 Let's calculate work done when things are dropped or lifted. Let's solve two problems on this. Here's the first one. A dumbbell of mass five kilogram drops to the ground from a height of 10 meters. Calculate the work done by gravity. We're given G is 10 meters per second square. So let's quickly go ahead and draw the situation. So we have a dumbbell whose mass is five kilogram. It's dropped from a height of 10 meters. So it just falls down. So this dumbbell just falls down from a height of 10 meters. And in doing so, we need to calculate the work done by gravity. Let's first write down what are the given things to us. I know the mass of this dumbbell. So let's write that down. The mass is given to be five kilograms. I know the height. The height is given to be 10 meters. And I'm also given the value of G to be 10 meters per second square. From this, how do I calculate work done? Well, we have seen from previous videos that work done by a force on any object equals the force multiplied by the displacement of that object. In our example, the object is the dumbbell. And the force acting on the dumbbell which we are asked to calculate is the force of gravity. So in our case, if we multiply the force of gravity on this dumbbell with the displacement of the dumbbell, we'll get the work done. So before we go ahead and do this, great idea to pause the video and see if you can try to get the answer yourself first. All right, let's see. First of all, notice we already know the displacement of the dumbbell, right? The dumbbell gets displaced by 10 meters, which is just the height through which it fell down. So we know that. So all we need to do now is calculate the force. Which force is this? This is the force of gravity. Do we know how to calculate force of gravity? Yes, we do. So if I keep my dumbbell somewhere over here as it was falling, then we know the force of gravity on any object is going to be the mass of that object times G. This is the force of gravity. So now that we know both the force and displacement, let's just plug in and see what we get. So force is just the mass times G and the displacement is just the height. Now one thing we need to be very careful over here is, remember, work done can be both positive and negative. It's positive when the force and displacement are in the same direction. It's negative if they're in the opposite direction. In our example, which one is it? A lot is the force is acting downwards. Even the displacement is downwards. So in our case, the work done is going to be positive. But before we continue and plug in, just think about what would have happened if I had thrown the dumbbell up. Now the force of gravity would still be acting downwards. Gravity always acts down, but our object or dumbbell would be going upwards in the opposite direction. So the displacement would be in the opposite direction of the force of gravity. In that case, the work done would be negative. So if you throw this dumbbell up, then gravity will do negative work. But of course, in our case, since the dumbbell is falling down, the gravity is doing positive work. All right, let's just go ahead and substitute the numbers and see what we get. Again, if we had not tried this before, great idea to pause the video and see what answer you get once you substitute. Okay, let's go ahead and plug in. So the work done, let me choose a brighter color. So the work done is going to be mass, which is five kilograms times G, which is 10 meters per second squared. This is our gravitational force, times the height, which is 10 meters. And so the work done becomes five times 10 is 50, 50 times 10 is 500. So we get 500. Let's look at the units. Don't forget the units. Kilogram meter per second squared. Let's keep that separate. That's the unit of force. That's the unit of force times meters. Now, kilogram meters per second squared, since it's the unit of force, we can also write as Newtons. So we'll write this as Newtons times meters. And so that's our work done. Work done by gravity is 500 Newton meter. But of course, remember Newton meter is also called Joules. So we can also say 500 Joules. That is the work done by gravitational force on our dumbbell. It's positive. All right, let's go ahead and solve another one. Here's a question. A woman slowly lowers a 20 kilogram barbell rod through a distance of 0.2 meters as shown below. Find the work done by the woman on the barbell. So she's exercising maybe. And so she takes that barbell rod and she's lowering it. So let's look at that. If you could see it, maybe it looks somewhat like this. She lowers it this way. That's given to us, okay? We need to calculate how much work the woman does on the barbell. So let's see. Let's again write on what's given to us. We know the mass of that barbell rod. So let me write that down here. It's given to be 20 kilogram. We know the distance through which it moves. Let me just call that as the height. That is given to be 0.2 meters. And again, we're given G to be taken as 10 meters per second square. And again, since we're asked to calculate the work done, we'll do it as force times displacement. We know the displacement. That is 0.2 meters. But what's the force? See here, we have to calculate the work done by the woman on the barbell. So this must be the force that the woman is putting on the barbell. How much is that? Well, I guess here's the clue. It's given that the woman is slowly lowering the 20 kilogram barbell. Imagine she's slowly lowering it without any acceleration. Think of it that way. All right? Then can you figure out what that force is going to be and what direction that force is going to be? Go ahead, give it a try. Pause the video and give that a try. All right, let's see. Let's consider when the barbell is somewhere in between when it's still moving down. Somewhere over here, let's say. Okay, now we know that gravity is pulling down on this barbell. So there is a force of gravity on it, which is mg, but this barbell is moving with a constant speed. It's slowly moving, no acceleration, let's say. Then the force on that barbell must be balanced, right? Because if the forces are not balanced, remember the barbell would accelerate. And so to balance this force, she must push up on that barbell with exactly the same force. And so the force with which she's pushing on the barbell should exactly equal to the weight of that barbell, equals mg. Now, of course, one question you might ask is if the two forces are exactly equal and balanced, why is the barbell moving? Why does the barbell just not stay at rest at the topmost point? That would be a pretty good question, okay? And here's how I like to think about it. Imagine that at the topmost point, her force becomes a little smaller than gravity because of which the gravity starts winning and the barbell starts moving down. That's how the barbell starts moving. She momentarily, just for a fraction of a second, puts a smaller force. But then once the barbell is in motion, her force will match that of gravity, making sure the barbell moves slowly with a uniform speed, okay? And if you think about it even more, then at the bottommost point, she needs to now stop that barbell, right? In order to stop that barbell, she now has to put a little larger force than the weight, again, momentarily. And so you see, at the top, it's a little smaller. The bottom, it's a little larger, so they kind of compensate. And of course, in between, for most of the motion, the force is equal to that of the weight. And so we can say overall, her force should be equal to the weight of the barbell. And so if we go ahead and plug in, since we know the force, our force is equal to the weight for most of the motion, it's going to be mg times h. But one thing to be careful about is it positive or negative work? Well, this time notice her push is upwards. Remember, it's this force that we are interested in because it's the work done by the woman. So her force is upwards, and the displacement is downwards. And so they are in the opposite direction. Ooh, so the work done becomes negative. That's something to be careful about. All right, now we can just substitute the values of mg and h. 10 times 0.2 is two, two times 20 is 40. And so our answer is going to be negative 40. Again, the units are going to be newtons, which is the unit of force, meter, newton meter, which is the same thing as a jewel. And that's our answer. So the work done by that woman on that barbell is going to be negative 40 jewels. And so I guess the most important thing we saw over here is that whenever you are lowering or raising any object, we can say that the force with which you're pushing on the object is pretty much equal to and opposite to the weight of the object, the gravitational force acting on the object.