A spring is compressed so as to add U units of potential energy to it. When this spring is instead stretched to one-half the distance it was compressed, its potential energy in the same units will be

1/4 of Ec

Explanation:

Given that a spring is compressed so as to add U units of potential energy to it. The elastic potential energy will be

Ec = 1/2Ke^2

When this spring is instead stretched to one-half the distance it was compressed, then new e = 1/2 e

Substitute e into the formula above.

Es = 1/2 × K × (1/2 × e)^2

Es = 1/2 × K × 1/4 × e^2

Or

Es = 1/4 × 1/2Ke^2

Substitute Ec into the Es above

Es = 1/4 of Ec

Therefore, its potential energy in the same units will be one - fourth of the potential energy when compressed.

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