A spring with k = 200 N/m is stretched 0.10 m from its equilibrium position. What is the potential energy stored in the spring?

A spring with k = 200 N/m is stretched 0.10 m from its equilibrium position. What is the potential energy stored in the spring?

• A. 0.25 J
• B. 1.0 J
• C. 2.0 J
• D. 5.0 J

Answer: (B)

The quantity stored in a stretched or compressed spring is 1/2 k x^2, where k is the spring constant and x is the displacement from equilibrium. Here, k = 200 N/m and x = 0.10 m, so x^2 = 0.01 m^2. Plugging in: 1/2 × 200 × 0.01 = 100 × 0.01 = 1.0 J. The units work out as joules (N·m). The energy depends on the square of the displacement, so only how far from equilibrium matters, not the direction of the displacement. If the energy were 0.25 J, you’d need x ≈ 0.05 m; for 2.0 J, x ≈ 0.14 m; for 5.0 J, x ≈ 0.22 m. So the given stretch of 0.10 m yields 1.0 J of stored energy.

The quantity stored in a stretched or compressed spring is 1/2 k x^2, where k is the spring constant and x is the displacement from equilibrium. Here, k = 200 N/m and x = 0.10 m, so x^2 = 0.01 m^2. Plugging in: 1/2 × 200 × 0.01 = 100 × 0.01 = 1.0 J. The units work out as joules (N·m). The energy depends on the square of the displacement, so only how far from equilibrium matters, not the direction of the displacement. If the energy were 0.25 J, you’d need x ≈ 0.05 m; for 2.0 J, x ≈ 0.14 m; for 5.0 J, x ≈ 0.22 m. So the given stretch of 0.10 m yields 1.0 J of stored energy.