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Unformatted text preview: CHAPTER 8 CONSERVATION OF ENERGY 199 C HAPTER 8 Answer to Checkpoint Questions . no . , , . ( a ) all tie; ( b ) all tie . ( a ) CD, AB, BC (zero); ( b ) positive direction of x . , , . decrease . ( a ) seventh excited state, with energy E ; ( b ) : eV Answer to Questions . J . ( a ) J; ( b ) J . c and d tie, then a and b tie . ( a ) and ( b ) all tie (same change in elevation) . ( a ) all tie; ( b ) all tie . all tie . ( a ) , , ; ( b ) , , . ( a ) ; ( b ) returns to its starting point and repeats the trip; ( c ) ; ( d ) . less than (smaller decrease in potential energy) . ( a ) increases from zero until shortly after t , then decreases to zero at t ; ( b ) decreases; ( c ) zero until t , then increases until t ; ( d ) constant until t , then decreases until t ; ( e ) zero until t , then increases until t ; ( f ) constant . ( a ) E < J, K < J; ( b ) E < J, K < J . ( a ) AB, CD, and then BC and DE tie (zero force); ( b ) J; ( c ) J; ( d ) J; ( e ) FG; ( f ) DE 200 CHAPTER 8 CONSERVATION OF ENERGY . ( a ) increasing; ( b ) decreasing; ( c ) decreasing; ( d ) constant in AB and BC, decreasing in CD Solutions to Exercises & Problems E As the particle moves from point A to point B , the work W done by F is equal to the loss of the corresponding potential energy of the system: W = U AB = U A U B . Thus U B = U A W = J J = J. E The elastic potential energy stored in the spring is given by U = kx , where k is the spring constant and x is the displacement of the end of the spring from its position when the spring is in equilibrium. Thus k = U x = ( )( J) ( : m) = : N/m : E ( a ) The vertical drop of the book of mass m is h = ( : m : m) = : m. The work done by the weight of the book is W = mgh = ( : kg)( : m/s )( : m) = J. ( b ) The change in the gravitational energy of the textbookEarth system is related to W by U = W . Thus U = J. ( c ) and ( d ) Denote the potential energy as U when the book is released and as U when it reaches the hands, then U = ( : kg)( : m/s )( : m) = J and U = ( : kg)( : m/s )( : m) = : J. E ( a ) The force of gravity is constant so the work it does is given by W = F d , where F is the force and d is the displacement. The force is vertically downward and has magnitude mg , where m is the mass of the ake, so this reduces to W = mgh , where h is the height from which the ake falls. This is equal to the radius r of the bowl. Thus W = mgr = ( : kg)( : m/s )( : m) = : J : ( b ) The force of gravity is conservative, so the change in gravitational potential energy of the akeEarth system is the negative of the work done: U = W = : J. CHAPTER 8 CONSERVATION OF ENERGY 201 ( c ) The potential energy when the ake is at the top is greater than when it is at the bottom by j U j . If U = at the bottom, then U = + : J at the top....
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 Fall '07
 GROUPTEST
 Energy, Potential Energy, mgh

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