Super quick question on spring and energy conservation

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SUMMARY

The conservation of energy in the context of springs is expressed through the equation for potential energy, specifically Us = 1/2 K x^2, where K is the spring constant and x is the displacement from the equilibrium position. The change in potential energy of the spring, denoted as [delta]Us, can be calculated by evaluating the difference in potential energy at two different displacements. This mirrors the approach used for gravitational potential energy, represented by Ug = mgh, where the change is determined by the difference in height.

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  • Understanding of Hooke's Law and spring constants
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  • Knowledge of gravitational potential energy calculations
  • Basic algebra for manipulating equations
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Students studying physics, particularly those focusing on mechanics and energy conservation principles, as well as educators seeking to clarify concepts related to springs and potential energy.

I_LoveCasey!
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Super quick question on spring and energy conservation!

Homework Statement


What does conservation of energy in equation form look like for spring?


Homework Equations



i know that [delta]K= k-k0
i know that [delta]Ug=mgh-mgh0

idk on [delta]Us= ...

The s,g stand for subscripts

The Attempt at a Solution


I thought that Us=1/2Kx^2 but it's not right
 
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Hi I_LoveCasey!,

I_LoveCasey! said:

Homework Statement


What does conservation of energy in equation form look like for spring?


Homework Equations



i know that [delta]K= k-k0
i know that [delta]Ug=mgh-mgh0

idk on [delta]Us= ...

The s,g stand for subscripts

The Attempt at a Solution


I thought that Us=1/2Kx^2 but it's not right

That is the formula for the potential energy of a spring. So if the spring displacement goes from x0 to x, what is the change in the springs potential energy?

(Do the same kind of thing that you did for the gravitational potential energy--the formula for gravitational potential energy is Ug=mgh, and so the change is the two terms that you have in your post.)
 

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