Copyright © 2012 Pearson Education Inc. PowerPoint ® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Chapter 6 Work and Kinetic Energy Modifications by Mike Brotherton

Copyright © 2012 Pearson Education Inc. Goals for Chapter 6 To understand and calculate the work done by a force To understand the meaning of kinetic energy To learn how work changes the kinetic energy of a body and how to use this principle To relate work and kinetic energy when the forces are not constant or the body follows a curved path To solve problems involving power

Copyright © 2012 Pearson Education Inc. Introduction The simple methods we’ve learned using Newton’s laws are inadequate when the forces are not constant. In this chapter, the introduction of the new concepts of work, energy, and the conservation of energy will allow us to deal with such problems.

Copyright © 2012 Pearson Education Inc. Work A force on a body does work if the body undergoes a displacement. Figures 6.1 and 6.2 illustrate forces doing work.

Copyright © 2012 Pearson Education Inc. Work done by a constant force The work done by a constant force acting at an angle  to the displacement is W = Fs cos . Figure 6.3 illustrates this point. Follow Example 6.1.

Copyright © 2012 Pearson Education Inc. Positive, negative, and zero work A force can do positive, negative, or zero work depending on the angle between the force and the displacement. Refer to Figure 6.4.

Copyright © 2012 Pearson Education Inc. Kinetic energy The kinetic energy of a particle is K = 1/2 mv 2. The net work on a body changes its speed and therefore its kinetic energy, as shown in Figure 6.8 below.

Copyright © 2012 Pearson Education Inc. The work-energy theorem The work-energy theorem: The work done by the net force on a particle equals the change in the particle’s kinetic energy. Mathematically, the work-energy theorem is expressed as W tot = K 2 – K 1 =  K. Follow Problem-Solving Strategy 6.1.

Copyright © 2012 Pearson Education Inc. Work and energy with varying forces—Figure 6.16 Many forces, such as the force to stretch a spring, are not constant. In Figure 6.16, we approximate the work by dividing the total displacement into many small segments.

Copyright © 2012 Pearson Education Inc. Stretching a spring The force required to stretch a spring a distance x is proportional to x: F x = kx. k is the force constant (or spring constant) of the spring. The area under the graph represents the work done on the spring to stretch it a distance X: W = 1/2 kX 2.

Copyright © 2012 Pearson Education Inc. Work done on a spring scale A woman steps on a bathroom scale. Follow Example 6.6.

Copyright © 2012 Pearson Education Inc. Motion with a varying force An air-track glider is attached to a spring, so the force on the glider is varying. Follow Example 6.7 using Figure 6.22.

Copyright © 2012 Pearson Education Inc. Power Power is the rate at which work is done. Average power is P av =  W/  t and instantaneous power is P = dW/dt. The SI unit of power is the watt (1 W = 1 J/s), but other familiar units are the horsepower and the kilowatt-hour.

Copyright © 2012 Pearson Education Inc. Work done by several forces Example 6.2 shows two ways to find the total work done by several forces. Follow Example 6.2.

Copyright © 2012 Pearson Education Inc. Using work and energy to calculate speed Revisit the sled from Example 6.2. Follow Example 6.3 using Figure 6.11 below and Problem-Solving Strategy 6.1.

Copyright © 2012 Pearson Education Inc. Forces on a hammerhead The hammerhead of a pile driver is used to drive a beam into the ground. Follow Example 6.4 and see Figure 6.12 below.

Copyright © 2012 Pearson Education Inc. Comparing kinetic energies In Conceptual Example 6.5, two iceboats have different masses. Follow Conceptual Example 6.5.

Copyright © 2012 Pearson Education Inc. Motion on a curved path—Example 6.8 A child on a swing moves along a curved path. Follow Example 6.8 using Figure 6.24.

Copyright © 2012 Pearson Education Inc. Force and power In Example 6.9, jet engines develop power to fly the plane. Follow Example 6.9.

Copyright © 2012 Pearson Education Inc. A “power climb” A person runs up stairs. Refer to Figure 6.28 while following Example 6.10.