Conservative Forces

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?

Gravitational Work  The work done by the force of gravity only depends on the vertical distance. d F =  mg h  h The path taken doesn’t matter y2y2 y1y1

Elastic Work  The elastic force exerted by a spring becomes work. W =  (1/2) kx 2W =  (1/2) kx 2 The work done by the spring as it compresses is negative.The work done by the spring as it compresses is negative.  Like gravity the path taken to the end doesn’t matter. -y W s =  ky 2 F s = -k(-y)

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. y1y1 F =  mg h y2y2

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

Nonconservative Force  Not all forces are conservative.  In particular, friction and drag are not conservative. next Negative work is done by friction to get here Negative work is also done returning the box F =  F N d dd F =  F N