Work and power

0:00- [Instructor] Earlier, rollercoaster used to start from a height, with a lot of gravitational potential energy, which then get converted into kinetic energy as the coaster goes down. But what you're seeing here, is an example of something called a launched a rollercoaster, because a rollercoaster launches from a low height and then goes up.

0:15How did the kinetic energy of the rollercoaster increase over here? Where did that energy come from, and how do we conceptualize that? Let's find out in this video. Let's start with a simple example. We have a ball at rest over here, so its kinetic energy is zero.

0:29Now, we kick that ball. So the ball now is moving, and therefore it has some kinetic energy. Where did it come from? Well, clearly we could say that, hey, it came from the kick. Clearly the energy must have transferred from the leg into the ball or something, right?

0:42But how did that energy get transferred? Well, when the kick was made... Well, sorry. When you kicked the ball, there was a force acting on it. And we know from Newton's laws, when there's an unbalanced force acting on an object, this is an unbalanced force, it accelerates the object, which means it speeds up the object, which means it increases the kinetic energy of the object.

1:01Woo. This means, whenever there's an unbalanced force acting on an object, there is an energy transfer happening. And this energy that got transferred due to that force, we give a name to that. We call it, "Work." Work, is the amount of energy that got transferred by this force.

1:20Now, this work is very loosely defined in our day-to-day life. Like for example, I could be sitting over here, and just thinking about something and say, I could say that I'm doing work. But notice in physics, it has a very specific definition. First of all, work is always done by a force.

1:32So whenever you're thinking about work in physics, always ask yourself which force is doing the work. Don't think in terms of whether the leg is doing the work, or the hand is doing. Uhn-uhn. Always ask yourself which force is doing the work. And remember, what does that work represent?

1:44How much energy got transferred. Since work is a representation of how much energy gets transferred, what will be the unit of work? Well, it should have the same unit as energy. It would be joules. And just like energy, it would be a scaler quantity. Okay, moving on.

2:00As the ball goes forward, it's going to stop. And that happens because there's frictional forces, there's air resistance. Let's forget about air resistance. Let's only consider frictional forces for now. So notice that means when the ball is moving forward, again, there's a force acting, and that is this time removing all of that kinetic energy, which means, again, work is being done, by which force this time?

2:23Frictional force. And again, if you want to ask how much work is done by this frictional force, you will say the amount of energy that is transfer, this time transferred outta the ball. And where does that energy go? Well, the energy goes in heating up the ground or something.

2:34So what difference do you find between the work done by the kicking force and the frictional force? The kicking force transferred kinetic energy into the ball. The frictional force transferred the energy, kinetic energy out of the ball. Why did that happen? What is the difference?

2:48Hey, we can see that when we kick the ball, the force was in the same direction of motion. So whenever you're putting the force in the same direction as the motion, you are transferring energy into that object. And therefore we say you're doing positive work. Think of positive work as transferring energy into that object.

3:08But look, friction is acting in the opposite direction, slowing it down, decelerating it. Ah. So whenever forces acting in the opposite direction, it removes the energy from the object, and therefore we say it is doing negative work. So our kicking force did positive work.

3:25The friction did negative work, removing all of that kinetic energy. Okay, what about if the force was not exactly in the same direction, but was slightly tilted up like this? Well, now notice still, the force is somewhat kind of parallel to the direction of the motion.

3:41So this is still going to do positive work. On the other hand, if the force was this way somewhat like this, nowadays, it's sort of kind of in the opposite direction. Not exactly, but sort of kind of. Therefore, now it will be doing negative work. That brings us to the question, what if the force is neither tilted backwards nor forwards, but exactly perpendicular?

4:05What happens then? Well, we've seen an example of that when we considered orbits. If you consider satellite going around the earth, it's in perfect circular orbit, then notice the direction of the gravitational force is exactly perpendicular to the direction of the velocity vector, right?

4:21So in this case, what's going to be the work done? Well, we know in this particular case, the satellite speed does not change. It neither increases nor decreases. Its potential, its kinetic energy stays the same, and its gravitational potential energy stays the same as well.

4:34Therefore, notice there is no energy transfer, which means this force does zero work. So whenever a force is acting perpendicular to the direction of the motion, we will say there is zero work. Zero work. Because it doesn't change the speed of the object. All it does is make the object turn.

4:56It acts like a centrivotal force. However, what if the orbit is not perfectly circular? In general, we know the orbit is elliptical. Now we do see gravitational force doing some work. For example, over here, notice, the force is somewhat kind of in the direction of the motion, therefore it's doing positive work.

5:13And because it's doing positive work over here, the kinetic energy increases. And that's exactly what we see. The kinetic energy increases. As the object comes closer, its speed increases. We've seen that before. And as it goes away over here, notice, it's somewhat kind of, the force is somewhat kind of in the opposite direction.

5:28And therefore, here it's doing negative work. And it is sucking the kinetic energy out of the object, and therefore its speed decreases, kinetic energy decreases. And again, we've seen that as it goes farther away, its kinetic energy decreases. Okay? Finally, in all these cases, we considered one single force acting on the object.

5:46What if there are multiple forces acting on the object? Then what do we do? Well, then we just calculate the work done by the net force. Okay? You add up all the forces, and now if the work done by the net force is positive, the kinetic energy will increase. If the work done by that net force is negative, the kinetic energy will decrease.

