Newton's second law of motion is very beautiful in its simplicity and in its power. It can be written using just three letters and a symbol. Here it is:

F = ma

Now let me expand that just a little bit for you: Force equals Mass times Acceleration. As in the previous article, we need to begin with a couple definitions...

Mass: The mass of an object is a measure of the amount of matter it is made of. "Oh!" you might say, "it's the object's weight!" Well...not really. You see, weight is a measure of how much gravity is pulling on you. If you go to the moon, your weight changes (if you weigh 180 pounds on earth, you'll weigh about 30 pounds on the moon!), but if you go to the moon, your mass doesn't change. Why would it? You're still made up of the same amount of matter wherever you go in the universe. Weight is measured with a spring scale, and mass is measured with an equal arm balance. Mass is measured in kilograms (metric), or slugs (if you want to use English units!). Let's stick with metric units.

Acceleration: Most people think they know what acceleration means. It means "speeding up," right? Well...not exactly. In physics, we can define acceleration this way: Acceleration is change in velocity. Well, sure, but how is that different from "speeding up?" 

The difference is this: according to our definition, slowing down is also an acceleration! Also, since velocity is both speed and direction, we don't have to change our speed to have an acceleration; we could also change our direction! Yes, that's right--changing your direction is a form of acceleration!

I like to tell my students that their car has three accelerators: the gas pedal, the brake, and the steering wheel!

Acceleration is measured in m/s². 
 

Putting it Together

So now that we've covered our definitions, we can go back and understand a little better what Newton was saying when he announced that F = ma!

When force is measured in Newtons, mass is measured in kilograms, and acceleration is measured in meters per second squared, then you can figure out the force simply by multiplying the mass and the acceleration! Let's take a look at some examples:

Example 1: My car has a mass of 1500 kg. It accelerates from 0 m/s to 88 m/s (meters per second is like miles per hour, except it's our standard metric unit for speed) in 8 seconds. How much force was applied to the car?

Answer 1: Since the car takes 8 seconds to speed up to 88 m/s, that means its acceleration is 11 m/s². Thus, the force is found as follows: F = (1500 kg)(11 m/s²) = 16,500 Newtons!

Example 2: I have a mass of 90 kilograms. Someone pushes me with a force of 200 Newtons. What will my acceleration be?

Answer 2: For this one, we need to do some algebra to solve F = ma for a. Divide both sides of the equation by m and you have a = F/m. So a = (200 Newtons)/(90 kilograms) = 2.22 m/s²

And, of course, if you knew the acceleration and the force, you could calculate the mass, but instead of giving you an example of that, we'll leave it as one of the questions!

What if two forces are acting on an object? Well, then you have to add those forces together before using Newton's law. If the two forces are in the same direction, you just add them. If they're in opposite directions, you subtract them. If they are at odd angles to each other, well, then you have to do some more fancy vector addition, and that's beyond what we're going to cover here!

Example 3: A 50 kilogram object is being pushed with a force of 50 Newtons east, and by a force of 20 Newtons west. What is the object's acceleration?

Answer 3: The total of the forces is 30 Newtons east (because the forces are in opposite directions, we subtract them). a = (30 Newtons)/(50 kilograms) = 0.6 m/s²

1.

Explain the difference between mass and weight.

2.

Explain why acceleration doesn't just mean "speeding up."

3.

If an 20 kg object is speeding up with an acceleration of 0.5 m/s², what is the force being applied to it?

4.

If a 50 Newton force is applied to a 5 kg object, what will the acceleration be?

5.

If an object is pushed with a force of 50 Newtons, and this results in an acceleration of 0.5 m/s², what is the mass of the object?

6.

John pushes a 50 kilogram object with a force of 20 Newtons, and Jill pushes the object in the same direction with a force of 25 Newtons. What is the object's acceleration?