# PHYS 2211 Module 8.2

## Conservative and Non-Conservative Forces

8.2 Conservative and Non-Conservative Forces

### Learning Objectives

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

• Characterize a conservative force in several different ways
• Specify mathematical conditions that must be satisfied by a conservative force and its components
• Relate the conservative force between particles of a system to the potential energy of the system
• Calculate the components of a conservative force in various cases

### Conservative Forces

The work done by a conservative force is independent of the path; in other words, the work done by a conservative force is the same for any path connecting two points:

The work done by a non-conservative force depends on the path taken.

Equivalently, a force is conservative if the work it does around any closed path is zero:

Discuss!

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

A single conservative force acts on a 4.80-kg particle within a system due to its interaction with the rest of the system. The equation Fx = 2x + 4 describes the force, where Fx is in newtons and x is in meters. As the particle moves along the x axis from x = 1.00 m to x = 4.51 m, calculate the following.

(a) the work done by this force on the particle

(b) the change in the potential energy of the system

(c) the kinetic energy the particle has at x = 4.51 m if its speed is 3.00 m/s at x = 1.00 m

### Gravitational Potential Energy and Elastic Potential Energy

Discuss!

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

A hockey puck slides without friction along a frozen lake toward an ice ramp and plateau as shown.  The speed of the puck is 4 m/s and the height of the plateau is 1 m.  Will the puck make it all the way up the ramp?

Practice!

Practice!