Potential Energy

Conservative force fields, gravitational, and elastic potential energy functions.

General idea of the topic

Potential energy is the energy associated with the position or configuration of a system under a conservative force. The work of that force does not depend on the path, only on the initial and final points, and equals minus the change in potential energy.

The topic studies two cases: gravitational potential energy, mgh near the surface, which depends on the height above a reference level, and elastic potential energy, ½kx² in a spring, which depends on its deformation.

What you will truly understand

By the end you will be able to compute the potential energy of both kinds, choose a convenient reference level and relate the force to the slope of the potential energy.

You will also know that only changes in potential energy matter, not its absolute value.

Recommended learning route

1. Gravitational Potential Energy: U = mgh, reference level and work of weight in rises and falls.
2. Elastic Potential Energy: U = ½kx², parabolic graph and work of the spring.

Physical criterion you must acquire

The essential criterion is to fix the reference level at the start and keep it throughout the problem: the value of U changes when it is moved, but ΔU does not. The elastic energy depends on the square of the deformation and therefore does not distinguish between stretching and compressing. The force is F = −dU/dx.

Connection with real problems

• dams and hydroelectric plants.
• springs, shock absorbers and trampolines.
• jumps and throws.
• energy storage.

Final goal of the topic

The final goal is to compute potential energies and use them to solve motion problems without knowing the forces at each instant.