Why Is There a Difference Between Loss in GPE and Gain in EPE in Spring Energy?

AI Thread Summary
The discussion focuses on the discrepancy between the loss in gravitational potential energy (GPE) and the gain in elastic potential energy (EPE) when a spring is stretched. The calculated loss in GPE is 0.785 J, while the gain in EPE is 0.392 J, leading to confusion about the difference. Participants highlight the importance of correctly applying formulas and understanding the forces involved in the calculations. Additionally, there is a query regarding the resultant force when the spring is set into simple harmonic motion (SHM) with an amplitude of 0.200m. Clarification is sought on the calculations and the underlying physics principles.
qazxsw11111
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A spring has an unstretched length of 0.650 and a weight of 0.400kg is attached and gently lowered till eqm point is reached. The spring is then stretched by a distance of 0.200m.

Loss in gpe=mgh=0.200x0.650x9.81=0.785 J
Gain in EPE=0.5 Fx= 0.5 x 0.400x 9.81 x 0.200=0.392 (?) Actually I don't really understand why this is so. But it is the answer.

Why are the two answers different?

Furthermore, if the spring is set into SHM with amplitude 0.200m, what is the resultant force at the lowest point of movement?
 
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qazxsw11111 said:
A spring has an unstretched length of 0.650 and a weight of 0.400kg is attached and gently lowered till eqm point is reached. The spring is then stretched by a distance of 0.200m.

Loss in gpe=mgh=0.200x9.81x9.81=0.785 J
Gain in EPE=0.5 Fx=0.392J

Why are the two answers different?

Furthermore, if the spring is set into SHM with amplitude 0.200m, what is the resultant force at the lowest point of movement?

in your gpe calc you use g twice and have no mass. Where Are you getting F for your epe? spell it out a little more for us.
 
Opps I typed too fast. I don't really understand why the EPE is so though...though I listed out the step according to answer scheme given. Anyone can help clarify?

Thanks.
 
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