Weight Force & Gravitational Acceleration

by Patrick Ford
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Hey, guys. So up until now we've been dealing with forces that act only on the horizontal axis like this. We're gonna start to look at some forces now to act on the vertical axis. And one of the main ones you're going to use in almost all of your problems is the gravitational or the weight force. So we'll be talking about this weight force and gravitational acceleration in this video. Let's check it out. So, guys, the main idea here is that all objects that are near the earth are affected by a phenomenon called gravity and gravity is going to produce a force. And one of the things that we've seen this chapter is that if you have forces that act on objects and there's no other forces, the next going to produce an acceleration because of F equals M A. If you have a net force, then there's gonna be some acceleration. So these these three related ideas here gravity the force due to gravity and the acceleration due to gravity. Let's talk about them in more detail. So, guys, whenever your textbooks measure this effect or phenomenon called gravity, really, all that all that is is It's a conceptual phenomenon that tells us that objects that have mass, for instance, like this asteroid and our earth over here are going to attract each other. So these two objects, because they have mass, they are going to attract each other like this. So how do they actually attract each other? Well, they do it by producing forces. So this force that is due to gravity basically what happens is you have this earth that is pulling on this asteroid, and I'm just gonna look at the asteroid for a second. There is a force due to gravity. So we actually have a name for that. It's called the Weight Force or the Gravitational Force. So really, this arrow is actually a vector. We're gonna call this W. But the other symbol that you might see for it is also equal to F. G. So you might also see f g. The equation is very straightforward. The weight force is just equal to little mg mass times, gravity, mass times, gravitational acceleration. This little G here and what you need to know about this weight forces that the units, just like all other forces, are in Newtons and what's special about this force is that it's always going to point towards the earth's center. So in this case, the asteroid, the weight forces going to point towards Earth Center like this now almost always in your problems, that's going to be pointing down towards the ground unless you explicitly told that the ground is somewhere else. All right, so now this force here is going to produce an acceleration. It's going to cause this asteroid to fall towards the earth. How do we actually calculate that acceleration? We can just use F equals Emma. So if this weight force here this F g, which is equal to MG here is the only force that's acting on this object, then we can use F equals to figure out this acceleration. The only force that's acting on this thing is little mg, and this is going to be equal to little m A. So what happens is our EMS are going to cancel, and your acceleration is just going to be little G. So this acceleration here, that's due to gravity, which has a name. It's also called The gravitational acceleration is really just a which is just the little G that we've been using for a bunch of chapters so far, all the way back to our motion chapters. We know that this little G near the Earth has a value. It's 9.8 near the Earth, and its units are not Newton's. Its units are going to be meters per second squared. Now when you need to know about this acceleration here. So we know that this object is going to accelerate down like this is that this acceleration is not constant. This acceleration does vary by location. For example, we know that the gravitational acceleration on the earth is that 9.8 that we've been using for some time now. But if you were to go to the moon or Jupiter or somewhere else, that gravitational acceleration is gonna have a different value on the moon. That's equal to 1.62. You might have seen those videos of astronauts who are bouncing around on the surface of the moon, and that's because the gravitational acceleration is weaker there so they can jump higher. They can balance all that kind of stuff. All right. So, again, just to recap the effect of gravity produces a force and that force always gonna point where the Earth Center that forces the weight force and it's given in terms of Newton's and that force, if it's the only force that's acting on an object, produces an acceleration called the gravitational acceleration. That's our little G, and that is equal to 9.8 m per second squared. That's the units. All right, so let's move on now. One thing you need to know about this weight force is that that term weight is actually used incorrectly in everyday language. What do I mean by that? Let's check out this example. Is this that you step on a bathroom scale and it measures your weight to be kg? So what is your real weight on the Earth's surface? Well, the reason that weight is in quotation marks like this is because the weight force is not supposed to be given in units of kilograms. Remember your weight force, just like all other forces has to be given in Newton's. So really, what's going on here, guys, is that scales don't measure weight. Instead, what scales measure as they measure your quantity of mass so mass, which is given in terms of kilograms is really just the quantity of matter. It's the amount of matter that makes up you or another an object or something like that, and this mass is not going to change at different locations. So, for instance, if you a 70 if you have 70 kg of mass on the earth's surface, if you go to the moon or Jupiter, it's still gonna be 70 kg, because the quantity of matter, the amount of stuff that makes up you hasn't changed. Wait, on the other hand, we know is given in terms of Newton's, and that's a force that's due to gravity. And unlike the mass, your force is going to change. This force does change depending on different locations. We can actually just see that by the equation, w equals mg. So just as the gravitational acceleration little G varies by location, then so does your weight force, because that's part of that equation. So your MG service or your weight force, just like little G will change based on different locations. So what's your real weight on the earth's surface? Well, if your mass is equal to 70 kg, then we can just use 70 kg times 9.8 and you're gonna get 686 Newtons. So that's your real weight on the Earth's surface. 70 kg is just your mass. Let's check out this next example here. If an object has 10 kg on the Earth, what's its mass on the moon? So basically what they're saying here is if M Earth is equal to 10, then what is M moon? Well, remember, guys that your mass, which is the quantity of matter, does not change debate based on your location. So if you have 10 kg on the moon, if that's your mass and that means that this object is going to be 10 kg. Sorry. If you're 10 kg on the earth's surface, then that means on the moon. It's also going to be 10 kg. So what's its weight on the earth? Well, how do we get Wait, We just use the equation. W equals mg. So if 10 kg, then that means the weight on the earth is going to be 10 times little G Earth, which is 9.8. So this is just gonna be 98. And that's Newton's So if the same object 10 kg will be put on the moon, its weight on the moon would be the 10 kg times the gravitational acceleration of the moon, which is 1.62. And so therefore be 16.2 Newtons. So your weight would be less, but your mass would be the same. That's it for this one. Guys, let me know if you have any questions.