Total work done on clay during Spring Compression

[Koscher]

Homework Statement

A 4.63-kg ball of clay is thrown downward from a height of 2.69 m with a speed of 5.01 m/s onto a spring with k = 1610 N/m. The clay compresses the spring a certain maximum amount before momentarily stopping.

b) Find the total work done on the clay during the spring's compression.

Homework Equations

U_s=integral(-kx dx)

The Attempt at a Solution

From part of the question I found the maximum compression of the spring to be 0.50230 m, and I know that is correct.

I thought that the total amount of work done on something by the spring's compression was equal to the integral that is in the relevant equations section.

Therefore, that is what I did. I U_s=integral(-kx dx) from 0 to 0.50230. The resulting answer was -203.106 J. But that is not correct, does anyone have some insight to what went wrong?

 

[Koscher]

Nevermind, i figured it out.

W = K_s + U_b

W=(-1/2)(1610)(0.50230²) + (4.63)(9.81)(0.50230)

W= -180.3 J