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Anderson Video - Dropping a Rock on Mars

Professor Anderson
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>> Hello class, Professor Anderson here. Let's take a look at a problem involving Newton's Law of Gravitation. Let's say you're on the surface of Mars and you are standing there and you drop a rock a height of 2 meters. Okay. So H equals 2 meters. And we want to know how long does it take to hit the ground? Okay. So, let's think about the forces that are acting on that rock. Okay. Here's the rock. And as soon as I let it go, gravity is of course pulling it down. And that's it, right? Gravity is the only thing pulling it down. And so gravity, according to Newton is GMm over R squared. So, if that's the only force, Newton also said that that's equal to the mass times the acceleration. And now look what happens, the little m's cancel out and we have acceleration is equal to G big M over R squared. And if you're at the surface of Mars. Then we just want the radius of Mars. Big M is of course the mass of Mars. G is the universal constant. Okay. The question was, how long does it take to hit the ground? And so to answer that we can go back to our kinematic equations. Y final equals Y initial plus VY initial times T plus 1 half A sub Y, T squared. Y final is zero. Y initial is H. V initial is zero, it starts from rest. Acceleration is that but it is of course downwards so we need to include a minus sign. And we have big G, big M over R squared. And we're going to multiply that by T squared. And now we can solve this equation for T. We get T is equal to 2 R squared times H divided by big G big M and all of that square rooted. Okay. And now we have all those numbers and so we can plug it in. So if you look in your textbook or you can look online you can find the radius of Mars. And the radius of Mars is 3.37 times 10 to the 6th. So we've got 3.37 times 10 to the 6th. We're going to square that. We're going to multiply it by 2. We're going to multiply by the height which we also said is 2 meters. Equals that. And now we divide by universal constant 6.67 10 to the minus 11. And we're going to also divide by mass of Mars which is 6.42 times 10 to the 23. Okay. And now we take the square root of that whole thing. And you should get T equals 1.03 seconds. Okay. Double-check my numbers on that, make sure you get the same thing. Your numbers will likely be different for the initial values. And, that should be clear. If you have any questions come see me in my office. Cheers.