Introduction

4.1 Introduction

In the previous chapter, we developed a complete language for describing motion — position, velocity, acceleration — all in quantitative terms. Uniform motion required only the concept of velocity; non-uniform motion brought in acceleration. But description is not explanation. We never asked what causes motion to begin with, or what makes it change. That is the question we now turn to.

The Common-Sense View of Force

Everyday experience gives a clear, intuitive answer: to move something that is at rest, you must push or pull it. A football lying on the ground does not move until someone kicks it. To throw a stone upward, you have to give it an upward push. A breeze makes tree branches swing; a strong wind can shift heavy objects. A boat drifts downstream in a flowing river without anyone rowing it — the water itself provides the push.

In all these cases, some external agency supplies a force. The same holds for stopping or slowing a moving object. A ball rolling down an inclined plane can be stopped by applying a force opposite to its direction of motion. So force appears to be the agent that starts motion, stops motion, or changes motion.

Action at a Distance

A stone released from the top of a building accelerates downward. No hand pushes it; no string pulls it. The cause is the gravitational pull of the Earth, acting across empty space. Similarly, a bar magnet attracts an iron nail from a distance without touching it. These are examples of non-contact forces — gravitational and magnetic forces — that can act on a body even when the agency is not in physical contact.

So the first big idea is this: a force is required to put a stationary body into motion, or to stop a moving body, or to change its motion in any way. And the external agency that provides this force may or may not be in contact with the body.

The Deeper Question: Uniform Motion

Now consider a different situation. A skater glides across a horizontal ice slab in a straight line at constant speed. No one is pushing her; she is not applying any force. Yet she continues to move uniformly. Is an external force required to keep a body in uniform motion?

This question — seemingly simple — has a long and tangled history. It leads directly to the central puzzle of the chapter: what is the true relationship between force and motion? The answer, as we will see, is not what common sense suggests. The next section takes up Aristotle's answer, which dominated thinking for nearly two thousand years, and the fallacy at its heart.