5.1 Force

The two major issues that this chapter will examine are:

What is a force?
What is the connection between force and motion?

We begin with the first of these questions in the table below.

What is a force?

A force is a push or a pull.

Our commonsense idea of a force is that it is a push or a pull. We will refine this idea as we go along, but it is an adequate starting point. Notice our careful choice of words: We refer to “ $a$ force,” rather than simply “force.” We want to think of a force as a very specific action, so that we can talk about a single force or perhaps about two or three individual forces that we can clearly distinguish. Hence the concrete idea of “a force” acting on an object.

A force acts on an object.

Implicit in our concept of force is that a force acts on an object. In other words, pushes and pulls are applied to something—an object. From the object’s perspective, it has a force exerted on it. Forces do not exist in isolation from the object that experiences them.

A force requires an agent.

Every force has an agent, something that acts or exerts power. That is, a force has a specific, identifiable cause. As you throw a ball, it is your hand, while in contact with the ball, that is the agent or the cause of the force exerted on the ball. If a force is being exerted on an object, you must be able to identify a specific cause (i.e., the agent) of that force. Conversely, a force is not exerted on an object unless you can identify a specific cause or agent. Although this idea may seem to be stating the obvious, you will find it to be a powerful tool for avoiding some common misconceptions about what is and is not a force.

A force is a vector.

If you push an object, you can push either gently or very hard. Similarly, you can push either left or right, up or down. To quantify a push, we need to specify both a magnitude and a direction. It should thus come as no surprise that force is a vector. The general symbol for a force is the vector symbol $\vec{F}$ . The size or strength of a force is its magnitude F.

A force can be either a contact force . . .

There are two basic classes of forces, depending on whether the agent touches the object or not. Contact forces are forces that act on an object by touching it at a point of contact. The bat must touch the ball to hit it. A string must be tied to an object to pull it. The majority of forces that we will examine are contact forces.

. . . or a long-range force.

Long-range forces are forces that act on an object without physical contact. Magnetism is an example of a long-range force. You have undoubtedly held a magnet over a paper clip and seen the paper clip leap up to the magnet. A coffee cup released from your hand is pulled to the earth by the long-range force of gravity.

NOTE In the particle model, objects cannot exert forces on themselves. A force on an object will always have an agent or cause external to the object. Now, there are certainly objects that have internal forces (think of all the forces inside the engine of your car!), but the particle model is not valid if you need to consider those internal forces. If you are going to treat your car as a particle and look only at the overall motion of the car as a whole, that motion will be a consequence of external forces acting on the car.