Newton's third law is one that surprises a lot of people. There are a couple ways that we can state it:

Forces come in pairs.
For every action there is an equal and opposite reaction.

Imagine that you and I are standing facing each other, and I suddenly lean forward and give you a push backward. You know what Newton says? Newton says that at the same time I'm pushing you backward, you are pushing me backward. Now, that may seem a little strange at first; after all, you're not consciously pushing me, so how could it possibly be true?

To see if we can make a little bit more sense of this little scenario, let's move it onto our almost-friction-free ice-skating rink. Now think about this very carefully: when I push you, you're going to move backwards, but what am I going to do?

If you've spent much time ice skating (or roller skating) you know the answer to that question. I will also move backwards! And if I'm moving backwards, you must have exerted a force on me, without even realizing it. (Why? Think about Newton's first law. If my velocity changed, there must have been an unbalanced force!)
 

Sitting on a Chair

So now let's take your brain for a little spin, and see if you can wrap your mind around this...when you are sitting on a chair, what keeps you from falling through the chair? Well, clearly the chair is providing an upward force to prevent you from falling. How big is that force? Newton tells us that the force is equal and opposite to the force you are applying to the chair. How big is that force? That force is your weight.

Okay so far? The chair is pushing up on your with a force equal to your weight.

Now let's say you get off the chair, and we set my little four-month-old son Toby on the chair. Now how much force is the chair applying to Toby? The answer is, it's pushing Toby upward with a force equal to his weight!

Wow...that's one smart chair! It knows enough to push you up much harder than it pushes my baby boy!

Okay, I'm being facetious...the chair isn't smart at all, but this is how the universe works.
 

Force of Gravity

Let's take another example. Forget the chair. You're just sitting on the ground. What is keeping you on the ground? Well, it's the force of gravity that the earth is applying to you. And that force is equal to your weight.

But now you know what that means, right? If the earth is applying a force, pulling you toward its center, then guess what! You are pulling the earth with the same amount of force!

What's really interesting about this is, if we knew both your mass and the earth's mass, we could use that information to calculate what kind of acceleration you are giving the earth, just by existing here on planet earth. Of course, that acceleration is so tiny no one will ever notice it. And besides, there's probably someone on the other side of the earth that's pulling in the other direction, balancing you out! :D
 

Back to the Rink

But let's forget about the earth for a minute, and go back to our ice skating example (we're going to use an ice rink because we can pretend there's no friction to complicate things). Imagine that you have a mass of 80 kg, and you push your friend who has a mass of 60 kg. Let's suppose, further, that we are able to measure the resulting acceleration of your friend. Let's say it was 0.2 m/s². Do you think you will have the same acceleration?

Let's find out...

We can calculate the force you applied to your friend: F = ma = (60 kg)(.2 m/s²) = 12 Newtons. Now, if that's the force you applied to your friend, it's also the force your friend applies to you. So nowyour acceleration can be calculated: a = F / m = (12 Newtons)/(80 kg) = 0.15 m/s².

Is that what you expected? You have a larger mass, and your acceleration will be smaller.

1.

If I'm applying a force of 20 Newtons on you, in a westerly direction, what is the force you are applying to me?

2.

What is the force with which you are pulling on the earth?

3.

There's a Chuck Norris joke: "Chuck Norris doesn't do push-ups; he pushes the earth down." Comment on this joke, in light of what you've read.

4.

Suppose you have a mass of 100 kg, and you push your friend with enough force to give him an acceleration of 0.6 m/s². If the result is that you have an acceleration of 0.4 m/s² in the other direction, what is your friend's mass?