8. Centripetal Forces & Gravitation

Newton's Law of Gravity

# Universal Law of Gravitation

Patrick Ford

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Hey, guys. So in this video, we're gonna talk about the universal law of gravitation. So the story is that Newton was sitting in a tree one day and apple fell and hit his head, and he realized that the force that causes the apple to fall to the earth is the same force that keeps the moon in orbit around the Earth. So basically, what Newton figured out was that all objects in the universe attract each other. They all exert gravitational forces on each other. So, for instance, in this diagram, I've got these two spheres, these two blue spheres here. And if they both are massive, so they have mass one and mass to then the gravitational force between them is known as Newton's gravitational law. And that equation is big G times, the product of both masses divided by r squared. Where G that capital G is just a number. It's known as the universal gravitational constant. It's 6.67 times 10 to the negative 11 here, the units for that number, you may or may not need to know those Just check your just check with your professor if you're unsure and that little are that's in the denominator. There is the distance between the objects centers of mass. So if you have these two massive objects here and they're separated by some distance, whoops they're separated by some. Distance are Newton's law of Gravitation says that mass to will pull on Mass one in this direction, but because of action reaction and because of everything attracts each other Mass one. Also a polls on mass to in that direction. The magnitude of those forces is given by this equation. And as for the direction, those things those forces air directed along a line that connects the two objects. So these forces always act on a line that connects the two objects centers, and that's basically it. That's the whole equation. The last thing I want to mention is that this capital G here is known as a universal constant, which means anywhere you go in the universe, that number is always going to be the same. Don't confuse that with little G, like we've seen in forces in telematics that 9.8 m per second squared. That's what's known as a local constant local constant means anywhere on Earth that you go, That number is going to be the same. But as soon as you go off of the earth or you go to different planet, that number is going to change. So just make sure that you know the difference between those two and you don't confuse them. Alright, guys, that's basically it. Let's go ahead and check out this example I've got here. So we've got to 30 kg fears and they're separated by 5 m. Suddenly get and draw that out. So I've got two spheres and there have a mass of 30 kg. So I've got mass. One equals 30 and I've got Mass two equals 30 and they're separated by a distance of 5 m. So they know that that is equal to five. And I'm asked to find out what the gravitational force is between them. So in other words, I need to find out what F G is equal to right? So that's not a six that's supposed to be a G Great. So we know the formula for Newton's law of gravitation. Thats f g equals capital G, the product of both of the masses divided by the distance between them squared. So I have all those variables. Well, let's check. I know that this capital G is just a constant. That's just a number. And I've got this mass here. That's 30 kg, the other mass. So I've got M one and M two, and I also have the distance between them. That's r equals 5 m. So I have all of those variables. I could go ahead and plug this stuff into my calculator, so just setting everything up. I've got f g equals. I've got 6.67 times, 10 to the minus 11. Then I've got the two masses 30 and 30 and I've got to divide them by the distance between them square that five. And so to do this, just make sure I've plugged in everything correctly, actually. Have little calculator that's gonna go and help us. So I'm gonna go ahead and plug all of this stuff in. So I've got 667 times. Whoops. Yep. Times 10 to the negative 11. And then I'm gonna multiply it by the two masses 30 and 30. And now we've just got a divided by in parentheses, the distance squared. Make sure that the nominators in parentheses because you don't want to mess up the order of operations. So if you go ahead and plug that in, we get the correct answer, which is that the force of gravity equals 2.4 times 10 to the minus nine, and the unit for that is in Newton's. So that's basically the gravitational force between these two spheres. Let me know if you guys have any questions, and if not, we're just gonna keep moving.

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