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Anderson Video - Free Fall and Gravity

Professor Anderson
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 >> Hello class, Professor Anderson here. Welcome to another edition of The Learning Glass Lectures on Physics. How are you guys today? Doing all right? >> Good. >> Good. Let's talk a little bit more about free fall and gravity and, as we go, if you guys have any questions, just raise your hand and we can chat about it. So what we said before was Newton's law of gravity applies to not only motion around here near the surface of the earth, but to other parts of the universe, and let's see what we can deduce from that force-law equation. So here's our Earth, and let's do the experiment that we are all familiar with. Let's take an object and let's drop it near the surface of the Earth. If we are near the surface of the Earth, we know what the force is. The force is GMe, where that's the mass of the Earth, mass of the object, divided by r squared. This is the mass of the Earth. This is M, the mass of the object, and we know what r is. If we're on the surface of the Earth, then r is just the radius of the Earth, and we know exactly what that is. This whole thing becomes g, where g is 9.8 meters per second squared. Okay, when you're near the surface of the Earth, the gravitational force is essentially constant, and it's equal to m times g, which comes from this universal law of gravitation, but let's say we go up to a very high altitude. Let's say here's our Earth, and now were going to drop that object from some very high altitude h. Let's calculate the acceleration of that object when it's up at this high altitude. There is, course, still a force on it. G, mass of the earth, mass of the object, divided by r squared, but now r is the distance from the center of the earth, and so you have to not only include the radius of the Earth, but you have to include the altitude each. So this becomes GMe times m over Re plus H quantity squared, and that, we can call G prime. Not derivative, just some other G, some other acceleration, and it is GMe over Re plus H quantity squared. That is certainly less than this G. since were adding something to the denominator, this has got to be less than G, and we know this already. The acceleration of objects up at altitude is certainly less than 9.8 meters per second squared. So it doesn't really matter what you put up there. If you put a satellite up there, right, and it's moving in a circle, it is accelerating, but it's accelerating with this value, not this value over here, okay? So not only does your weight decrease with altitude like we talked about, but also, your acceleration decreases with altitude. If you drop a ball at the top of the Empire State Building, it accelerates a little bit less than if you drop a ball at the bottom of the Empire State Building. Okay, it's not much, but it is a little bit less, and it's certainly measurable