About this video
Energy is a number we assign to an object or group of objects, measured in joules, and the energy of moving things is called kinetic energy. Kinetic energy depends on mass and speed: it increases linearly with mass (double the mass, double the energy) but with the square of the speed (double the speed, four times the energy; triple the speed, nine times).
You'll be able to
- explain that kinetic energy is the energy of motion, measured in joules.
- explain that kinetic energy depends on mass and speed.
- use the linear relationship with mass to predict kinetic energy.
- use the square relationship with speed to predict kinetic energy.
Key words
- energy
- A number we assign to an object or group of objects, always measured in joules.
- joule (J)
- The unit used to measure energy.
- kinetic energy
- The energy an object has because it is moving.
- linear relationship
- When one quantity changes by some factor, the other changes by exactly the same factor, giving a straight-line graph.
- square of the speed
- The speed factor multiplied by itself; doubling speed (2) gives 2 x 2 = 4 times the kinetic energy.
Transcript
- [Instructor] A moving tennis ball has energy, but what exactly is energy and what does it depend on? That's what we're gonna figure out in this video. So let's begin. So what's energy? Well, we use this term in our everyday life, but in science it has a very specific meaning.
Think of energy as a number that we assign to an object or a group of objects, and it is measured in joules. So energy is a quantity that's always measured in joules. And guess what? The energy that we associate with moving things, we call that kinetic energy.
Moving stuff has kinetic energy. But what does the kinetic energy depend on? Well, let's see. One factor that decides how much kinetic energy an object has is its mass. So if you compare the motion of a tennis ball, let's say, that of a wiffle ball, let's say that both of them are moving at exactly the same speed, then guess what?
Because the tennis ball has more mass, it'll end up with more kinetic energy. So more mass, you tend to have more kinetic energy. Okay, what else besides the kinetic energy? Well, it's the energy of motion. So the second thing that matters is the speed. This time, consider two tennis, ball identical masses, okay?
But one is moving much faster than the other. Guess which one has more kinetic energy? It's the one that's moving faster. Something that moves faster will have more kinetic energy. So the two things that kinetic energy depend on are the mass and the speed. More the mass or more the speed, more the kinetic energy.
But now comes the next question, how exactly do they depend on the mass and speed? So let's analyze. Let's first consider the connection between mass and the kinetic energy. To analyze, let's consider a bunch of balls with different masses, okay? And we are gonna throw them with exactly the same speed.
Let's say 10 meters per second. Alright? And figure out what the kinetic energy is. And let's say here are the numbers that we record. Okay? First of all, let's see if this makes sense. We can see as the mass increases, the kinetic energy also increases. They have the same speed, so this kind of makes sense.
But now if you want to see an exact connection, what is the connection between the mass and kinetic energy, one of the cool ways to do that is to actually plot a graph. So let's do that. Let's plot a graph of kinetic energy versus the mass. And if you put these numbers over here, what we see is that they pretty much lie on a straight line.
That's interesting. What does that mean? Well, what that means is if you consider an object which has, let's say a mass of 0.2 kilogram, in this particular case, if it's moving at 10 meters per second, it'll have a kinetic energy of 10 joules, right? Okay. Now think about this.
What if you consider an object which has twice the mass, 0.4 kilogram? Then it'll have twice the kinetic energy. Ooh, do you see the relationship? If the mass doubles, the kinetic energy doubles? What happens if the mass becomes half? Well, if the mass halves from 0.2 to 0.1, oh, look, the kinetic energy also halves.
So we can see the connection between mass and kinetic energy. We say this is a linear connection. Kinetic energy increases linearly with mass. With whatever factor the mass increases, the kinetic energy will also increase by exactly the same factor. And this is pretty important because now we can use this to predict what kinetic energy would be for any other mass that's moving at this particular speed, 10 meters per second.
For example, let's say we had a bowling ball whose mass was six kilograms. Okay, it's nowhere over here. Okay? Could we predict what its kinetic energy is if it was also moving at the exact same speed, 10 meters per second? Why don't you pause the video and think about this?
Alright, well, because we have a linear relationship, what we can do is we can look one of these numbers, we can see, oh, we can actually see here. And we know that if it's, you know, a 0.06 kilogram object, we'll have a kinetic energy of three units. This has 100 times more mass, and therefore its kinetic energy will also be 100 times more than over here.
And so it'll have a kinetic energy of 300 joules. Does that make sense? This is what it means to have a linear relationship. So kinetic energy increases linearly with mass. Alright, next up, let's see the connection between kinetic energy and speed. Does it also increase linearly?
Let's see. This time we'll take objects of exactly the same mass because it's the speed that we are worried about, right? So let's consider tennis ball, which has a mass of 0.06 kilograms. We are gonna throw it at different speeds and note down in kinetic energy.
And these are the numbers that we end up with. And again, first of all, sense check. As the speed increases, we see the kinetic energy increasing. That makes sense. But the big question is, what is the connection? So again, let's plot a graph. This time we'll plot a graph of kinetic energy versus speed.
And when you do that, what do you get? Ooh. Do you know, it is no longer in a straight line. In fact, you get some kind of a curve. What does this mean? Let's analyze. If you consider the kinetic energy when the speed is at 10 meters per second, it happens to be three joules.
Okay? Now what happens when the speed is 20 meters per second? We get the kinetic energy to be 12. Do you notice something interesting? The speed has doubled, but look, the kinetic energy has not doubled. It has increased by four times. Ooh. So when you double the speed, the kinetic energy increases four times.
That's interesting. What would happen if we were to, say, triple the speed? Well, let's see. W hen the speed is five meters per second, we get the kinetic energy to be 0.75 joules. Now let's triple that. Let's make the speed 15 meters per second and find the kinetic energy to be 6.75.
This is nine times higher, okay? Because 0.75 times nine gives you 6.75, which means when we triple the speed, the kinetic energy increase nine times. When we doubled it, it increased four times. When we triple the increase nine times, woo, that means you see it's increasing by the square of the number.
Kinetic energy increases by the square of the factor by which the speed increases. So we say kinetic energy increases with the square of the speed. It's not linear, it increases with the square. So putting it all together, we realize that energy is the quantity measured in joules and the energy associated with objects motion is what we call kinetic energy.
And the kinetic energy increases linearly with mass and it increases with the square of the speed.
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