The third law, weight and the normal force.

Step 1 of 6

Forces come in pairs

How does a fan move a cart? It pushes the air backwards, and the air pushes the fan, and the cart with it, forwards. Show the forces is On: behind the cart is the arrow of the fan pushing the air, and above it the arrow of the air pushing the cart.

This is Newton’s third law: when one body exerts a force on a second body, the second exerts a force on the first that is equal in size and opposite in direction. The two forces are called an action–reaction pair, but neither comes “first”: they appear together and vanish together.

Try it: change Fan push and follow the labels of the two arrows.

Back to the experiment ↑

Step 2 of 6

Why the pair does not cancel

If the two forces are equal and opposite, how does the cart accelerate? Think about it before you answer: which body does each of them act on?

Step 3 of 6

Weight

The Earth pulls every body downwards. That force is the body’s weight, and it equals the mass times the acceleration due to gravity, $g = 9.81\ \mathrm{m/s^2}$$g =$$9.81\ \mathrm{m/s^2}$⁠:

$W = m g$⁠

Mass and weight are two different things. Mass, in kilograms, is the amount of matter in a body and a measure of its inertia, and it is the same everywhere. Weight is a force, in newtons, and on the Moon it is about six times smaller.

The cart’s mass is now 2.5 kg. Work out its weight, then choose On under Show the forces to check it on the weight arrow, pulling down.

Step 4 of 6

Falling together

A heavy body is pulled down harder: change Cart mass and watch the weight arrow grow in proportion to the mass. But a heavy body also has more mass to accelerate. When a body falls without air, its weight is the only force on it, and the second law gives

$a = \frac{W}{m} = \frac{m g}{m} = g$$a =$$\frac{W}{m} =$$\frac{m g}{m} =$$g$⁠

The mass cancels: every body falls with the same acceleration, 9.81 m/s². A feather falls slowly only because of the air.

Step 5 of 6

The normal force

The cart does not fall through the track, because the track pushes it upwards. That force is the normal force: the force a surface exerts on a body pressed against it, at right angles (“normal”) to the surface. Here it equals the weight, because the cart does not accelerate up or down, so by the first law the net vertical force is zero.

Notice: the weight and the normal force both act on the cart. So they are not an action–reaction pair, even when they are equal and opposite.

Step 6 of 6

In summary

• Newton’s third law: when one body exerts a force on a second, the second exerts on the first a force equal in size and opposite in direction.
• The two forces of a pair act on different bodies, so they do not cancel each other. To tell whether a body accelerates, add only the forces on it.
• Weight is the force with which the Earth pulls a body: $W = m g$⁠, in newtons. Without air every body falls with acceleration $g$⁠.
• The normal force is a surface’s push, at right angles to it. On a level surface with no other vertical forces it equals the weight, but it is not the weight’s partner: the weight’s partner is the cart’s pull on the Earth.