Equilibrium revisited

Constant speed when the resultant force is equal to zero

The central idea of this episode is laid out in Newton's first law of motion and can be summarised as follows:

When an object is moving at constant speed there is no resultant force acting on it.

Or alternatively:

When an object is moving at constant speed the resultant force acting on it is zero.

A rather special constant speed is zero: that's what Alice recorded for her handbag, as she was – as seen from both Bob's and Charlie's points of view – co-moving with it. Many of the examples in the SPT: Forces topic, in equilibrium, that just sat beside us on the laboratory bench, with a constant speed of zero, had forces that added to zero.

Now generalise to any constant speed: you can do this by switching to another's point of view. For example, from Alice to Charlie, or from Alice to Bob.

A resultant force of zero might be achieved because there are no forces acting at all (unlikely in the real world, but possible in the farthest corner of the universe).

Alternatively, it might be that there are forces acting but they add to nothing: the resultant force is zero. In the simplest case, there might be a forward driving force and a backwards retarding force. The retarding force is most often a frictional force: some combination of grip, slip and drag. Indeed, in everyday situations when objects are moving, the frictional force is always present to oppose the motion. The frictional force balances the driving force and thereby cancels its effect.

It does not matter whether the value of the speed is 2 metre / second, 3 metre / second, 20 metre / second or 40 metre / second, if the speed is constant then the forces add to zero and the retarding force is equal to the driving force. The resultant force is zero.

Some examples of constant motion

Here is an example of constant motion: a person sliding a heavy box along the ground at a constant speed.

Use the interactive diagram to explore the most significant forces acting on the person, the box and the ground. Notice how the forces acting on the box add to zero, leading to a constant motion.

The constant speed cyclist

A cyclist moving at a constant speed provides a driving force through the action of their legs, turning the back wheel against the ground, whilst the ground and the air provide retarding forces. When the bicycle is travelling at a constant speed these retarding forces balance the driving force. Use the interactive diagram to see how the forces balance, resulting in motion at a constant speed. (If you doubt that the ground provides retarding forces, try pedalling with a flatter tyre, or across bumpier ground.)