6. Work and Energy Work Definitions: This is line integral Example: Find work done by a force on a particle that is moving from the origin to the point P=(1,1) along three shown below paths if the force is a) From (0,0) to (0,1) to (1,1): b) From (0,0) to (1,1) along straight line, so that x=y: c) From (0,0) to (1,1) along a quarter circle centered at (0,1): 1

Work-Kinetic energy theorem definition Newton’s law definition Definition: (kinetic energy) 2

mg θ θ dr = rdθ r rim Example: Find the work done by gravity on a pebble of mass m as it rolls from the rim to the bottom of a spherical bowl of radius r. B A 3

4 Potential energy and conservative forces is path independent Definition of potential energy: Conservation of mechanical energy: Definition of conservative forces: Nonconservative forces:

5 Example: