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Anderson Video - Weight on Earth vs Moon

Professor Anderson
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HellO class, Professor Anderson here. Let's attack this question of how much you weigh on the earth versus how much you weigh on the moon. What we just saw was gravity due to the earth pulling us down as a force f sub g, which is negative g mass of the earth, mass of us divided by the radius of the earth square. And we plugged in those numbers and what we saw was that is negative m times little g, which we know, right. Little g is 9.8 meters per second squared. So let's say that the mass of you is 100 kilograms. Let's see what this number is then. We get 100 kilograms times 9.8 meters per second squared, all in SI units we get 980 Newtons. What about your weight? Well, remember when we talked about weight what we said was your weight is really how hard is the floor pushing up on you or if you're standing on a scale what's the normal force of that scale pushing back up on you. And this is why when you are in freefall you feel weightless. Put a scale underneath you everything's falling at the same rate you don't feel any weight at all. There's nothing pushing back up on you, but when you're standing on the earth, and you're not accelerating up or down then that normal force is exactly equal to mg because you're not accelerating. And so your weight, your perceived weight is just mg and now we know what that is. It's 980 Newtons, Okay. The negative sign we took into account right there already, so this is your perceived weight. All right. That's when you're on the earth. Let's now compare that number to the moon. Okay. You're going to go up to the moon and you can do the same experiment. You're going to stand on scale. Let's see what the normal force is pushing back up on you. So let's change everything to the moon. We now have the mass of the moon, the radius of the moon. The force we will call f sub m. Your mass of course stays exactly the same. If you have a mass of a 100 kilograms on the earth, you go to the moon, you're still a mass of 100 kilograms. What changes is the force on you, and let's calculate what f sub m is in this case. It's still negative gm1, m2 over r squared, but now of course we have the mass of the moon, the mass of you, and the radius of the moon quantity squared. And let's punch in some of those numbers and see what we get. I have them right here for you. This is still 6.67 times 10 to the minus 11. The mass of the moon is 7.36 times 10 to the 22 kilograms. We're going to stay in SI units here. The radius of the moon is 1.74 times 10 to the 6 meters. Okay, and if you punch in all those numbers into your calculator, you should get something around negative 162 Newtons. All right. And so you say my weight on the moon is the size of this normal force, but the normal force is just equal to mg on the moon we'll call it. And that is 162 Newtons. So this is your weight on the moon. So you knew the answer before we started. You of course weight less on the moon because the mass of the moon is much smaller. Even though the radius of the moon is smaller that's not enough to compensate for that smaller amount of mass, and so you weigh 6 to 7 times less on the moon. Okay. And you're familiar with this already, because when those astronauts went to the moon. You know, when they went to the moon, right. And you saw them jumping around, even though they have like giant backpacks full of, you know, equipment and air containers and things like that, right. They're able to jump pretty high, bounce around on the moon. And that's because there's not as much gravity pulling on them. They don't weight as much. And so their muscles which have developed on the earth are strong, big quadricep muscles, and when you flex those muscles and you jump on another planet that doesn't pull you down as hard, you can jump higher. In fact if we did like Olympics on the moon be able to jump really, really high, right. Be able to jump really, really far. Be able to break all sorts of records. So really that's what we should do. We should just develop humans on earth, put them up on the moon. Let them compete. Really be fun.