Kinetic energy

0:00- [Instructor] What's common between your morning hot coffee and a beautiful song coming from a guitar? To answer that question, we need to explore what kinetic energy is, and that's what we'll do in this video, but let's zoom out a little bit. What exactly is energy to begin with?

0:13Well, I always found defining energy can be very hard. In fact, it can be very circular, so it could be hard to understand, actually, and so as you're trying to define over here, let's try to understand its features and see why it's so useful for us. So the first feature of energy is that it is a scalar quantity, and whenever I hear that something is scalar, I am always excited about it, because scalar means it has no directions.

0:37It can be easily added up. It's just a number, so that's awesome. It's a number that is measured in the standard unit of joules. So you can have kilojoules, megajoules, you can also have non-standard units, like calories, that we use in our day-to-day life, but the standard unit of energy is joules.

0:56So energy so far is, think of it as a number with no direction which is measured in joules. Okay, what else? Well, another important thing is, we can categorize energy into three broad categories. The first one is a number that you assign to moving things, energy due to motion, which we call kinetic energy, the focus of this video, so for example, moving baseball has kinetic energy.

1:19If the baseball is moving faster, it has more kinetic energy, okay? Energy assigned to moving things due to their motion. All right, what else? You can also assign energy based on where they're located, which we call potential energy. In fact, this is slightly more nuanced, and this will be the focus of the next video, but this is more interesting, because potential energy is not just a number that you assign to a thing, like kinetic energy.

1:43It's a number that you assign to a group of things based on their relative positions. For example, if you consider earth and the ball as a group, then based on how far they are, you can assign a number to it, the potential energy. Now, if that distance changes, it'll have a different potential energy.

2:06So yes, there are nuances to it, but we'll tackle that in the next video, so don't worry too much about it. Okay, what else? We have covered energy due to motion. We also have energy based on their relative positions. What else? Well, we can also have energy due to electromagnetic radiation.

2:24Think about light, x-rays, and all of those things. They, too, have energy, and that's something we'll tackle in a future unit all together, but now comes the big question, Why should we care about energy in the first place? Here's why. Think about any process happening in the nature, for example, nuclei fusing together in the core of our sun or maybe leaves absorbing sunlight to create glucose, photosynthesis, or consider a roller coaster that's just speeding down.

2:49In all these things, a lot of changes are happening, but the one thing that doesn't change, turns out, is the total energy. The total energy, turns out, stays the same throughout the process. This means maybe kinetic energy would decrease, but that would result in an equal increase in, say, potential energy or maybe the energy of electromagnetic radiation.

3:09Whatever you do, the total energy never changes, and that's the reason we care about it. We call this the conservation of energy. This is awesome because we can use this to predict stuff. For example, if I want to know how much is the speed of the rollercoaster as it as it falls down, as it comes down a little bit, I can use energy conservation.

3:29I can use the fact that total energy is conserved to make that prediction, and we love doing this because energy is a scalar quantity, so we can just directly add them up. We don't have to worry about their directions, and that's why sometimes, using energies to predict things is much more easier than using other things like, say, using forces or accelerations, because they are vector quantities.

3:49So ultimately, that's the reason why we love energy, because it's a conserved quantity. Total energy throughout a process stays the same. All right, so with that in mind, for the rest of the video, let's just focus on kinetic energy. So how do you calculate kinetic energy of any moving object?

4:06Well, kinetic energy of any moving object is given by the expression half MV squared, where M is the mass of the object and V is the speed of the object. Think of it as the magnitude of the velocity. I don't care about the direction, I only care about the speed, so speed squared.

4:24So you can immediately see that kinetic energy is directly related to mass and the speed, and that makes sense, because it's the energy of motion, so more the speed, more the kinetic energy, but you also see more the mass, more the kinetic energy. So two objects can have the same speed, but have different kinetic energies because they could have different masses, so mass also matters.

4:46Now, one thing we can immediately see from this is that we can try to look at the units of energy by looking at this formula. So if you look at the unit, you get mass, which is kilograms, and speed is meters per second, but it's squared, so it's meters squared per second squared, but we know that this is energy.

5:06so that is the same thing as joules, so we can now see what joules really is in the more fundamental units. Joules, at the end of the day, is basically kilograms meter squared per second squared. But let's try to get a feeling for joules by taking a few examples, so let's take an example.

5:21Let's say we throw a baseball, and we know the mass of the baseball. Let's say it's about 0.15 kilograms, and let's say this is a baseball thrown at about 90 miles an hour, a fastball, so which roughly translates to about 40 meters per second. What is the kinetic energy of this baseball?

