Work and Kinetic Energy Chapter 6 Work and Kinetic Energy

To understand and calculate the work done by a force 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

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.

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

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.

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.

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

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.

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.

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.

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.

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

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.

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.

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

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.

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.

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.

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

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