Quick question on energy conversions

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The discussion centers on the energy conversion of a ball bearing dropped onto a spring, focusing on the relationship between kinetic energy (KE), gravitational potential energy (GPE), and elastic potential energy (EPE). The initial viewpoint suggests that the energy conversion can be expressed as 0.5mv² = mgy + 0.5Fy, considering the area under the force-displacement graph for EPE. However, the provided answer indicates that the correct relationship is 0.5mv² = mgy + Fy, interpreting Fy as the work done by the spring. The confusion arises from whether F should represent the average force exerted by the spring, as the force varies during compression. The key takeaway is to clarify the definitions of energy types and the role of average force in this context.
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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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