3.4 Energy p Work Work is done on a body when a force, F, or a component of that force acts on the body, causing it to be displaced some distance, d. W = F ║ x D Work = Force parellel x distance (Units: 1 Joule = 1 Newton * meter) (Units: 1 J = 1 N * m) FAFA F║F║ d ѳ W = (F x cos ѳ ) x d F ║ = F A x cos ѳ

3.4 Energy p. 96 Work Done by a Changing Force 1. Area under force-distance graph with varying force This graph shows three different force being used to push a lab cart three different distances. The total work done is the sum of the work done through each separate distance, A, B, and C. The work done during each distance is the area under graph line for each section. W T = W A + W B + W C Total work done.

3.4 Energy p Area under a force-distance graph with average force In this case the force continually changes as the spring is stretched over distance. The average force will have to be used to determined the total work done. W T = F ave x d F ave = (F 1 + F 2 ) 2 F ave = ( ) 2 W T = 3.0 N x 0.5 m = 1.5 J

3.4 Energy p Area under a force-distance graph with force changing radically with distance In this case the force is changing so dramatically that a simple way of determining the force is not available. Although the area under the curve is still equal to the work done, determining this area is not simple. One could try making very small rectangles and solving for each rectangles area and then adding up all those areas or one could wait until one learns calculus to determine the total work done.

3.4 Energy p. Kinetic Energy Any object that has mass and is moving contains kinetic energy. E k = ½ mv 2 Since work is done to acceleration an object to some speed: W = ½ mv ½ mv 1 2 v1v1 v2v2 W = ΔE k

3.4 Energy p Potential Energy Potential energy is stored energy. The energy could be stored in chemical bonds, chemical Potential energy, in stretching materials, Elastic potential energy or moving an object against a gravitational field, gravitational potential energy. h Gravitation Potential Energy E P = mgh Elastic Potential Energy E p = ½ kx 2 x

3.4 Energy p. 101 Power Power is the rate at which work is done or the rate at which energy is transformed from one form to another. Power = Work done Time Energy transformed Time = P = W t (Units: 1 Watt = 1 Joule/sec = 1 J/s) 1 horsepower (hp) = 750 W A common unit for measuring power is a horsepower, the work done by a horse in a given time period.

3.4 Energy In this section, you should understand how to solve the following key questions. Page # Work and Components #1– 3 Page#98Quick Check #1 – 2 Page#99Quick Check #1 – 3 Page#100 Quick Check #1 – 3 Page#101 Quick Check #1 – 3 Page #104 – Review Questions #1 - 16