# PHYS 2211 Module 7.3

## The Work-Energy Theorem

Recommended Reading

7.3 The Work-Energy Theorem

### Learning Objectives

By the end of this section, you will be able to:

• Apply the work-energy theorem to find information about the motion of a particle, given the forces acting on it
• Use the work-energy theorem to find information about the forces acting on a particle, given information about its motion

### The Work-Energy Theorem

The net work done on a particle equals the change in the particle’s kinetic energy:

#### Problem-Solving Strategy: Work-Energy Theorem

1. Draw a free-body diagram for each force on the object.
2. Determine whether or not each force does work over the displacement in the diagram. Be sure to keep any positive or negative signs in the work done.
3. Add up the total amount of work done by each force.
4. Set this total work equal to the change in kinetic energy and solve for any unknown parameter.
5. Check your answers. If the object is traveling at a constant speed or zero acceleration, the total work done should be zero and match the change in kinetic energy. If the total work is positive, the object must have sped up or increased kinetic energy. If the total work is negative, the object must have slowed down or decreased kinetic energy.

Discuss!

Consider how you would answer these questions. Then bring this to class for a group discussion.

(a) A 5.33 kg block initially at rest is pulled to the right along a horizontal, frictionless surface by a constant horizontal force of 8.0 N. Find the block’s speed after it has moved 7.9 m.

(b) Suppose that the magnitude of the force is doubled. Through what displacement will the block travel before reaching the same final speed found above?

Practice!

Practice!

Discuss!

Consider how you would answer these questions. Then bring this to class for a group discussion.

A 1-kg particle moving along the x-axis experiences the force shown in the graph. If the particle’s speed is 2 m/s at x = 0 m, what is its speed when it gets to x = 5 m?