Solving for Kinetic Energy Lost in Spring Gun

[TS656577]

Homework Statement

A ball of mass m = 56 g is shot with speed vi = 20 m/s (in the negative direction of an x axis) into the barrel of a spring gun of mass M = 222 g initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. Assume that the increase in thermal energy due to friction between the ball and the barrel is negligible. What fraction of the initial kinetic energy of the ball is stored in the spring?

Homework Equations

m1v1=(m1+m2)v2
K=.5mv^2

The Attempt at a Solution

I found the final velocity to be -4.03 m/s by using m1v1=(m1+m2)v2 and got v2 to be -4.03m/s. From here I am kind of stuck. It means that its stored as potential energy...so U=Ki-Kf and I have Ki as 0 and Kf as 2257.49. Would i take the potential divided by the Kinetic?

 

[6767]

Hi
your on the right tracks

 

[TS656577]

but if you take the potential divided by kinetic, you get division by 0

 

[TS656577]

still stumped