P HYSICS NOTES
Newton’s Third Law
When a force is exerted on an object, there must be an agent which is applying the force. In other words, a force
always involves two things interacting with each other.
If you were to kick a bowling ball, you would be applying a force on the ball. And yet, it would certainly hurt your
toe. Why does it hurt you when you’re the one exerting the force on the bowling ball? The answer must be that the
ball is also exerting a force on your toe.
Newton’s 2nd law is not sufficient to explain what happens when two or more objects interact. For instance, the 2nd
law says that when a hammer hits a nail, exerting a force on it, the nail will accelerate. But this doesn’t tell us how
the force of the hammer on the nail is related to the force of the nail on the hammer. We need another statement
which describes how two objects interact with one another—this statement, as we’ll see, is Newton’s 3rd law.
Consider a hammer hitting a nail. The hammer certainly
exerts a force on the nail as it drives it from rest into the
wall. The force exerted on the nail will be in the direction
that the nail accelerates—toward the wall.
At the same time, the nail exerts a force on the
hammer. If you are not sure about this, imagine hitting
the nail with a glass hammer. It’s the force of the nail on
the hammer that would cause the glass to shatter.
If you think about it, any time object A pushes or pulls
on object B, object B pushed or pulls back on object A.
This example of the hammer and the nail illustrates what
we call an interaction.
An interaction is the mutual influence of two objects on each other.
The forces involved in an interaction between two objects always occur as a pair.
If object A exerts a force
on object B, then object B exerts a force
on object A.
These two forces,
and
, are sometimes called an action/reaction pair. However, this can be
misleading. It is not true that one of the forces acts, and then the other force reacts. Instead, both forces
occur simultaneously. They are both action and reaction at the same time.
We’ve seen that every force is paired up with a different force, and that these two forces act simultaneously on
different objects. But we haven’t yet said how the directions and the magnitudes of the pair of forces compare.
Newton was the first to recognize how these forces compare, and today we know this as Newton’s 3rd law.
Newton’s 3rd Law
Every force occurs as one member of a pair of forces. No force ever exists alone.
 The two members of a force pair act on two different objects (e.g. hammer and nail).
 The two members of a force pair point in opposite directions and are equal in magnitude.
The two forces in a pair are of equal magnitude
and in the opposite direction.
Each force in the pair acts on a different object.
You might be wondering how any object ever
accelerates if every force is met with an opposing
force of equal magnitude. Don’t all the forces just
cancel and we’re left with a net force of zero? No!
It is true that every force is met with an opposing
force of equal magnitude, but these forces act on
two different objects! It is the net force on one
particular object that determines if that object
accelerates or not. So even though the forces come
in pairs, they do not cancel each other because
they are not exerted on the same object.
Consider the second point of Newton’s 3rd law. It seems reasonable that the two forces act in opposite directions. I
push the car forward, and it pushes me backward. When swimming, I kick the water backward and it propels me
forward. However, this idea that the two forces in a pair are of the same strength (same magnitude) is by no
means obvious. Indeed, this is what causes us the most trouble in applying Newton’s 3rd law because it seems so
counter to our intuition.
Here’s an example of this unusual idea. Suppose you are a stunt person and you have just jumped off a ten-story
building. You are falling toward the large inflated safety pad below. It is the earth which is exerting the downward
force on you, causing you to accelerate toward the ground. So there you are in midair, being pulled to the ground
by the earth. Now Newton’s 3rd law says that you must be exerting a force with exactly the same strength on the
earth, in the opposite direction. In other words, you must be pulling up on the earth just as much as it is pulling
down on you! But is this really true? It certainly doesn’t seem like you are pulling up on the earth.
The source of the puzzlement is that Newton’s 3rd law equates the size of the forces acting on you and the earth, and
not your and the earth’s acceleration. The acceleration of each object depends not only on the force applied to it,
but also, by Newton’s 2nd law, on its mass. So you and the earth do in fact feel forces of equal strength from the
other, but because the earth’s mass is so large (5.98 1024 kg!), it undergoes an extremely small acceleration up
toward you, while you being of little mass undergo a large acceleration downward toward the earth.
m = 70 kg
Newton’s 3rd law states that as you are
falling toward the earth due to its force on
you, you must be exerting on the earth a
force of equal magnitude and in the opposite
direction.
The reason it doesn’t seem like this is the
case is because of the earth’s enormous
mass.
Newton’s 2nd law:
m = 5.98 1024 kg
The earth and you experience the same
force, but the earth accelerates about 10-24 as
less, since it is about 1024 times as massive!
It is the forces that are equal, and not the
accelerations.