Elastic potential energy

Definition

Elastic potential energy is the energy stored in elastic materials as a result of their stretching or compressing. It is quantified by the equation $U = \frac{1}{2} k x^2$, where $k$ is the spring constant and $x$ is the displacement from equilibrium.

5 Must Know Facts For Your Next Test

1. Elastic potential energy depends on both the spring constant $k$ and the displacement $x$ squared.
2. The unit of elastic potential energy is Joules (J).
3. It can be converted entirely into kinetic energy in an ideal, frictionless system.
4. Hooke's Law, which states that $F = -kx$, describes the force exerted by a spring, directly relating to elastic potential energy.
5. In simple harmonic motion, the total mechanical energy is conserved and oscillates between kinetic and elastic potential energy.

Review Questions

• What variables determine the amount of elastic potential energy stored in a spring?
• How does Hooke's Law relate to elastic potential energy?
• What happens to elastic potential energy during one complete cycle of simple harmonic motion?

Related terms

Spring Constant: A measure of a spring's stiffness, denoted by $k$, with units N/m.

Simple Harmonic Motion: Oscillatory motion under a restoring force proportional to displacement, typically described by sinusoidal functions.

Kinetic Energy: The energy an object possesses due to its motion, given by $KE = \frac{1}{2} mv^2$.