Guys, now that we understand how to calculate work done by constant forces, in this video, we're going to take a look at a specific force, which is the force of gravity. I'm going to show you how to calculate the work that is done by gravity. The whole idea here is that because gravity is a force, the m*g that we always plug into our free body diagrams, then that means that gravity can do work. 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, when 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 2 different scenarios here. Gravity acts vertically. Right? Your m*g points down. So we're going to look at two different situations when objects are falling, going down, or when they're rising and going up. Let's just get to the example here. Right?
In this first example, we have a 5.1-kilogram book that's falling from a 2-meter bookshelf. We've got this diagram here to help us out with this. We've got some information about the speed right before it hits the ground. In this first part here, we want to calculate the work that is done on the book by gravity. We want to figure out Wg. Remember, when we calculate work, you're always just going to start from Fdcosθ. You need to know the force, the distance, and the angle between those vectors. Our force F really just becomes mg. So your distance now, if your book is falling downwards, then it is just going to undergo displacement of Δy, and it's going to go downwards like this. Right? The angle between those two vectors is just 0 degrees. θ = 0, and we know that this term just becomes 1. So your work is really just W = mg × Δy. 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 Δy, is really just the 2 meters that it falls. You're going to get a work that is 100 joules, and that's the first part.
Part B asks us to calculate the kinetic energy right before it hits the ground. This is going to be the kinetic energy final, really. When the book is on the bookshelf, our kinetic energy is actually equal to 0. Right? It's not moving. When gravity is going to pull this thing downwards, it's going to have some velocity right before it hits the ground. Remember that kinetic energy is really just 12mv2. Kinetic energy is just going to be 12 times 5.1 times 6.262, and you go ahead and plug this in, and you're going to get a kinetic energy of 100 joules. Notice how we get the same exact number here, and that is no coincidence. Remember that work is really just a transfer of energy. When the force of gravity does 100 joules of work on the box, then the box basically gains 100 joules of kinetic energy.
Alright, let's move on to the second part now, which is when objects are rising or going up. We're going to take a look at a problem here in which a rock is thrown vertically upwards, and we want to calculate the work and energy. The setup of these problems is going to 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 Fdcosθ, what happens is that your force is still going to be mg. Your distance is still going to be Δy. Right? But now, the angle between those two is going to be 180 degrees because your m*g points down, and your Δy points up. So your cosine is going to be -1. So your work that is done by gravity just becomes negative mg × Δy. When you have objects that are going up, it's just going to be negative. This is going to be 2 for your mass, 9.8, and the maximum height is 11.5. So you're going to get the work of negative 225 joules.