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Remedial Algebra I25 chapters | 248 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson and you will see how you can calculate the force of attraction between two objects. Learn why our planets don't spin themselves out of orbit around the sun.

Have you ever wondered why our planets keep spinning around our sun? How come the planets don't spin themselves out of orbit? What is keeping them in place? And what is keeping us from floating off into space?

The answer to these questions comes from a man named Isaac Newton who wanted to know what was keeping our planets in orbit. So, for about 10 years in the late 1600s, he observed and studied the planets. What he came up with was his **law of universal gravitation** that explains the attraction or force that exists between any two masses or objects. This is the force that we commonly call gravity.

But did you know that this force is present between any two bodies? That's right; you yourself are exerting a force of attraction on everything around you. So, why aren't things being pulled towards you? Because the earth is much larger, it exerts an even larger force of attraction that pulls on things of greater force than you. In a sense, the earth wins when it comes to attracting things to it. You can't beat Earth.

This is the force that Sir Isaac Newton created a formula for. So, today, we have a way to calculate the force or attraction between two objects. We can use this formula to see how much greater the force of gravity is between a basketball and the earth and between the basketball and us to see who wins.

What is this formula? The formula is *F* = *G**((*m* sub 1**m* sub 2)/*r*^2), where *F* is the force of attraction between the two bodies, *G* is the universal gravitational constant, *m* sub 1 is the mass of the first object, *m* sub 2 is the mass of the second object and *r* is the distance between the centers of each object. Notice how I've used the word mass instead of weight. This is because mass is different from weight.

You see, your weight is dependent on the amount of gravity that is pulling you down. That is why, in space, you are weightless. Your weight now is different, but your mass stays the same no matter how much gravity is pulling you down. Your mass tells you how much stuff you are made of. No matter where you are, the amount of stuff that you are made of stays the same, and that is your mass.

The universal gravitational constant, *G*, is approximately 6.67x10^-11 N (m/kg)^2 where *N* is the Newton, a measurement of force. As a constant, this value doesn't change even if the masses change or the distance changes. No matter what numbers you plug into the other variables, the *G* will always be 6.67x10^-11 N (*m*/*kg*)^2. All your answers for force from this formula will use the Newton, *N*, measurement. Your masses, *m* sub 1 and *m* sub 2, use the kilogram, kg, measurement and your distance, *r*, uses the meter, m, measurement.

So now, let's see how much greater the force from the earth is on the basketball than the force we exert on the ball.

We know *G* is 6.67x10^-11 N (m/kg)^2. Now we need to know the mass of the basketball, the earth and us. We do a bit of researching and we find that the mass of the earth is 5.97x10^24 kg and the mass of a basketball is 0.62 kg. For the human, us, I'm going to use a good mass of 68 kg. For the distance between the basketball and us to the center of the earth, it is 6,360,000 m.

In the first calculation between the earth and the basketball, my *m* sub 1 will be the earth's mass of 5.97x10^24 kg and my *m* sub 2 will be the basketball's mass of 0.62 kg. Really, though, I can put either mass in either of these variables. As long as I have the two objects that I am concerned about. I also have my *r* as 6,360,000 m. So, plugging all these numbers into our formula, we get *F* = 6.67x10^-11*((5.97x10^24*0.62)/6,360,000).

To evaluate this formula, I first multiply the top numerator to get 5.97x10^24*0.62 = 3.70x10^24. Dividing this by 6,360,000, we get 5.82x10^17. And finally, multiplying this by 6.67x10^-11, we get an answer of 3.88x10^7 N. Okay, that looks like a pretty big number.

Now let's see how much force is between us and the basketball. For *m* sub 1, I am going to put our mass of 68 kg, and for *m* sub 2, I am putting the basketball's mass of 0.62 kg. The radius I am keeping the same. Plugging these numbers in, I get *F* = 6.67x10^-11*((68*0.62)/6,360,000).

To evaluate, I first multiply the 68 and the 0.62 to get 42.16. I then divide this by 6,360,000 to get 6.63x10^-6. Then I multiply by 6.67x10^-11 to get an answer of 4.42x10^-16 N.

Comparing these two numbers, I see that, wow, the force between the earth and the basketball is a lot greater than the force between a little human and the basketball. No wonder the earth wins every time and things don't magically stick to me.

Let's recap what we've learned now. The force we know as gravity is really **Newton's law of universal gravitation**, which explains the attraction or force that exists between any two masses or objects. The formula he came up with is *F* = *G**((*m* sub 1**m* sub 2)/*r*^2), where *F* is the force of attraction between the two bodies, *G* is the universal gravitational constant, *m* sub 1 is the mass of the first object, *m* sub 2 is the mass of the second object and *r* is the distance between the centers of each object. The universal gravitational constant, *G*, is approximately 6.67x10^-11 N (*m*/*kg*)^2, where *N* is the Newton, a measurement of force. Using this formula, we see why the earth exerts a strong enough force to keep us from floating away.

Once you've finished with this lesson, you should have the ability to:

- Identify the formula for Newton's law of universal gravitation
- Use this formula to find the gravitational force between objects
- Differentiate between mass and weight
- Explain why the earth exerts such a strong force on objects with this formula

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Remedial Algebra I25 chapters | 248 lessons | 1 flashcard set

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