Potential Energy, Kinetic Energy, and the Work-Energy Theorem for AP Physics B & C

Practice problems for these concepts can be found at: Energy Conservation Practice Problems for AP Physics B & C

Kinetic Energy and the Work-Energy Theorem

We'll start with some definitions.

What this second definition means is that work equals the product of the distance an object travels and the component of the force acting on that object directed parallel to the object's direction of motion. That sounds more complicated than it really is: an example will help.

A box is pulled along the floor, as shown in Figure 14.1. It is pulled a distance of 10 m, and the force pulling it has a magnitude of 5 N and is directed 30° above the horizontal. So, the force component that is PARALLEL to the 10 m displacement is (5 N)(cos 30°).

One newton. meter is called a joule, abbreviated as 1 J.

• Work is a scalar. So is energy.
• The units of work and of energy are joules.
• Work can be negative … this just means that the force is applied in the direction opposite displacement.

This means that the kinetic energy of an object equals one half the object's mass times its speed squared.

The net work done on an object is equal to that object's change in kinetic energy. Here's an application:

Here, because the only horizontal force is the force of the brakes, the work done by this force is W_net.

Let's pause for a minute to think about what this value means. We've just calculated the change in kinetic energy of the train car, which is equal to the net work done on the train car. The negative sign simply means that the net force was opposite the train's displacement. To find the force:

Potential Energy

Potential energy comes in many forms: there's gravitational potential energy, spring potential energy, electrical potential energy, and so on. For starters, we'll concern ourselves with gravitational potential energy.

Gravitational PE is described by the following equation:

PE = mgh

In this equation, m is the mass of an object, g is the gravitational field of 10 N/kg on Earth, and h is the height of an object above a certain point (called "the zero of potential").³ That point can be wherever you want it to be, depending on the problem. For example, let's say a pencil is sitting on a table. If you define the zero of potential to be the table, then the pencil has no gravitational PE. If you define the floor to be the zero of potential, then the pencil has PE equal to mgh, where h is the height of the pencil above the floor. Your choice of the zero of potential in a problem should be made by determining how the problem can most easily be solved.

REMINDER: h in the potential energy equation stands for vertical height above the zero of potential.

Practice problems for these concepts can be found at: Energy Conservation Practice Problems for AP Physics B & C