A spring with k = 100 N/m is stretched so that the displacement from equilibrium is 0.25 m. What is the potential energy stored in the spring?

A spring with k = 100 N/m is stretched so that the displacement from equilibrium is 0.25 m. What is the potential energy stored in the spring?

• A. 3.125 J
• B. 0.3125 J
• C. 6.25 J
• D. 1.0 J

Answer: (A)

Stretching or compressing a spring stores energy proportional to the square of how far you are from equilibrium, described by U = 1/2 k x^2. With k = 100 N/m and x = 0.25 m, the energy is U = 0.5 × 100 × (0.25)^2 = 50 × 0.0625 = 3.125 J. So the spring stores 3.125 joules of potential energy. Using a different formula or forgetting the square would give different numbers, which is why this value is the correct one.

Stretching or compressing a spring stores energy proportional to the square of how far you are from equilibrium, described by U = 1/2 k x^2. With k = 100 N/m and x = 0.25 m, the energy is U = 0.5 × 100 × (0.25)^2 = 50 × 0.0625 = 3.125 J. So the spring stores 3.125 joules of potential energy. Using a different formula or forgetting the square would give different numbers, which is why this value is the correct one.