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1999MechanicsSolutions

# 1999MechanicsSolutions - Solutions to the 1999 AP Physics C...

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Solutions to the 1999 AP Physics C Mechanics Exam 1) a) ( 29 ( 29 ( 29 gh M m v M m v M m mv f f + = + + = 2 0 2 1 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 θ θ θ θ cos 1 2 cos 1 2 cos 1 2 cos 2 1 0 2 - + = - + = + = - = - = = gL m M m v gL M m v M m mv gL v L L g gh v o f f f b) r mv mg F r mv mg F T T 2 2 + = = - ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 θ θ θ cos 2 3 cos 1 2 cos 1 2 2 - + = - + + + = - + + + = + + + = g M m F M m g g M m F L gL M m g M m F r v M m g M m F T T T T c) Answers will vary. One idea: Attach the block to a spring and measure the amplitude of the oscillations that result when the dart is fired into the block. Use the amplitude in an energy analysis to determine the speed of the block, and then use conservation of momentum to determine the speed of the dart. d) m bv m F a bv F - = = - = ( 29 ( 29 b mv v b m x v v b m x dv b m dx dv b m dx dx b dv m m b dx dv m bv dx dv v a dv v dx a f v v x f o 0 0 0 0 0 = - - = - - = - = - = - = - = - = = = L L cos θ h F T mg

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2) a) 2 r GmM F - = where M is the mass enclosed by a sphere of radius r (Shell Theorem) Cr r Gm r r Gm r GmM F r r V M - = - = - = - = = = = ρπ ρπ ρπ
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1999MechanicsSolutions - Solutions to the 1999 AP Physics C...

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