A 10.0-g bullet is fired into, and embeds itself in, a 2.30-kg block attached to

Question

A 10.0-g bullet is fired into, and embeds itself in, a 2.30-kg block attached to a spring with a force constant of 16.9 N/m and whose mass is negligible. How far is the spring compressed if the bullet has a speed of 300 m/s just before it strikes the block and the block slides on a frictionless surface? Note: You must use conservation of momentum in this problem because of the inelastic collision between the bullet and block.

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nb: I've already tried using KE + PE= 0 and did not get the right answer (1/2mv^2=1/2kx^2; does not give the right answer)

Explanation / Answer

First find the speed of the block immediately after being hit, using conservation of momentum:

(mv)1 = (mv)2
(0.010 kg)(300 m/s) + (2.30 kg)(0 m/s) = (2.31 kg)(v)
v = 1.3 m/s

Now use conservation of energy to find how far the spring is compressed from the moment the block-bullet mass hits the spring, till when it stops and the spring is fully compressed:

KE1 + PE1 = KE2 + PE2

KE = (1/2)mv

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