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Physics 101:  Lecture 10 Potential  Energy & Energy Conservation  ,[object Object],Hour Exam 1:  Today! -(no) cheating! -conflict in  151 , 5:15pm -regular exam – room assignments
Review ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Preview ,[object Object],
Preflight 4 ,[object Object],“ everything”  “nothing” “ conservative vs. nonconservative / Wnc” “ The equations were kind of confusing…” “ Understanding what the symbols mean”  sign of kinetic and potential energies. . “ physics is difficult; it takes too much WORK and ENERGY to understand it.  ” “ don't really understand work...  ” Studying for the exam
Work Done by Gravity 1 ,[object Object],W g   = (mg)(S)cos  S = h W g  = mghcos(0 0 ) = mgh  y = y f -y i  = -h W g  = -mg  y   mg S y x mg S y x Y i  = h Y f  = 0 Y i  = h Y f  = 0
Work Done by Gravity 2 ,[object Object],W g   = (mg)(S)cos  S = h   W g  = mghcos(180 0 ) = -mgh  y = y f -y i  = +h W g  = -mg  y mg S y x Y f  = h Y i  = 0
Work Done by Gravity 3 ,[object Object],W g   = (mg)(S)cos    S = h/cos  W g  = mg(h/cos  )cos  W g  = mgh   y = y f -y i  = -h W g  = -mg  y   h  mg S
Work and Potential Energy ,[object Object],[object Object],[object Object],[object Object],[object Object]
Conservation ACT ,[object Object],[object Object],[object Object],[object Object],[object Object],correct
Skiing Example (no friction) A skier goes down a 78 meter high hill with a variety of slopes. What is the maximum speed she can obtain if she starts from rest at the top? Conservation of energy:  W nc  =   K +   U K i  + U i  = K f  + U f   ½ m v i 2  + m g y i  = ½ m v f 2  + m g y f 0 + g y i  = ½ v f 2  + g y f   v f 2  = 2 g (y i -y f ) v f  = sqrt( 2 g (y i -y f )) v f  =   sqrt( 2 x 9.8 x 78) = 39 m/s 26 0 = K f -K i  + U f  - U i
Pendulum ACT ,[object Object],[object Object],[object Object],W = F d cos   .  But    = 90 degrees so Work is zero. h Conservation of Energy (W nc =0)  W nc  =   K +    U 0  = K final  - K initial  + U final - U initial   K initial  + U initial  = K final +U final 0 + mgh = ½ m v 2 final  + 0 v final  = sqrt(2 g h)
Pendulum Demo ,[object Object],h Conservation of Energy (W nc =0)  W nc  =   K +    U 0  = K final  - K initial  + U final - U initial  K initial  + U initial  = K final +U final 0 + mgh initial  = 0 + mgh final   h initial  = h final
Lecture 10,  Preflight 1  ,[object Object],[object Object],“ they will all have the same speed at the bottom.”   “ The ball being dropped will reach the ground fastest since it doesn't have to travel as far.” 1 2 3 correct
Lecture 10,  Preflight 2 ,[object Object],[object Object],Conservation of Energy (W nc =0)  W nc  =   K +    U K initial  + U initial  = K final +U final 0 + mgh = ½ m v 2 final  + 0 v final  = sqrt(2 g h)  1 2 3 correct
Skiing w/ Friction A 50 kg skier goes down a 78 meter high hill with a variety of slopes. She finally stops at the bottom of the hill. If friction is the force responsible for her stopping, how much work does it do? Work Energy Theorem: W nc  = K f -K i  + U f  - U i   = ½ m v f 2  - ½ m v i 2  + m g y f  – m g y i =  0+0+0 - g y i  m =  – 764 x 50  Joules = -38200  Joules Similar to bob sled homework
Galileo’s Pendulum ACT ,[object Object],[object Object],h 1 h 2 m Conservation of Energy (W nc =0)  W nc  =   K +    U K initial  + U initial  = K final +U final 0 + mgh 1  = 0 + mgh 2   h 1  = h 2
Power (Rate of Work) ,[object Object],[object Object],[object Object],P = W / t =  m g h  / t = (70 kg) (9.8 m/s 2 ) (5 m) / 7 s = 490 J/s  or 490 Watts
Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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みなさんこんにちはこれ何文字まで入るの?40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの?えこ...
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Lecture10

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  • 9. Skiing Example (no friction) A skier goes down a 78 meter high hill with a variety of slopes. What is the maximum speed she can obtain if she starts from rest at the top? Conservation of energy:  W nc =  K +  U K i + U i = K f + U f ½ m v i 2 + m g y i = ½ m v f 2 + m g y f 0 + g y i = ½ v f 2 + g y f v f 2 = 2 g (y i -y f ) v f = sqrt( 2 g (y i -y f )) v f = sqrt( 2 x 9.8 x 78) = 39 m/s 26 0 = K f -K i + U f - U i
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  • 14. Skiing w/ Friction A 50 kg skier goes down a 78 meter high hill with a variety of slopes. She finally stops at the bottom of the hill. If friction is the force responsible for her stopping, how much work does it do? Work Energy Theorem: W nc = K f -K i + U f - U i = ½ m v f 2 - ½ m v i 2 + m g y f – m g y i = 0+0+0 - g y i m = – 764 x 50 Joules = -38200 Joules Similar to bob sled homework
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Editor's Notes

  1. Careful that independent of path really but does depend on initial and final points.