Chapter 6: Work and Energy

1. Chapter 6: Work and Energy Christopher Chui Chapter 6: Work and Energy - Christopher Chui

2. Work Done by a Constant Force • Work is defined to be the product of the magnitude of the displacement times the component of the force parallel to the displacement, or W = Fd cos q • Unit for work is joule, or 1 J = 1 N-m • In British units, work is in ft-lb. • 1 J = 107 ergs = 0.7376 ft-lb. • A force can be exerted on an object and yet do NO work Chapter 6: Work and Energy - Christopher Chui

3. Problem Solving for Work • Choose an xy coordinate system // to the plane • Draw a free body diagram showing all forces • Determine any unknown force • Find the work done by a specific force on the body by using W = Fd cos q • Find the net work done on the body either adding algebraically work done by each force, or find the net force on the object, and use Wnet = Fnetd cos q Chapter 6: Work and Energy - Christopher Chui

4. Translational Kinetic Energy • KE = ½ mv2 • Work-Energy Principle: Wnet = DKE • The net work done on an object is equal to the change in its kinetic energy • If the net work done on an object is positive, then the object’s kinetic energy increases; if the net work done is negative, then the KE decreases; if the work done is 0, then the KE is constant (its speed is constant) Chapter 6: Work and Energy - Christopher Chui

5. Potential Energy • Potential energy is the energy associated with forces that depend on the position of a body • The most common PE is gravitational PE • PEgravitation = mgy • Change in PE is physically meaningful • Change in PE is the work required of an external force to move the object without acceleration between the two points • Spring equation (Hooke’s law): Fs = - kx • Elastic PE = ½ kx2 Chapter 6: Work and Energy - Christopher Chui

6. Conservative and Nonconservative Forces • Conservative forces: gravitational, elastic, electric • Nonconservative forces: friction, air resistance, tension in a cord, motor or rocket propulsion, push or pull by a person • PE can be defined only for a conservative force • WNC = DKE + DPE Chapter 6: Work and Energy - Christopher Chui

7. Conservation of Mechanical Energy • If only conservative forces are acting, the total mechanical energy of a system neither increases nor decreases in ANY process. It stays constant—it is constant • KE2 + PE2 = KE1 + PE1 • Conservation of energy when PE is elastic • Conservation of energy when only gravity acts • Frictional forces are dissipative forces, because they reduce the total mechanical energy Chapter 6: Work and Energy - Christopher Chui

8. Problem Solving—Conservation of Energy • Draw a force diagram • Determine the system for which energy will be conserved • Decide the initial and final locations • If the body changes height, choose the lowest point to be 0 • If springs are involved, choose the unstretched spring position to be x (or y) = 0 • If no friction or other nonconservative forces act, then apply conservation of mechanical energy • Solve for the unknown quantity • If friction is present, add WNC = DKE + DPE Chapter 6: Work and Energy - Christopher Chui

9. Power • Power is the rate at which work is done • Average power = work / time = energy transformed / time • 1 watt = 1 J/s • 1 horsepower = 550 ft-lb/s = 746 W Chapter 6: Work and Energy - Christopher Chui