts potental and/or knetc energy ncreases. There are derent types o potental energy: Gravtatonal energy Elastc potental energy (energy n an stretched sprng) Others (magnetc, electrc, chemcal, ) Physcs Dr. Abdallah M. Azzeer 1
2 Gravtatonal Potental Energy Potental Energy (PE) Energy assocated wth poston or conguraton o a mass. Consder a problem n whch the heght o a mass above the Earth changes rom y 1 to y : y W grav =? UP W g =  mg s =  mg (y y 1 ) s F HAND v = const a = Down W g = +mg s mg W g =  mg ( y y 1 ) y 1 Physcs 3 mgy U g gravtatonal potental energy (PE) U U 1 =U W g =  mg ( y y 1 )= U 1 U =  U g W g =  U g Changng the conguraton o an nteractng system requres work example: ltng a book The change n potental energy s equal to the negatve o the work done U But Work/Knetc Energy Theorem says: W = K g W W U K K U Physcs 4 Dr. Abdallah M. Azzeer
3 K U Total Mechancal Energy The change n potental energy s equal to the negatve o the work done U W But Work/Knetc Energy Theorem says: W = K W U K K U K K1 U U1 K U K1 U1 cons tant E Total mechancal energy NOTE that the ONLY orces s gravtatonal energy whch dong the work The sum o K and U or any state o the system = the sum o K and U or any other state o the system In an solated system acted upon only by conservatve orces Mechancal Energy s conserved Physcs 5 Example 8.1 A bowler drops bowlng ball o mass 7 kg on hs toe. Choosng loor level as y=, estmate the total work done on the ball by the gravtatonal orce as the ball alls. Let s assume the top o the toe s.3 m rom the loor and the hand was.5 m above the loor. U mgy J U mgy J W g U U U 3.4 J 3 y y J Physcs 6 Dr. Abdallah M. Azzeer 3
4 b) Perorm the same calculaton usng the top o the bowler s head as the orgn. Assumng the bowler s heght s 1.8 m What has to change? Frst we must re compute the postons o ball at the hand and o the toe. Assumng the bowler s heght s 1.8 m, the ball s orgnal poston s 1.3 m, and the toe s at 1.77 m. U U mgy J mgy J Wg U U U 3.J 3J Physcs 7 F S kx Work done by Sprng dw F dx S S W x F dx x kx dx k x x Elastc Potental Energy 1 S x S x 1 U kx S W U U U S S S S Physcs 8 Dr. Abdallah M. Azzeer 4
5 Conservatve Forces (a) A orce s conservatve work done by that orce actng on a partcle movng between ponts s ndependent o the path the partcle takes between the two ponts (b) The total work done by a conservatve orce s zero when the partcle moves around any closed path and returns to ts ntal poston Physcs 9 Conservatve Forces To repeat the dea on the last slde: We have seen that the work done by a conservatve orce does not depend on the path taken. W W 1 = W Thereore the work done n a closed path s. W 1 W W NET = W 1 W = W 1 W 1 = W 1 Physcs 1 Dr. Abdallah M. Azzeer 5
6 Work done by gravty L:\13 Phys LECTURES SLIDES\13Phys_Sldes_T1Y3839\CH7Flash W g = F. r = mg r cos = mg h W g = mgh (Depends only on h!) W NET = W 1 + W W n r m m m g h = F r 1 + F r F r n = F (r 1 + r r n ) = F r = F h W g = mg h h m r 1 r r r 3 mg Depends only on h, not on path taken! r n Physcs 11 Nonconservatve orces: A orce s nonconservatve t causes a change n mechancal energy; mechancal energy s the sum o knetc and potental energy. Example: Frctonal orce. Ths energy cannot be converted back nto other orms o energy (rreversble). Work does depend on path. For straght lne W =  d For semcrcle path W =  ( d /) Work vares dependng on the path. Energy s dsspated The presence o a non conservatve orce reduces the ablty o a system to do work (dsspatve orce) Physcs 1 Dr. Abdallah M. Azzeer 6
7 Energy dsspaton: e.g. sldng rcton As the parts scrape by each other they start smallscale vbratons, whch transer energy nto atomc moton The atoms vbratons go back and orththey have energy, but no average momentum. The ncreased atomc vbratons appear to us as a rse n the temperature o the parts. The temperature o an object s related to the thermalenergythas.frctontranserssome energy nto thermal energy Physcs 13 When there s NO work done by APPLIED FORCES, the total mechancal energy s constant or CONSEVED I W a K +U = K 1 +U 1 +W a OR K + U= W nc W nc = work done by ANY other orces than gravtatonal orce sprng orces (e.g. any appled non conservatve orce or rctonal orce) Physcs 14 Dr. Abdallah M. Azzeer 7
8 Three dentcal balls are thrown wth the same ntal speed rom the top o a buldng. v v cosθˆ v snθjˆ Total Energy 1 E K U mv mgh g At y = 1 1 E mv mv mgh v v g h ˆ : v v c o s θ y x jˆ : v v sn θ gt 1 y h v snθ t gt v snθ v sn θ gh t g v y v sn θ gh v v v v sn θ gh v cos θ x y v g h Physcs 15 READ Quck Quz 8.7 & 8.8 A ball connected to a massless sprng suspended vertcally. What orms o potental energy are assocated wth the ball sprng Earth system when the ball s dsplaced downward? Physcs 16 Dr. Abdallah M. Azzeer 8
9 READ Example 8. A ball s dropped rom a heght h above the ground. Intally, the total energy o the ball Earth system s potental energy, equal to mgh relatve to the ground. At the elevaton y, the total energy s the sum o the knetc and potental energes. Physcs 17 Example 8.3 Nose crusher? A bowlng ball o mass m s suspended rom the celng by a cord o length L. The ball s released rom rest when the cord makes an angle A wth the vertcal. (a) Fnd the speed o the ball at the lowest pont B. (b) What s the tenson T B n the cord at pont B? (c) The ball swngs back. Wll t crush the operator s nose? Physcs 18 Dr. Abdallah M. Azzeer 9
10 Example 8.4 (a) An actor uses some clever stagng to make hs entrance. M actor = 65 kg, M bag = 13 kg, R = 3 m What s the max. value o can have beore sandbag lts o the loor? R cos R (b) Freebody dagram or actor at the bottom o the crcular path. (c) Freebody dagram or sandbag. K U K U 1 M actorv M actor gy y R R cos θ R (1 cos θ ) Physcs 19 v gr(1cos θ ) How we can obtan v???? F T M g M y actor actor T=M g M actor actor v R v R For the sandbag not to move a= T=M bag g =6 Physcs Dr. Abdallah M. Azzeer 1
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