6:02And if it's zero, the kinetic energy will stay the same. This is what we call the work energy theorem. This time, we're considering the work done by all the forces together, the network done, that will equal to the change in the kinetic energy. Let's take one final example, just to make sure that we understand this.

6:20Okay? In this particular case, let's say we are gonna take a ball in our hand, and slowly rise it up slowly rise it up, slowly, and bring it to a stop over here, which means the kinetic energy here is zero. The kinetic energy here is also zero. So what does it change in the kinetic energy?

6:35Zero. That means the network work done on the ball is zero. Wait, how does that make any sense? Clearly, my force must have done some work. Then why do we say the network done over here is zero? Can you pause the video and think about it? Alright. Again, remember, think about the forces.

6:52There is a force that my hand is putting on the ball upwards, and because it's in the same direction of motion, my hand is clearly doing a positive work. The force from my hand is clearly doing a positive work. So because of that, the energy, the kinetic energy of the ball should have increased.

7:07It would have increased if there were no other forces. But there is another force. There is gravity. And look, gravity is acting downwards in the opposite direction of the motion, and therefore it's doing negative work. And you know when you do negative work, you remove kinetic energy from the object.

7:22Ah, so you can see what's going on. The force from the hand is trying to add kinetic energy to the ball, but hey, gravity is removing the kinetic energy from the ball. That's why the kinetic kinetic energy did not change. And that's why the total work done is zero.

7:38Makes perfect sense, right? Because it's positive work, negative work, total work then becomes zero. But you might ask, "Well, where did that energy go?" Because if the force from the hand did transfer energy into the ball, but it didn't get stored as kinetic energy, but where did it go?

7:51Well, it didn't get stored as kinetic energy, but look, the gravitational potential energy has increased. So, it got stored as gravitational potential energy. Don't worry, the energy doesn't go anywhere. You can always keep track of where that energy went. But in all these cases, we only considered how much work, or how much energy was being transferred, right?

8:14But in more practical cases, we are also interested in how quickly that work is being done, or how quickly that energy is being transferred. And that is also, that quantity is called, power. So, think of power as the rate of doing work. Basically, how quickly this work is being done, or how quickly the energy is being transferred.

8:34And mathematically, we can say power is work done per time. Okay? Or energy transferred per time. So what will be its units? It's units will be joules per second. It'll also be a scale up quantity. And joules per second is called watt, named after James Watt. For example, if the motor inside your pump, let's say, delivers a power of hundred or thousand watts, what does it mean?

9:03Well, it just means that the motor, or the pump, is basically doing thousand joules of work. It's doing a thousand joules of work, in say, raising that water or something. A thousand jus of work per second. That's all it means. So if I wanted to now know how much work the pump does in five seconds, we'll just multiply this number by five.

9:24Because this is the work done per second. Multiply that by five, you get work done in five seconds. So that's 5,000 joules. Makes sense, right? So this thousand watt is also called kilowatt. You can also have megawatts and so on and so forth. But there's also another unit of power, not a standard unit of power, but you probably have heard it.

9:42It's called horsepower. We use this usually in mechanical machines and all of that. Because earlier, we used to use horses for all our mechanical work, right? So the horsepower, you can kind of sort of think as an old unit that basically meant, like you know, how much power, or how much work a horse can do per second.

10:03But of course, I say "Kind of, sort of," because different horses have different amount of power, and it'll also vary, depending upon whether the horse is tired or not. But anyways, today we just think of this, you know, as a different unit. And the way we think about horsepower, the way we define horsepower, is there's a conversion.

10:19One horsepower is roughly around 746 watt. You can just use W for watt. Okay, yeah, 746 watt. Okay, finally, coming back to our pump, where does the pump get this energy from? Because remember, energy can neither be created nor destroyed. Well, you know, it's if it's running on electricity, it's using electrical energy to actually raise that water.

10:41And, electrical company also charges you for how much energy you consume, electric energy your devices consume. They don't care about the power, they don't care about how quickly you consume that energy, they only care about how much energy you consume, right?

10:56So they will charge you for the joules you consume, not the watts. But a joule is a very tiny unit of energy. So electrical companies or electric. So when it comes to electricity, we have a bigger unit of energy, which we often call "kilowatt power." Now, I used to always eat confused thinking that hey, kilowatt R is a unit of power, but no, remember, it's not just kilowatts, it's kilowatt hour power multiplied by time, which is the unit of work done or energy transfer.

11:30So that's the unit of energy. And what does a kilowatt hour mean? This means if you have any device, any electrical device that's consuming a kilowatt power, meaning a kilo joules or a thousand joules per second, and you use it for one hour, okay, then whatever the total energy is consumed by that device, is what we call a kilowatt hour, one unit of electric energy.

11:55And your electric company charges you for how many kilowatt hours you consume, say per month. So coming back over here, how is the kinetic energy of the rollercoaster increasing? Well, turns out there are motors over here that are delivering continuously some power, meaning they are transferring some energy into the rollercoaster per second.

12:16How do they transfer energy? Well, by doing work. In other words, they are pushing the rollercoaster in the same direction of the motion. So they're doing positive work. And then that kinetic energy transfers into gravitational potential energy, and then it changes back into kinetic energy, and so on and so forth.

12:31And finally, when the rollercoaster comes to a stop, how does it comes to a stop? Again, there are motors doing work, but this time they're pushing in the opposite direction of the motion, which means they're doing negative work, removing the kinetic energy from the rollercoaster.

12:49Beautiful, isn't it?