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

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

• A. 2 J
• B. 1 J
• C. 0.4 J
• D. 20 J

Answer: (B)

The energy stored in a spring when it is compressed or stretched comes from the work done to move it from its rest length. This energy is U = 1/2 k x^2, where k is the spring constant and x is the displacement from equilibrium. Here, k = 100 N/m and the compression is x = 0.2 m. Plugging in: U = (1/2) × 100 × (0.2)^2 = 50 × 0.04 = 2 J. So the spring stores 2 joules of potential energy. The 1 J option would come from misapplying the formula (missing the 1/2 factor). The energy grows with the square of the displacement, so doubling the compression would quadruple the energy.

The energy stored in a spring when it is compressed or stretched comes from the work done to move it from its rest length. This energy is U = 1/2 k x^2, where k is the spring constant and x is the displacement from equilibrium.

Here, k = 100 N/m and the compression is x = 0.2 m. Plugging in:

U = (1/2) × 100 × (0.2)^2 = 50 × 0.04 = 2 J.

So the spring stores 2 joules of potential energy. The 1 J option would come from misapplying the formula (missing the 1/2 factor). The energy grows with the square of the displacement, so doubling the compression would quadruple the energy.