Final answer:
The energy stored per unit extension in a spring can be calculated using the formula PE = 1/2kx², where PE is the potential energy, k is the spring constant, and x is the extension or compression of the spring.
Step-by-step explanation:
The energy stored per unit extension in a spring is given by the formula PE = 1/2kx², where PE is the potential energy stored in the spring, k is the spring constant, and x is the extension or compression of the spring.
For example, if a spring has a constant of k = 10 N/m and is stretched or compressed by x = 0.1 m, the energy stored per unit extension would be PE = 1/2 * 10 * (0.1)² = 0.05 J.
In this equation, the spring constant measures how stiff the spring is, and the extension or compression measures how much the spring is stretched or compressed from its equilibrium position.
The student has asked about the energy stored per unit extension in a spring when it is stretched or compressed. The energy E stored in a spring with spring constant k can be calculated using the formula PE = 1/2 kx², where x is the displacement from its undeformed position.
To find the energy stored per unit extension, one would divide the potential energy by the extension, that is, E/k. Hence, the answer is (a) E/k.