# Simple harmonic motion problem.

## Homework Statement

A 10.0-g bullet is fired into and embeds in a 2.00-kg block attached to a spring with a spring constant of 19.6 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 friction-less surface?

F=kx

## The Attempt at a Solution

I tried to solve for the momentum of the system after the impact, which is mass * velocity = 0.01 kg * 300 m/s = 3 N*s. Don't know where to go from there...help.

## Answers and Replies

Well its a conservation of momentum problem at first, as you said. Once the bullet collides the block is going to have a certain amount of kinetic energy. What happens when the spring is completely compressed? Does it have kinetic energy? If not, where did the energy go?

Also don't forget that W = ∫Fdx

I believe you can do this solely using conservation of energy...or I might be wrong. But still, don't only focus on the momentum. Focus on the transfer of energy.

Is energy conserved in a completely inelastic collision?

Additionally I gave you the only equation you need to know: work is the integral of Fdx. You can use that, along with the equation for kinetic energy, to find the energy equation you need to solve the problem. Think about it. Post if again if you need more help.

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During the collision kinetic energy IS NOT conserved. That is why you need conservation of momentum to determine the velocity of the block + bullet after the collision.
Then you can use conservation of energy as long as you ignore trivial energy losses such as air resistance.