The friction force $\vec{f}{}_{\text{P}}$ (force of surface on person) is an example of propulsion. It is the force that a system with an internal source of energy uses to drive itself forward. Propulsion is an important feature not only of walking or running but also of the forward motion of cars, jets, and rockets. Propulsion is somewhat counterintuitive, so it is worth a closer look.

If you try to walk across a frictionless floor, your foot slips and slides backward. In order for you to walk, the floor needs to have friction so that your foot sticks to the floor as you straighten your leg, moving your body forward. The friction that prevents slipping is static friction. Static friction, you will recall, acts in the direction that prevents slipping. The static friction force $\vec{f}{}_{\text{P}}$ has to point in the forward direction to prevent your foot from slipping backward. It is this forward-directed static friction force that propels you forward! The force of your foot on the floor, the other half of the action/reaction pair, is in the opposite direction.

The distinction between you and the crate is that you have an internal source of energy that allows you to straighten your leg by pushing backward against the surface. In essence, you walk by pushing the earth away from you. The earth’s surface responds by pushing you forward. These are static friction forces. In contrast, all the crate can do is slide, so kinetic friction opposes the motion of the crate.

FIGURE 7.7 shows how propulsion works. A car uses its motor to spin the tires, causing the tires to push backward against the ground. This is why dirt and gravel are kicked backward, not forward. The earth’s surface responds by pushing the car forward. These are also static friction forces. The tire is rolling, but the bottom of the tire, where it contacts the road, is instantaneously at rest. If it weren’t, you would leave one giant skid mark as you drove and would burn off the tread within a few miles.

FIGURE 7.7 Examples of propulsion.

EXAMPLE 7.2 Towing a car

A tow truck uses a rope of negligible mass to pull a car along a horizontal road, as shown in FIGURE 7.8. Identify all interactions, show them on an interaction diagram, then draw free-body diagrams of each object in the system.

FIGURE 7.8 A truck towing a car.

VISUALIZE The interaction diagram of FIGURE 7.9 represents the objects as separate circles, but with the correct relative positions. The rope is shown as a separate object, but the description “negligible mass” means that we can ignore the gravitational force on the rope. Many of the interactions are identical to those in Example  7.1. The system—the objects in motion—consists of the truck, the rope, and the car.

FIGURE 7.9 The interaction diagram.

FIGURE 7.9 Full Alternative Text

The three objects in the system require three free-body diagrams, shown in FIGURE 7.10. Gravity, friction, and normal forces at the surface are all interactions that cross the system boundary and are shown as external forces. The car is an inert object rolling along. It would slow and stop if the rope were cut, so the surface must exert a rolling friction force $\vec{f}{}_{\text{C}}$ to the left. The truck, however, has an internal source of energy. The truck’s drive wheels push the ground to the left with force $\vec{f}{}_{\text{T on S}}$. In reaction, the ground propels the truck forward, to the right, with force $\vec{f}{}_{\text{T}}$.

FIGURE 7.10 Free-body diagrams of Example 7.2.

FIGURE 7.10 Full Alternative Text

We next need to identify the forces between the car, the truck, and the rope. The rope pulls on the car with a tension force $\vec{T}{}_{\text{R on C}}$. You might be tempted to put the reaction force on the truck because we say that “the truck pulls the car,” but the truck is not in contact with the car. The truck pulls on the rope, then the rope pulls on the car. Thus the reaction to $\vec{T}{}_{\text{R on C}}$ is a force on the rope: $\vec{T}{}_{\text{C on R}}$. These are an action/reaction pair. At the other end, $\vec{T}{}_{\text{T on R}}$ and $\vec{T}{}_{\text{R on T}}$ are also an action/reaction pair.

NOTE   Drawing an interaction diagram helps you avoid mistakes because it shows very clearly what is interacting with what.

REVIEW Make sure you avoid the common error of considering $\vec{n}$ and $\vec{F}{}_{\text{G}}$ to be an action/reaction pair. These are both forces on the same object, whereas the two forces of an action/reaction pair are always on two different objects that are interacting with each other. The normal and gravitational forces are often equal in magnitude, as they are in this example, but that doesn’t make them an action/reaction pair of forces.