6. Intro to Forces (Dynamics)

Vertical Equilibrium & The Normal Force

# Anderson Video - Weight During a Full Moon

Professor Anderson

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>> Matt Anderson: Okay, let's ask you a question. Do you weigh less during a full moon? >> Yes? >> Matt Anderson: Okay, why? >> Because it's closer to the earth? >> Matt Anderson: Because the moon is closer to the earth. Well, not exactly, right? What does a full moon mean? A full moon means it is reflecting sunlight across its entire area, its entire cross-sectional area. And what that means is that a full moon is typically right above you. Okay? The sun is over here. And it's shining onto the full face of the moon and you observe that as a full moon. If the moon is over here, then it's a half moon. If it's over here, it's a half moon. And if it's over here, then you just see a little sliver of it, okay? So, the full moon really just has to do with position of the moon in the sky relative to you. Now, if it's directly behind the earth, you of course have the shadow of the earth, and that's -- that happened recently, right? We had the lunar eclipse. And so, if the shadow of the earth crosses the moon, then it turns dark, and sort of reddish, and that's a lunar eclipse. But let's say we just have the case where we're standing on the earth, and the moon is right above us. Let's ignore the sun for a second. What do you think, Faye? Do you weigh less when the moon is there, compared to the moon in some other position? >> I honestly don't know. >> Matt Anderson: Okay. Good. Does anybody else have a thought? I mean, why would you weigh less during a full moon? I mean, if you're a werewolf, shouldn't you weigh more? You're growing hair and stuff, right, and nails, right? Anybody else have a thought? What's your name? Jorge? >> Yes. >> Matt Anderson: Let's talk to Jorge for a second. Jorge, do you weigh less during a full moon? >> Probably yes because of the gravitational pull might be less upon you because the moon is right above you as opposed to a different direction. >> Matt Anderson: Ah-ha. Alright. So, what we said was gravity pulls on everything in the universe. So, if I put the moon over here, then there are two things pulling on me, right? I have the force due to the earth, but I also have the force due to the moon, which granted, it's going to be less than the force of the earth, but they're still in the same direction. And if I have more force pulling me down, then that scale underneath me pushing back up, has to push harder. So, now if I take the moon, and I put it over on the other side, then we know what's going to happen. This force changes direction. The earth is pulling down on me, but the moon is pulling up on me. Let's see if we can calculate this picture now. Alright? So, I have a few things that are acting on me. I have the force of the earth pulling down. I have the force of the moon, pulling up. And I also have the normal force, N, of the ground pushing up on me. And that normal force N is what we call our weight. How hard is the ground or the scale underneath me, pushing up on me? Okay, so we've got sum of the forces in the Y direction. What do we have? We have F of the moon going up. We have N of the normal force going up. We have the force of the earth pulling us down. If we're standing there without accelerating, then this is equal to zero. And so now we can solve this for N. N is just going to be FE minus FM. And we know exactly what those things are. FE is G Mass of the earth, mass of me, divided by the radius of the earth squared. F of the moon is going to be G Mass of the moon, mass of me, but now what do I want to put down here? Jorge? What should I put in the denominator of this equation? >> The radius of earth plus yourself and-- >> Matt Anderson: The radius of earth plus what? >> Also the radius of the moon. >> Matt Anderson: Okay. The radius of the earth, which is this. The radius of the moon, is that. But I might be missing something, right? >> Yes. Drawing a blank. >> Matt Anderson: Okay. Let's go back to this equation here. Right? G M1 M2 over R squared. What is this R? What does that represent? >> The radius. >> Matt Anderson: No. >> No, sorry. >> Matt Anderson: Usually we write it for a radius. >> Right. >> Matt Anderson: But again, we've run out of letters. Okay? So, we're using it as something different now. Okay, what does this R represent in Newton's Universal Law of Gravitation? It is the distance between-- >> Two objects. >> Matt Anderson: -the two objects. M1 and M2. So, really what I want is this distance here. What is this distance, and it is pretty close to the distance between the earth and the moon. Okay, you can make a small correction based on the size of the earth. But it's pretty much close to the distance between the earth and moon. Okay? That's the important part. How far am I from the moon? So, we're going to put our M right there. Alright, and now we can factor out some stuff. We have the big G. We have a little M. And then we have mass of the earth over RE squared. We have mass of the moon, divided by REM squared. And if you plug in all these numbers, and we're going to let M equal 100 kilograms, and you plug in all those numbers, you're going to get something like 982 newtons, whereas on the earth, if you were very careful with your numbers, you weighed 983 newtons. Okay? And you can double check those numbers yourself and make sure we're making sense. But it's basically one part in a thousand less when the moon is full and above you, versus other times. Okay? You do weigh less during the full moon. Not very much at all. Probably not enough that you would notice, okay? But maybe you would, I don't know. When I go out under the full moon, I like to jump around. Maybe it's easier for me to jump around because I weigh less, okay? Let's think about this for a second. This says that not only is the earth pulling on me, and not only is the earth pulling on the moon, but the moon is pulling on me and in fact, the moon is pulling on the earth. And you probably already know that. You know that the moon is pulling on the earth. Why do you know that? What effect on the earth is due to the moon pulling on it? Well, I was thinking of something more direct that you might observe say, when you go to the beach. What's your name? >> Oh, Aiden [inaudible]. >> Matt Anderson: Aiden? Okay, had the mic to Aiden. Aiden, what do think? Is there anything that we can observe on the earth that tells us, "Yes, the moon is pulling on us?" >> Aren't the tides affected by the moon? >> Matt Anderson: The tides. That's exactly right. Okay, the tides are because of the moon. You don't have the moon here, we don't have tides anymore. Ocean would just sit there static, not move around, except a little bit maybe due to wind or weather patterns like that. But you wouldn't have this sloshing of the oceans. So, when it's high tide, here in San Diego, when it's high tide, you should be able to point exactly to where the moon is. The moon is pulling that water towards you, so the moon's got to be back over there. And when it's low tide, it's pulling it the other way. So, it's got to be over there somewhere. The moon sloshes those oceans around on the earth, and that's the tides.

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