Chapter 6

1. Chapter 6 Work and Kinetic Energy

2. 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

3. 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.

4. Work • A force on a body does work if the body undergoes a displacement. • Figures 6.1 and 6.2 illustrate forces doing work.

5. 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.

6. 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.

7. Work done by several forces • Example 6.2 shows two ways to find the total work done by several forces. • Follow Example 6.2.

8. Kinetic energy • The kinetic energy of a particle is K = 1/2 mv2. • The net work on a body changes its speed and therefore its kinetic energy, as shown in Figure 6.8 below.

9. 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 Wtot = K2 – K1 = K. • Follow Problem-Solving Strategy 6.1.

10. 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.

11. 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.

12. Comparing kinetic energies • In Conceptual Example 6.5, two iceboats have different masses. • Follow Conceptual Example 6.5.

13. 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.

14. Stretching a spring • The force required to stretch a spring a distance x is proportional to x: Fx = 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 kX2.

15. Work done on a spring scale • A woman steps on a bathroom scale. • Follow Example 6.6.

16. 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.

17. 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.

18. Power • Power is the rate at which work is done. • Average power is Pav = 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.

19. Force and power • In Example 6.9, jet engines develop power to fly the plane. • Follow Example 6.9.

20. A “power climb” • A person runs up stairs. Refer to Figure 6.28 while following Example 6.10.