Conservative Forces

1. Conservative Forces

2. Path Dependence • What happens to work as a rollercoaster goes down hill then up again? • What if the roller coaster took a less steep path?

3. Gravitational Work • The work done by the force of gravity only depends on the vertical distance. y2 d F = -mg h h q y1 The path taken doesn’t matter

4. Elastic Work • The elastic force exerted by a spring becomes work. • W = -(1/2) kx2 • The work done by the spring as it compresses is negative. • Like gravity the path taken to the end doesn’t matter. Ws = -(1/2)ky2 Fs = -k(-y) -y

5. Reversible Process • If an object is acted on by gravity or elastic force has its path reversed the work done is the opposite sign. • This represents a reversible process. y2 F = -mg h y1

6. Closed Path • If the work done by a force doesn’t depend on the path it is a conservative force. • Conservative forces do no work on a closed path. From 1 to 2, the path A or B doesn’t matter From 1 to 2 and back to 1, the path A then the reverse path B gives no work

7. Nonconservative Force • Not all forces are conservative. • In particular, friction and drag are not conservative. d Negative work is done by friction to get here F = -mFN -d Negative work is also done returning the box F = mFN next