A spring with k = 100 N/m is compressed by x = 0.2 m. What is the elastic potential energy stored?

• A. 0.5 J
• B. 20 J
• C. 2 J
• D. 200 J

Answer: (C)

Elastic potential energy in a spring comes from the work required to compress or stretch it. The energy stored is U = (1/2) k x^2, because the force in a spring is F = kx and integrating F with respect to x from 0 to the displacement gives the half-k times x-squared result.

With a spring constant k = 100 N/m and compression x = 0.2 m, the energy is U = 0.5 × 100 × (0.2)^2 = 2 joules. So the energy stored is 2 J. This shows why the value isn’t 0.5 J, 20 J, or 200 J: energy grows with the square of the displacement, so the given numbers yield 2 J rather than those other amounts.