How Does Momentum Conservation Determine Spring Compression in a Collision?

[ntox101]

Homework Statement

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?

Homework Equations

law of conservation of momentum.

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.

 

[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.

 

[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.

 

[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.

 

[noblegas]

bump

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