# Conservation of Energy Challenge Problem

1. Homework Statement
A 2.0 kg cart has a sping with k= 5000 N/m attached to its front, parallel to the ground. This cart rolls at 4.0 m/s toward a stationary 1.0 kg cart.

a) What is the maximum compression of the spring during the collision?

b) What is the speed of each cart after the collision?

2. Homework Equations

KE=(1/2)mv^2 Us=(1/2)kx^2

3. The Attempt at a Solution

I got the first part:

Using first conservation of momentum and assuming the cars stick together momentarily
then using conservation of energy

(2kg)(4m/s)=(3kg)v1
v1= 2.67 m/s
(.5)(2kg)(4m/s)^2=(.5)(5000N/m)(x)^2 + (.5)(3kg)(2.67m/s)^2
x= .046 m

But I'm not sure what to do with the second part. Any suggestions?

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But I'm not sure what to do with the second part. Any suggestions?
That's the easiest part. Since this was a completely elastic collision, the elastic co-eff =1. So, final relative velocity = initial relative velocity. This, combined with the conservation of momentum, gives you two unknowns with two eqns.

Of course, you can also use conservation of total KE, but that's lengthier.

Good job in solving part A.