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Answer to Question #84220 in Classical Mechanics for Dave

Question #84220
A 1.50 kg wooden block is hanging motionless from a 2.00 m massless string. A 125 g arrow is
shot at 55.0 m/s at the block and sticks into it, causing the block to swing.
- What is the maximum height the block/arrow system will swing with respect to the
original position of the block? (0.912 m)
- What would be different about this situation if the arrow passed through the block, but
slowed down in the process? Explain in terms of momentum and energy
Expert's answer

The law of the conservation of the momentum gives

mv_i=(m+M) v_f

The law of the conservation of the energy gives

((m+M) v_f^2)/2=(m+M)gH

So, the maximum height the block/arrow system

H=(v_f^2)/2g=1/2g [(mv_i)/(m+M)]^2=1/(2×9.81) [(0.125×55.0)/(0.125+1.50)]^2=0.912 m

If the arrow passed through the block, then the maximum height the block decreases. This is because law of the conservation of the momentum in this case gives

mv_i=mv_a+Mv_b

So, the initial speed of the block is less with respect to previous case

v_b

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