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Anderson Video - Newton's Universal Gravitation

Professor Anderson
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 >> Okay, hello class. Welcome back to another lecture on physics. This is our learning glass approach to lectures on physics. I wanted to talk to you about gravity for a second and the super ball is of course the best friend of the physicist and you should just always carry a super ball with you wherever you go. Just fun to play with it all right. But let's think about the super ball for second. If I hold up this super ball like so, are there forces that are acting on the super ball right now? What you guys think? Yes. What is the net force acting on the super ball? >> Zero. >> Why zero? >> Because [inaudible]. >> Okay, who said zero? What's your name? >> Adam. >> Adam -- can you hand the mic back to Adam. Adam and I will have a little chat real quick. Okay, Adam here's my super ball. I'm holding it stationary. What's the net force acting on the super ball? >> Zero. >> Zero. Why? >> Zero. Why? >> Because there's a normal force applied to it and gravity as well. >> Okay, so I'm applying a force holding it up, gravity is applying a force down. Now I'm going to let it go. After I let it go what was the net force on the super ball before it hit the table? >> Whatever its potential energy was. >> Okay, potential energy is not a force though right? Of course related to the force. So after I let it go is the net force on the ball zero? >> No. >> No. What is it? >> It's the force of gravity. >> It's the force of gravity, that's right. So force of zero, I let it go, the force is mg down. Once it hits the table and compresses the bottom of the super ball what's the net force on it? Is it a zero? Is it not zero? That's a tough question, right? Let's reverse it for second. Here's the super ball. It's going to go up. What is the force on the ball at the top of its motion? What is the net force on it? >> Zero. >> Okay, why do you say it's zero? >> Because for a moment in time it's not moving. >> It's not moving. Velocity is zero. But what is Newton's second law? Newton's second law doesn't have velocity in it. Newton's second law has what? >> Mass times acceleration. >> Mass times acceleration. So does this thing have acceleration at the top of its motion? >> Yes. >> Yeah, it certainly does. Remember acceleration is delta v over delta t. In other words is it about to change its speed? >> Yeah. >> Absolutely. It was zero but we know in the next instant it's going to be falling again. So in fact the super ball as soon as it leaves my hand it has a force on it due to gravity that is down while it's on the way up, down when it's at the top of a motion, down when it's going back down. As soon as it leaves my hand it's mg the whole time. So, back to the question of when it hits the table here, when it comes to rest and it's in contact with the table is the force on it zero or is it not zero? Adam, what do you think? >> Well at one point the net force on it is zero but then the ball compresses a little and I'd say the force is greater than zero. >> Yes, exactly right. The ball compresses like a spring is compressed and when a spring is compressed there's a net force on it. And there's certainly a net force on it when it's compressed because we know in the next instant it's going to bounce and start to come back up. So there is some delta v. All right, fun with superballs. This is all tying in to this idea that gravity exhibits a force. The gravity from the earth pulling down on that super ball made the super ball fall towards the earth but it doesn't just apply to the super ball on the earth, it of course applies to you on the earth and it also applies to the moon in its orbit, in its orbit, and the earth in its orbit around the sun. It applies universally. And this was the huge step by Newton which was Newton's universal law of gravitation. What he said was the following -- a force of gravity is negative g, m1, m2 divided by r squared. M1 is of course the mass of one object m2 is the mass of the other object. So if mass one was the earth then mass two would be our super ball. G -- well let's do r first and then we'll worry about g -- r is the distance between the two. And if you have spherical objects then its center of mass to center of mass, distance, and then finally g is the universal gravitational constant and it has a particular number. We'll give you a few digits here. 6.673 times 10 to the -11, Newton meter squared per kilogram squared. What about this negative sign? That negative sign just means it's attractive. Masses are attracted together which is a good thing because if masses weren't attracted together guess what? As soon as the big bang happened and we had expansion of the universe stuff would never come back together. Planets would never form. Stars would never form. The only reason that planets and stars form is because gravity is pulling them together and if none of those stars formed and none of those planets formed you wouldn't be here, I wouldn't be here, none of us would be here and so we wouldn't have to worry about this universal law of gravitation at all. Maybe that would be better, I don't know. It's not too bad. All right, let's think about the two masses here, m1 and m2. R we said if they're spherical its center of mass to center of mass which for a sphere it's right in the middle of the object. G is the universal gravitational constant. This says there is a force on m1 due to m2 trying to pull it towards it but there is also a force of exactly equal magnitude, opposite direction, on m2 and we know exactly what that force is. The magnitude of that force is g, m1, m2 over r squared. Any two objects in the universe are attracted together by gravity for any object in the universe which is kind of weird to think about, right? Because you're all familiar with being stuck on the earth, right? But you're not as familiar with being attracted to other objects. So for instance if I'm in outer space and my space shuttle is floating over there somewhere and I can't get to it, how do I get to that space shuttle? Well, we talked about this before with the idea of conservation of momentum. If I had a wrench in my hand I could throw a wrench the other way and I would be propelled towards the space shuttle, but I could also just wait. There is a force due to gravity on me pulling me towards the space shuttle and that means I am exhibiting a force on the space shuttle pulling it towards me. So if I just sit there and wait eventually I will come together with the space shuttle. Now that could be a very long time. You might run out of air. Why? Because g in si units is a pretty small number, right? We've got a 10 to the -11 there so that force is going to be very small but it is not zero. There is still a force trying to pull you back together. All right, so this was a major step in the history of physics because once Newton wrote this down it essentially tied the universe together and there was all sorts of religious spiritual implications of this but basically from a physics point of view before Newton we didn't know that we were literally tied to the rest of the universe and then after Newton we did know that. At the very least we are tied together through gravity.