### Video Transcript

Which of the following statements most correctly describes Newton’s third law of motion?

So let’s go through these one by one, pick them apart, and see which one ends up being correct.

Number one: When a force is applied to an object, the object exerts a force in the opposite direction to the applied force that is proportional to the mass of the object that the force is applied to.

This is very much a lot of information. So let’s underline the important bits. “When a force is applied to an object”, this statement says that the object exerts a force in the opposite direction to the applied force. And that force is proportional to the mass of the object that the force is applied to. Let’s see which bits are correct and which bits are wrong.

The first underlined bit, the object exerts a force when a force is exerted on that object. That’s true. This statement says that that force is in the opposite direction to the applied force. That’s also true. And finally, this statement says that that force is proportional to the mass of the object that the force is applied to. This part is wrong. The mass of the object that the force is applied to has nothing to do with the equal and opposite force exerted by that object. One of the most common ways of stating Newton’s third law is that every action has an equal and opposite reaction. Now this statement is not a complete statement of Newton’s third law. However, it does mention that every action has an equal and opposite reaction. And in order to have an equal reaction force, it can’t be dependent on the mass of the object that the force is applied to. It just has to be an equal reaction force. So statement one is wrong.

Moving on to number two, when a force is applied to an object, the object exerts an equal-sized force in the direction of the applied force.

So the object exerts an equal-sized force in the direction of the applied force. As we’ve already seen, the object on which the force is exerted does exert a force back. That force does have to be equal-sized. But it needs to be opposite as well, not in the direction of the applied force. So statement two is also wrong.

Happily then, we can move on to number three. When a force is applied to an object, the object exerts a force in the opposite direction to the applied force that is proportional to the mass of the object that applies the force.

Breaking it down once again, “the object exerts a force”, we’ve seen that’s true. “In the opposite direction to the applied force”, that’s also true. But this time it says that it’s proportional to the mass of the object that applies the force. Once again, if the force has to be equal and opposite, it can’t be dependent on any of the masses of the objects. And therefore, statement three is also wrong. So it looks like statement four should be the correct one. But let’s confirm that that’s the case.

When a force is applied to an object, the object exerts an equal-sized force in the opposite direction to the applied force.

Here, it says the object is exerting a force; true. An equal-sized force that is; that’s also true. And in the opposite direction to the applied force, correct and correct. Therefore, it looks like number four is the correct statement of Newton’s third law of motion.

Now an important aside, the statement “every action has an equal and opposite reaction” is not a complete statement of Newton’s third law. We’ve mentioned this earlier. It does account for the fact that the reaction force is equal and opposite. But it doesn’t say anything about which object is exerting the reaction force. So let’s look at an example to help us out.

Let’s say we’ve got a person over here, really really badly drawn. But, they’re exerting a force on this pink box. Let’s say that force is 50 newtons. Well, we know that that force has to have an equal and opposite reaction. But what’s important to know, is that it’s the box that’s exerting a 50-newton force on the person. And of course, that force is equal in magnitude, so 50 newtons as well, and opposite in direction, so to the left, just as we would expect it to be. But the important thing to remember is that it’s the box that’s exerting the reaction force on the person.

So going back to our initial question, our final answer is that statement four most correctly describes Newton’s third law of motion. That statement once again, is that when a force is applied to an object, the object exerts an equal-sized force in the opposite direction to the applied force.