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Let's say we would take a little excursion to the moon So here we are sitting one the surface of the moon, so this is the moon right there, and with us the excursion to the moon we brought two things, we brought ourselves a concrete brick So that's my brick right over there That's my concrete brick my orange concrete brick I also brought a bird feather with us, so this is the bird feather so this is the bird feather, and my question to you is if I were to hold both the brick and the feather at the same time and I would let go of both of them at the same time and ask you which one of them will hit the surface of the moon first what would you say? If you base you experience on earth, on earth if you take a brick and a feather, a brick would fall and goes straight down the brick would just fall immediately to the earth quite quickly accelerating quite quickly, well the feather would kind of float around you have a feather on earth, on earth it will just kind of float around if will go that way and that way, and it will slowly make its way down to the ground So on earth, at least at the present of air it looks like the brick will hit the ground first but what would happen at the moon? what is intereseting about the moon is we have no atmosphere we have no air, to kind of provide resistance for either the brick or the feather, so what do you think is going to happen? So your first temptation let's just say you use the universal law of gravity, so what is the force of gravity on the brick? So the force on the brick well you can calculate that up the force of gravity on the brick is going to be equal to big G is going to be equal to big G times the mass of the moon I say that M for mass the subscript is lowercase m for moon the mass of the moon times the mass of the brick divided by the distance between the brick and the center of the moon squared, so this is the distance between the brick and the center of the moon and you square it, fair enough, that's the force on the brick what's going to be the force on the feather? The force due to gravity on the feather another way to think about that the weight of the feather on the moon so what is the force on the feather? we are doing the same calculation the force on the feather is going to be equal to big G, big G times the mass of the moon times the mass of the feather divided by the distance between the center of the feather center of the moon squared that's the distance of the moon squared So if you look at both of these expression, they both have this quantity right over here, G times the mass of the moon divided by the distance between this height and the center of the moon squared so they both have this exact expression on it So let's replace that expression, let's just call that the gravitational field on the moon define any number of the mass will tell you the weight of that object on the moon, or the gravitational force acting downard on that object on moon so this is the gravitational field on the moon it's called g sub m, and all of this is all of this quantity combined so we simplified that way, the force on the brick due to the moon is going to be equal to lower case g on the moon normally we will use this lower case g for the gravitational constant on earth with the gravitational field on earth or sometime the gravitational acceleration on earth but now it's refering to the moon so that's why the lower case subscript m it's equal to that times the mass of the brick for the case of the feather, the force on the feather is equal to all this business, so that is the g sub m, is equal to g sub m times the mass of the feather so now assuming that the mass of the brick is much greater than the mass of the feather, so let's going to assume, a reasonable thing to assume that the mass of the brick is greater than the mass of the feather, than the mass of the feather what's going to be their relative forces? Here you have the greater mass times the same quantity you have the smaller mass times the same quantity so the mass of the brick is greater than the mass of the feather completely reasonable to say that the force of gravity on the brick is going to be greater than the force of gravity on the feather so if you do all of this so every thing we've done to this point is correct, you might say hey it's gonna be more force due to gravity one the brick, and that's why the brick will be accelerated down more quickly, but what you need to remember is there is more force that's being gravitational force on this brick but it also has greater mass and we remember the larger the mass is, the less acceleration it will experience for a given force So what really determine how quickly either of these things fall is their accelerations and let's figure out their accelerations So we knew that, I will do this on a neutral color we know that force is equal to mass time acceleration So if we wanna figure out the acceleration of the brick we could write it the other way the acceleration, if we divide both side by mass we get acceleration is equal to force divided by mass acceleration is vector quantity and force is also vector quantity and in this situation we will use, I'll use, we're not using any actual value so if I were using actual values, I will use negative number for downwards and positive values for upwards so we are not using any signs here we assume that the direction is being implicitly given so what is the acceleration of the brick the acceleration of the brick, lower case b I'm writing the acceleration of the brick is going to equal to the force applied to the brick, the force applied to the brick which is force applied to the brick divided by the mass of the brick but the force applied by the brick we already know here it is little g on the moon, the gravitational field on the moon times the mass of the brick and we are dividing that by the mass of the brick So the acceleration on the brick on the moon the acceleration the brick will experienc is the same thing as gravitional field expression it is g sub m, this is how quickly it would accelerated on the moon I will do the same thing for the feather and you can see what this is going the acceleration of the feather is gonna be the force on the feather the force on the feather divided by the mass on the feather the force on the feather is g sub m, g with the subscript m times the mass of the feather,times the mass of the feather and we are gonna divide that by the mass of the feather and so once again it's acceleration is gonna be the same quantity so they are both going to accelerate with the same rate downward which tells us they will both hit the ground the same way they will both accelerate from the same time at the same point and they will both have the same velocity when they hit the ground thye both will hit it at exactly the same time despise one having a larger mass so the reality is that larger mass does create a larger gravitational because it has a larger mass it has a larger gravitational attraction to the moon, but because of the mass the attraction gives the same acceleration with something with a smaller mass so any mass on the same level on the surface of the moon would experience the same acceleration So now the quite natural question is if it's true on moon it should also be true on earth and it would be true on earth if you did this exactly the same experiment and you evacuate all the air from the room, you didn't have air resistance you hold a brick and a feather, you let them go at the same time they will both hit the ground at the exactly the same time It's not intuitive to imagine a feather just falling at the same way as a brick would but it would if you evacuate all the air so the answer, the reason why we see this over here, you get the sense if we talk about evacuating the air, is that the difference between the brick and the feather is all due to air resistance if you took the same brick or if you took the same thing with mass of a brick and you will flatten it out so it has more air resistance so if you have flatten it out so if you have flatten it out but let's say it has same mass this thing will fall slower than that because it will have more air resistance it will have more air that kind of collide into provide resistance as it falls and if you took a feather if you compact it really really small the same mass of the feather, you make it so small that you will kind of cut through the air you'll see it drop a lot faster so the real difference between how things fall on earth if you have no air they will all fall at the exactly the same rate and only because of the air they fall differently and the air does two things for constant pressure so you have two object with the same shape, the object that is heavier that has more weight will fall faster because it will provide more net force against the air pressure if you have something that has the same weight an obeject that is more air dynamic will fall faster the one that cut through the ones that have least air resistance and there is a little experiment you can try in the comfort of your own room right now take a brick, or not a brick, take a book take a book like this, and you can drop it you can take another piece of paper or even you know a post card or something you will see the postcard will fall much slower than this book but what you do is put the postcard on top of the book so the book is essentially breaking air resistance for the postcard what you will see is if you put it on top of a book you will see they will fall with exactly the same rate