# Collision and Momentum

1. Nov 24, 2009

### ntox101

1. The problem statement, all variables and given/known data

A 1.0-kg block at rest on a horizontal frictionless surface is connected to an unstretched spring ( k =200 N/m ) whose other end is fixed. A 2.0-kg block whose speed is 4.0 m/s collides with the 1.0-kg block. If the two blocks stick together after the one-dimensional collision, what maximum compression of the spring occurs when the blocks momentarily stop?

2. Relevant equations

law of conservation of momentum.

3. The attempt at a solution

So far I started off by finding velocity after the collision.

Okay, the latex references are god-awful. I used algebra to modify the law of conservation of momentum and plugged in the values required and the velocity when the 2 blocks collide, I got 2.66 m/s . I then used that to calculate the kinetic energy of the masses when collided, and got 10.6J.

I just want confirmation that I am on the right track and any other helpers would be greatly appreciated.

Last edited: Nov 24, 2009
2. Nov 24, 2009

### ideasrule

Yup, you're definitely on the right track. Also, all your calculations are right so far.

Now just figure out the stretch of the spring using its potential energy.

3. Nov 24, 2009

### ntox101

Okay, maybe a stupid question. How do I find that out? I know that $$U_{s}$$ = $$\frac{1}{2}$$ k $$x^2{}$$. Isn't the variable x the horizontal distance stretched? If so, that variable isn't given.

4. Nov 25, 2009

### Nebozilla

You should know the energy of the combined mass and its conserved. If I'm reading it right you aren't given x since you are trying to find the maximum compression of the spring which is x.

5. Nov 25, 2009

### noblegas

Now that you found your final velocity, all of your variables are known and you can just apply the equations for conservation of energy.