Work, Energy, and Power

Learning Objectives

Define work in the physics context and calculate it using W = Fd cos(θ).

Define and calculate kinetic energy (KE = ½mv²) and gravitational potential energy (PE = mgh).

State and apply the Principle of Conservation of Energy.

Define and calculate power (P = W/t).

The Language of Energy Transfer

In physics, work, energy, and power have very specific definitions that describe how forces and motion relate to energy.

Work

Work (W) is done when a force causes a displacement of an object. For work to be done, the force must have a component in the direction of the motion.

Formula: W = Fd cos(θ)

F is the magnitude of the applied force.

d is the magnitude of the displacement.

θ is the angle between the force vector and the displacement vector.

The SI unit of work is the Joule (J). One joule is the work done by a force of one newton acting over a distance of one meter.

Energy

Energy (E) is the capacity to do work. It also has the unit of Joules.

Kinetic Energy (KE): The energy of motion.

Formula: KE = ½mv²

m is the mass of the object.

v is the speed of the object.

Potential Energy (PE): Stored energy due to an object's position or configuration.

Gravitational Potential Energy (PEg): Energy stored due to an object's height in a gravitational field.

Formula: PE = mgh

m is the mass, g is the acceleration due to gravity (~9.8 m/s² on Earth), and h is the height relative to a zero point.

The Work-Energy Theorem and Conservation of Energy

Work-Energy Theorem: The net work done on an object equals the change in its kinetic energy (W_net = ΔKE).

Principle of Conservation of Energy: In an isolated system, the total energy remains constant. Energy can be transformed from one form to another (e.g., potential to kinetic), but it cannot be created or destroyed.

Formula: KEᵢ + PEᵢ = KEₒ + PEₒ

This is a powerful tool for solving problems involving falling objects, roller coasters, and pendulums where energy is converted between kinetic and potential forms.

Power

Power (P) is the rate at which work is done or energy is transferred.

Formula: P = W/t = ΔE/t

W is the work done, and t is the time taken.

The SI unit of power is the Watt (W). One watt is equal to one joule per second (1 J/s).

A more powerful engine can do the same amount of work in less time.

Key Terms

Work: In physics, the measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement. Measured in Joules (J).
Kinetic Energy: The energy which an object possesses due to its motion, equal to one half the mass of the body times the square of its speed (KE = ½mv²).
Potential Energy: The energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Gravitational potential energy is PE = mgh.
Power: The rate of doing work or of transferring heat, i.e., the amount of energy transferred or converted per unit time. Measured in Watts (W).