# Is there more energy stored within a spring resistant to stretch?

I m doing a lab for physics.

We put equal masses on two different springs.

One spring stretched further than the other spring under the same amount of force.

Which spring stores the most potential energy and how does elasticity relate to the storing of potential energy.

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I believe Randy P has answered correctly.

Let's say the two springs had spring constants that were in 1/2 ratio.

In other words, the stiffer spring would stretch only 1/2 the amount under the same force (weight).

SPE {Spring Potential Energy} = 1/2(spring constant)x² {where x = stretch amt}

With the same force acting on both springs, the stretch of the stiffer one would be 1/2 of the other.

Let k = stiffer spring's constant

Let x = amount of stretch of stiffer spring under the constant force mentioned above

The SPE of the stiffer spring = 1/2kx²

Compare that with the SPE of the other (less stiff) spring = 1/2(k/2)(2x)² = 1/2k(4/2)x² = kx²

So the LESS stiff spring stores a greater SPE in this vertical hanging weight example.

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• The mass lost gravitational potential energy mgh from going down a distance h. This energy is being stored in the spring as potential energy.

Which spring has a larger value of mgh? That's the one with the most stored energy.

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