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

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SUMMARY

The discussion centers 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 calculations provided indicate a loss in GPE of 0.785 J and a gain in EPE of 0.392 J. The confusion arises from the different energy values and the need for clarification on the calculation of EPE, particularly the force used in the equation. Additionally, the discussion touches on the resultant force in simple harmonic motion (SHM) at the lowest point of movement.

PREREQUISITES
  • Understanding of gravitational potential energy (GPE) calculations
  • Familiarity with elastic potential energy (EPE) formulas
  • Knowledge of simple harmonic motion (SHM) principles
  • Basic physics concepts related to forces and energy conservation
NEXT STEPS
  • Review the derivation of gravitational potential energy (GPE) formulas
  • Study the calculation methods for elastic potential energy (EPE) in springs
  • Explore the principles of simple harmonic motion (SHM) and its equations
  • Investigate the relationship between force, mass, and energy in mechanical systems
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Students studying physics, educators teaching energy concepts, and anyone interested in understanding the mechanics of springs and energy transformations in physical systems.

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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