Work Done By Gravity

by Patrick Ford
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Hey guys, so now that we understand how to calculate works done by constant forces in this video, we're going to take a look at how a specific force which is the force of gravity. So I'm gonna show you how to calculate the work that is done by gravity. So the whole idea here is that because gravity is a force, that's the MG that we always plug into our free body diagrams, then that means that gravity can do work. So, just remember a quick definition of work is that it's the transfer of energy. And the way we figure out whether it's positive or negative is it's positive when the force goes along with the motion, whether it helps your motion and it's negative work whenever the force points against your motion. Right? So, we're really just going to take a look at two different scenarios here. Gravity acts vertically. Right? You're Ngos points down. So we're gonna look at two different situations when objects are falling, going down or when they're rising and going up. So let's just get to the example here. Right? So in this first example we have a 5.1 kg book that's falling from a two m bookshelf. We've got this diagram here to help us out with this and we've got some information about the speed right before it hits the ground. And in this first part here, we want to calculate the work that is done on the book, bye gravity. So we want to figure out W. G. That's how we're really that's how we're going to write the work done by gravity. So how do we do this? Remember when we calculate works? You're always just gonna start from F. D. Co signed data. You need to know the force, the distance and the angle between those vectors. So let's check this out when you have the book that's falling downwards. The only force that's acting on it is your MG. Is that that force of gravity that pulls things downwards. So your FD cosign data really just becomes MG. So your distance. Now if your book is falling downwards then it's just going to undergo displacement of delta Y. And it's gonna go downwards like this right now. Some books are also going to use delta H just in case you see that letter, they really just mean the same exact thing. So your distance in F. D. Cosign Theta really just becomes delta Y. Now what about the angle between those two vectors? Well they both point downwards, they're basically parallel which means that the angle between them is just zero degrees or theta equals zero. And we know that this term just becomes one. So your work is really just W. Equals MG times delta Y. And because your force, your MG points along your direction of motion, then gravity is going to do positive work. So in part we just do MG times delta Y. And we've got all of our numbers right? We've got the mass, which is 5.1, we've got 9.8 for G. And then the displacement, the delta Y. Is really just the two m that it falls. And notice how we plugged in. Everything is positive. So you're gonna get a work that is 100 jewels. And that's the first part. So let's look at the part B. Now, part B asks us to calculate the kinetic energy right before it hits the ground. So in part B we want the kinetic energy and this is gonna be the kinetic energy final really. Um So if you take a look at our diagram here, what happens is that one of the book is on the bookshelf, like here are kinetic energy is actually equal to zero, right? It's not moving. And then we know that gravity is going to pull this thing downwards and then it's gonna have some velocity right before it hits the ground. So we want to figure out the kinetic energy here at this point, we'll remember that kinetic energy is really just one half M. V. Squared and we've got those numbers. So kinetic energy is just going to be one half times the mass of 51 Let me go and write that again. So you've got one half Times 5.1 times the 6.26 squared. And you go ahead and plug this in and you're gonna get a kinetic energy of 100 jewels. So notice how we get the same exact number here and that is no coincidence. Remember that work is really just a transfer of energy. So when the force of gravity does 100 jewels of work on the box, then the box basically gains 100. So the work is equal to 100 jewels. And so therefore the box gains 100 joules of kinetic energy. All right, so let's move on to the second part now, which is when objects are rising or going up now, we're gonna take a look at a problem here in which Iraq is thrown vertically upwards now and we want to calculate the work and energy. And the basic idea here is that the set up of these problems is gonna be the same. Your gravitational force still points downwards. But now because this block has a velocity that's up, your displacement vector is actually going to point up now instead of down. So really when you go through your FD cosign theta, what happens is that your force is still gonna be MG, your distance is still gonna be delta. Why? Right, those are positives. But now the angle between those two things is not going to be zero because your MG points down and your delta Y. Points up so your co sign now is going to be 180 we know this becomes negative one. So really what happens? I'm sorry. So really what happens here is that your work that is done by gravity just becomes negative MG times delta. Why? Because your force and your motion point in opposite directions, gravity is actually going to do negative work when things are going up. Let's take a look at this example. Now we've got a rock that we're throwing vertically upwards, right? So it's got some velocity like this. We know this initial velocity is 15 and now it happens, it's gonna rise to a maximum height of 11.5. That's basically what my delta Y. Is. So this delta Y. Is equal to 11 0.5. So in this first part here, we want to calculate now the initial kinetic energy K. Initial. So really we're gonna do one half M. V. Initial times of starting the initial square. Right? So we have one half times the two kg rock times the 15 m per second squared. And you end up with a kinetic energy of 225 jewels. That's what you start off with here at the bottom. So we have K. E. Initial is to 25. So now what happens is we want to calculate the work now in part B. So we want to calculate the work that is done on the rock by the force of gravity. That's W. G. And when you have objects that are going up really, this is just gonna be negative MG times delta. Why? Because again your force and motion are opposite. So you're W. G. Is just gonna be negative. This is going to be uh 5.1. This is gonna be too for your mass. This is gonna be 9.8 and now you're gonna have a delta Y. It says that the maximum height is 11.5. So this is your delta Y. Like this, right? And so if you go ahead and calculate this, you're gonna get negative 225 jewels. So notice here again how we get the same exact numbers. And the idea here is that you have all this kinetic energy when you first throw the rock upwards. But remember that as it goes up, the force of gravity is doing negative work on the rocks when it gets to the top here and it finally stops, the kinetic energy is equal to zero. It's basically lost all of its energy because of work. All right, so that's it for this one. Guys, let me know if you have any questions.