Quick question on energy conversions

[qazxsw11111]

A ball bearing is dropped from rest and falls at speed v just before hitting a spring. The spring compresses by a distance of y, and all energy is converted into elastic potential energy in the spring. We are supposed to find F exerted by spring.

The conversion of energy, according to me, is
0.5mv² [KE]-->mgy [GPE] +0.5 Fy [EPE, imagine the Force against Displacement graph and EPE is area under it]

However, the answer given is,
0.5mv²-->mgy + Fy [I suppose this is work done]

Which is correct and why? I am confused.

Thanks.

 

[Doc Al]

We are supposed to find F exerted by spring.

The force exerted by the spring varies as the spring compresses. Is F supposed to be the average force?