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Physics: High School18 chapters | 211 lessons

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Lesson Transcript

Instructor:
*David Wood*

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

This lesson explains how gravity works mathematically and teaches you how to use Newton's Law of Gravitation to solve problems. A short quiz will follow.

I have a friend who invented something remarkable. He owns a breakfast place and in breakfast places you have to butter a HUGE amount of toast. It gets rather annoying. So he invented something called 'The Butter Gun.' It's a hand-held gun. You take a stick of butter and load it in. The Butter Gun has heating coils inside that melts the butter. Then, once it's ready, you point the butter gun at some toast, press the trigger, and splat, the butter shoots out and covers your toast.

He showed it to me and I tried it, but I only used a single slice of toast. So this ENTIRE stick of butter came flying out and coated the toast. It was practically an inch thickâ€¦ so disgusting! What you need to do, he told me, is move the gun further back and put lots of slices of toast next to each other. If you have four pieces of toast, the butter will be thinner. Nine pieces of toast, thinner still. So you have to get the balance just right to get the thickness you want.

When my friend showed me how it works, I realizedâ€¦ this is kind of like something in physics. It's kind of like an inverse-square law. If you put your single slice of toast, at a distance, *d*, you get 1-inch thick butter. If you move back to a distance, 2*d*, you'll cover 4 pieces of toast at a thickness of 1/4-inch of butter. If you move to a distance, 3*d*, you'll now have 9 pieces of toast and the butter will be 1/9th of an inch thick.

So, if we were to write this relationship between the distance and the thickness of butter as an equation, we would say that the butter falls off as 1/*d*^2. At 2*d*, for example, you put 2*d* into this equation, and you get 2^2, which is 1/4. And at 3*d*, you get 3^2, which gives you 1/9. Or, in other words, if you double the distance, you don't half the thickness of butter, you divide the thickness of butter by a factor of 4 (2^2 gives you 4).

This is like something in physics called an **inverse-square law**. The light from the sun, for example, follows an inverse-square law. And the topic we're talking about in today's lesson - gravity - also follows an inverse square law. If you double the distance between two objects, you cut the force of gravity to a quarter ((1/2)^2). If you triple the distance, you cut the force of gravity to a ninth ((1/3)^2).

Newton didn't just discover his three laws of motion. He also discovered a law about gravity. We call this Newton's Universal Law of Gravitation. **Newton's Law of Gravitation** says that every object in the universe attracts every other object; even you and your computer have a gravitational attraction towards each other, though it is very small. We see it more clearly with huge things, like the planet Earth. If you throw a ball in the air, the ball falls because the Earth has a big mass and a big gravitational attraction.

Newton's Law of Universal Gravitation looks like this: *Fg* = (*G* * *M*1 * *M*2) / *d*^2, where *Fg* is the force of gravity between two objects, measured in newtons; *G* is the gravitational constant of the universe (which in our universe is always 6.67 * 10^-11; that's just a number you plug into the equation); *M*1 is the mass of one of the objects, measured in kilograms; *M*2 is the mass of the other object, also measured in kilograms; and *d* is the distance between the centers of the two objects, measured in meters.

There are two types of questions we're going to look at in this lesson. In the first, you just plug numbers into the equation.

So, if you wanted to calculate the force of gravity between, say, a 4-kilogram lawnmower and the planet Mars, you would multiply big *G* (which is 6.67 * 10^-11) with the mass of Mars (which is 6.4 * 10^23), with the mass of the lawnmower, and divide it by the distance from Earth to Mars (which is an average of (2.25 * 10^11 meters^2). You have to square that distance. That squared part is really important because that's what makes gravity an inverse-square law.

In this case, the answer turns out to be 3.4 * 10^-9 newtons. Or, in other words, the force is so tiny that you can never actually observe it. That's why gravity is only really apparent for large objects that happen to be nearby.

Another type of question is called an inverse-square law question. It's where they make changes to a situation and ask how it would affect the force between the objects. For example, if you triple the distance between two objects and half the mass of one of the objects, what will happen to the force between them?

To solve that problem, we do a before and after equation. Before, let's pretend everything had a value of 1. Both objects had a mass of 1 kilogram and they were 1 meter apart. And let's not worry about big *G* because that's the same before and after anyway.

Before, we have 1 times 1, divided by 1^2, which equals one newton. The question said to triple the distance and half one of the masses. So, we have 0.5 multiplied by 1, divided by 3^2. That comes out as 1/18. So, the force becomes an 18th of what it was. And that's it; we're done!

According to **Newton's Law of Gravitation**, everything in the universe attracts everything else in the universe gravitationally - even lawn mowers and the planet Mars. Gravity is the force that keeps planets in orbit and causes balls to fall back to the Earth. The force of gravity is an **inverse-square law**, which means that if you double the distance, you decrease the force by a factor of 4 - not 2, as you might expect. And we can use Newton's Universal Law of Gravitation to calculate the strength of the force of gravity between any two objects.

Newton's Law of Universal Gravitation looks like this: *Fg* = (*G* * *M*1 * *M*2) / *d*^2, where *Fg* is the force of gravity between two objects, measured in newtons; *G* is the gravitational constant of the universe (which in our universe is always 6.67 * 10^-11; that's just a number you plug into the equation); *M*1 is the mass of one of the objects, measured in kilograms; *M*2 is the mass of the other object, also measured in kilograms; and *d* is the distance between the centers of the two objects, measured in meters.

Completing this lesson should prepare you to:

- Define inverse-square law
- Describe Newton's Law of Gravitation and recall the equation for it
- Explain how to solve two types of calculations using the equation

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Physics: High School18 chapters | 211 lessons

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