Which equation represents elastic potential energy?

Which equation represents elastic potential energy?

• A. PE = mv^2
• B. PE = \frac{1}{2}kx^2
• C. PE = mgh
• D. PE = W/t

Answer: (B)

The equation that represents elastic potential energy is \( PE = \frac{1}{2}kx^2 \). This formula is derived from Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is compressed or stretched from its rest position (denoted as \( x \)). In this context, \( k \) is the spring constant, which measures how stiff the spring is; a larger \( k \) indicates a stiffer spring. When a spring is compressed or stretched, work is done against the spring's restoring force, and this work is stored as elastic potential energy. The factor of \( \frac{1}{2} \) in the equation arises from integrating the force over the distance stretched/compressed, leading to this specific form. This equation is specifically applicable to spring systems and is essential for understanding energy storage in elastic materials. It highlights how the energy stored in a spring increases with the square of the displacement from the equilibrium position, meaning even small stretches or compressions can significantly increase the potential energy stored in the system.

The equation that represents elastic potential energy is ( PE = \frac{1}{2}kx^2 ). This formula is derived from Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is compressed or stretched from its rest position (denoted as ( x )). In this context, ( k ) is the spring constant, which measures how stiff the spring is; a larger ( k ) indicates a stiffer spring.

When a spring is compressed or stretched, work is done against the spring's restoring force, and this work is stored as elastic potential energy. The factor of ( \frac{1}{2} ) in the equation arises from integrating the force over the distance stretched/compressed, leading to this specific form.

This equation is specifically applicable to spring systems and is essential for understanding energy storage in elastic materials. It highlights how the energy stored in a spring increases with the square of the displacement from the equilibrium position, meaning even small stretches or compressions can significantly increase the potential energy stored in the system.