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Question

A spring is compressed to one-third of its original compression. Compared with the energy stored initially (18 J), the new stored energy is _______.

The correct answer is

2 J

The elastic potential energy stored in a spring is \(U = \frac{1}{2}kx^2\), so \(U \propto x^2\).

The compression becomes one-third: \(x_2 = \frac{x_1}{3}\).

\(\frac{U_2}{U_1} = \left(\frac{x_2}{x_1}\right)^2 = \left(\frac{1}{3}\right)^2 = \frac{1}{9}\).

\(U_2 = \frac{18}{9} = 2\ \text{J}\).

Hence, the answer is 2 J.

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