Quick question on energy conversions

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The discussion centers on the energy conversion of a ball bearing dropped from rest, impacting a spring. The key equations involve kinetic energy (KE) represented as 0.5mv², gravitational potential energy (GPE) as mgy, and elastic potential energy (EPE) as 0.5Fy. The confusion arises between the total energy conversion and the work done by the spring force. The correct interpretation is that the force exerted by the spring, F, is the average force during compression, as the force varies with displacement.

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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.
 
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qazxsw11111 said:
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?
 

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