How far does a putty block compress a spring after an inelastic collision?

[jwang023]

Homework Statement

A 0.440 kg block is attached to a horizontal spring that is at its equilibrium length, and whose force constant is 23.0 N/m. The block rests on a frictionless surface. A 5.90*10^-2 wad of puddy is thrown at the block, hitting it with a speed of 2.50 m/s and sticking. How far does the putty block system compress the spring?

Homework Equations

I wrote down the equation for springs. U= 0.5kx^2

The Attempt at a Solution

I have drawn a picture and figured out the momentum of the puddy onto the block, but not sure what to do after that.

 

[ehild]

Calculate the velocity of the block-puddy system.

ehild

 

[jwang023]

I have found the velocity of the puddy block. Trouble is, I'm having a hard time relating it back to the spring constant.

 

[ehild]

After collision, the forces are conservative, as the friction does not count. The block and puddy together have some kinetic energy. They push the spring and the spring exerts force on them, and the total energy of the moving mass + spring is conserved. On what depends the energy of the spring?

ehild

 

[jwang023]

Ok I get it. I went and found the Kinetic energy of the block/puddy after I found the final velocity of the two. Since you said that they were conserved I set the K=Uspring. and solved for x after converting meters to centimeters. Thanks for the help! :)