5:38Why don't you pause the video and see if you can find this out yourself? All right, let's do this, so kinetic energy is half MV squared. We know the mass, we know the speed, so we can just plug in. So that makes it half into 0.15 times 40 squared. So 40 squared, I can directly write as 1,600.

6:03Four squared is 16, so you get 1,600, and yeah, we can simplify this. This makes it eight, so you get 800, and I can do this in my head. So eight times five is 40, eight, one, zero, eight, so 12, so I get 120, and then these two zeros, and then I have the two decimals, so one, two, so I get 120, so lemme just add these extra zeros.

6:30So I get about 120 joules of kinetic energy, and remember, these are realistic numbers. This is basically a fastball, so you can kind of get a feeling for the amount of joules that we deal with in our daily life. All right, let's take another example, not a daily life example. (laughs) Let's take the example of a space probe that's going around Jupiter.

6:52As we speak right now, it's happening, okay? The mass of this space probe is given. We know the kinetic energy of that space probe. In fact, the kinetic energy keeps changing as it goes through the orbit, but at one particular moment, let's say the kinetic energy is this much.

7:05We want to figure out what the speed of that space probe is. Again, encourage you to pause the video and see if you can figure this out yourself first, all right? Again, I know my kinetic energy is half MV squared, but this time, we need to figure out what V is.

7:20K is given to me, M is given to me, so what I try to do next is I try to isolate V, so let's rearrange this. To isolate V, I'll multiply by two on both sides and divide by M on both sides, so I'll get 2K divided by M equals V squared, but I don't want V squared, I want V.

7:41How do I do that? Well, I take a square root on both sides, so lemme do that, take square root on both sides, and so now, I will have V on the right hand side. So lemme just write that over here, so V equals square root of 2K divided by M, and now we can plug in.

8:00So if you plug in, what do we get? We have two times the kinetic energy is given to me, and I be a little bit more careful now. These are big numbers, so lemme just write them down first and then divide by M, so M is given to me as 1.59 times 10 to the power three.

8:18All right, so the first thing I do is, I simplify this. I'll take my calculator and do that over here, so two multiplied by 4.33. I'll ignore the 10 powers for now, okay? Divided by 1.59, 1.59. That gives me 5.4, if I round it up, 45, so let's write that. So that gives me V equals, let me write that over here, square root of 5.45 times 10 to the power.

8:51What is this? Well, 10 to the power divided 12, you have the power three is 10 to the power 12 minus three, which is 10 to the power of nine. Now I can take the square root of this, but taking square root of 10 to the power nine is difficult. Taking square root of 10 to the power even numbers is easy, because you just become half.

9:0710 square, the squared becomes 10 to the power one. 10 to the power four, the square becomes 10 to the power two. So I just have to take this, so before taking the square root, let me convert this into an even number, and the way to do that is I can, well, one way to do that is basically, I'll say this is 54, I'll take one 10 out, so I'll let 54.5 times, since I took one 10 out from here, I'm remaining with only eight tent over here, so 10 to the power of eight.

9:35It's an even number. Now I can take the square root. I know this will be 10 to the power four after the square root, and so I just have to take this square root of 54.5, which I'll do that again over here. Let me just take the square root. Where is the square root? I can't find the square root.

9:50Okay, I just need to do scientific, okay? So now 54.5, take the square of that, I get 7.38. 7.38. so I get about 7.38 times 10 to the power of four meters per second. Now, remember in general, when you take a square root of any number, mathematically, the answer is plus or minus.

10:10You have two answers for that, because square of two is four, square of minus two is also four, right? So technically, I should get a positive and a negative number, but since V is the speed, speeds can't be negative. That's why we know we only take a positive number, and so our answer is a positive number.

10:30That brings us to our original question, what's common between these two? Well, a hot coffee, we say, has thermal energy in it, right? Hotter it is, more thermal energy. But if you were to zoom in, when things are hot, basically, their atoms are jiggling faster, or they're moving very fast.

10:46In other words, they have more kinetic energy. So thermal energy, at a microscopic level, is basically kinetic energy. Similarly, if you look at sound energy, we might think of it as a different kind of energy, but again, if you were to zoom in and look at it, what exactly is sound energy?

11:04Sound energy is where atoms or molecules of the medium, like, say, the air, are basically moving back and forth in unison. We call that as a sound wave. But at the end of the day, that energy is basically energy of motion of these atoms and molecules, so again, it is kinetic energy at a microscopic level!

11:21So what's common between them is they're not new forms of energy, they are both kinetic energy at a microscopic level. Now, of course, remember, because there are also multiple particles and they're all interacting with each other based on their relative position, there's also potential energy.

11:36So yes, there's both kinetic and potential energy, but the takeaway is, it's not new form of energy! (laughs) Thermal energy and sound energy are basically kinetic and potential energies at the micro level.