WEBVTT physics/high-school-physics/selhorst-jones 00:00:00.000 --> 00:00:06.000 Hi, welcome back to educator.com, today we are going to be talking about power and simple machines. 00:00:06.000 --> 00:00:13.000 Let is just start off with, what would you say is the difference between a go-kart, a family car and a race car is? 00:00:13.000 --> 00:00:20.000 I will be honest, there are a lot of differences, but I would say their main difference is their top speed. 00:00:20.000 --> 00:00:22.000 It is high fast they can go. 00:00:22.000 --> 00:00:25.000 How quickly they can get in going a certain speed. 00:00:25.000 --> 00:00:32.000 You are going to get a lot of difference in how fast a race car can get from 0 to 60, ad how fast the family van can get from 0 to 60. 00:00:32.000 --> 00:00:37.000 The major issues here are, how fast they can go at their maximum, how much power can they put out. 00:00:37.000 --> 00:00:40.000 What is the idea of power? 00:00:40.000 --> 00:00:49.000 So far we have talked about speed and its connection to energy, but we have not talked about different rates of gaining that kinetic energy, we have just talked about it being there. 00:00:49.000 --> 00:00:57.000 We have not talked about the difference between getting it to going fast quickly, we have only been talking about going fast versus going really fast. 00:00:57.000 --> 00:01:06.000 There has been, the speed that you are going at, there has been no talk about how fast you can get to go in that speed, what is your acceleration has had no effect on this. 00:01:06.000 --> 00:01:14.000 That is where power is going to come in, we are going to start talking about how quickly an object or system gains energy. 00:01:14.000 --> 00:01:17.000 Consider the idea that we are climbing a flight of stairs. 00:01:17.000 --> 00:01:30.000 Let us assume that we weigh 50 kg, for me 50 kg is fairly well under my weight. 00:01:30.000 --> 00:01:32.000 The stairs are 5 m high. 00:01:32.000 --> 00:01:33.000 There are two scenarios. 00:01:33.000 --> 00:01:37.000 In one of them, you climb the stairs in 5 s you really hustle. 00:01:37.000 --> 00:01:39.000 But in the other one, it take you 30 s. 00:01:39.000 --> 00:01:48.000 In both these scenarios, we are going to have the exact same amount of energy at the end, the same amount of potential energy, (not develop the same power.) 00:01:48.000 --> 00:01:53.000 We climb the same height, we are dealing with the same gravity, we have the same mass. 00:01:53.000 --> 00:01:55.000 But, very different scenarios. 00:01:55.000 --> 00:02:00.000 How fast you climb those stairs, that is something we should talk about, and care about. 00:02:00.000 --> 00:02:09.000 In both cases, we have that same gain of energy of gravity, 50×9.8×5, so in both cases we have 2450 J, when we make it to the top of the stairs. 00:02:09.000 --> 00:02:11.000 But they are clearly very different scenarios. 00:02:11.000 --> 00:02:18.000 So we need a way to talk about the interaction between work and energy, and time. 00:02:18.000 --> 00:02:22.000 Work and energy, and how fast we are able to put work and energy into a system. 00:02:22.000 --> 00:02:25.000 How quickly we are able to change the work and energy in a system. 00:02:25.000 --> 00:02:27.000 This is going to really matter for some applications. 00:02:27.000 --> 00:02:37.000 For that race car, we want to be in a race car that can put massive quantity of energy into its system, really fast it can get off the starting line and win the race. 00:02:37.000 --> 00:02:52.000 With this idea, we make a really simple creation to call this power, just, power = work/(amount of time it takes), work/time, that will give us a way to talk about how much work we are able to deal with in how much time. 00:02:52.000 --> 00:03:00.000 Just like velocity was how much distance we have gone, divided by how much time to do it, we het a very similar idea with work/time for power. 00:03:00.000 --> 00:03:05.000 With power defined as work/time, we can easily create a few equivalent formulae. 00:03:05.000 --> 00:03:11.000 First, since work is a measure of how much energy is being shifted around, we know work = change in energy, always. 00:03:11.000 --> 00:03:19.000 Another formula is, power = Δenergy/time. 00:03:19.000 --> 00:03:21.000 There is another interesting formula we can create. 00:03:21.000 --> 00:03:26.000 Alternately, we can look back to how we originally formulated work. 00:03:26.000 --> 00:03:42.000 Work = F.d = Fdcosθ, in this case it is going to help us to use that dot product. 00:03:42.000 --> 00:03:44.000 This allows us to use velocity. 00:03:44.000 --> 00:03:49.000 Power = work/time = F.d/time. 00:03:49.000 --> 00:04:13.000 We pull off that force, and we get, F.d/time, but distance/time = velocity, so, we get, F.v, so, Power = F.v, which also, if we do not want to use the dot product, Fv×cosθ. 00:04:13.000 --> 00:04:17.000 That same idea that worked with work, works with power. 00:04:17.000 --> 00:04:26.000 So, F.v, or ΔEnergy/time, or work/time, these are all same way to say power. 00:04:26.000 --> 00:04:28.000 What unit is power in? 00:04:28.000 --> 00:04:47.000 Work and energy are both in joules, time is in seconds, so, power = work/time, implies, J/s is the unit for power. 00:04:47.000 --> 00:04:55.000 For ease, we can call 1 J/s a watt, watt is in honour of James Watt who has done a lot of work with energy in 1800's. 00:04:55.000 --> 00:04:58.000 A watt is a measure of weight. 00:04:58.000 --> 00:05:07.000 Just like 1 m/s is the rate that you are moving at, 1 J/s, 1 watt is the rate that you are putting energy into a system. 00:05:07.000 --> 00:05:14.000 One moment, you could have a totally different power, the next moment, just like your velocity can change. 00:05:14.000 --> 00:05:24.000 watt gives us an instantaneous measure of how much energy is going into a system, that is the definition of power. 00:05:24.000 --> 00:05:43.000 In other unit systems, there is also the horse power, you probably heard cars referred to in terms of horse power, and the kilowatt hour, another way of saying watts×time, watt×1000×time. 00:05:43.000 --> 00:05:56.000 Horse power, kilowatt hour, all ways of saying power, that is why energy bills involve these things, cars involve these things, you see these things any time you want to talk about how quickly we can get energy into, or out of the system. 00:05:56.000 --> 00:05:59.000 We are going to make a little tangent here. 00:05:59.000 --> 00:06:08.000 This does not directly have to do with power, but I know, it has been driving you crazy that we have not discussed block and tackle system more. 00:06:08.000 --> 00:06:31.000 I know you remember block and tackle problems extremely well, we talked about them in advanced uses of Newton's second law, and they seemed like magic, they seemed absolutely incredible, and it has been blowing your mind, you keep thinking about it, how is it possible, Physics must be lying, fret no more, I am going to make it better for you. 00:06:31.000 --> 00:06:34.000 Finally we have the understanding of work and energy to see how those systems make perfect sense. 00:06:34.000 --> 00:06:41.000 There is nothing magical about them, there is nothing insane about them, the world is not coming apart as it seems, it makes perfect sense when you look at it in terms of energy. 00:06:41.000 --> 00:06:51.000 I know you love thinking about it, but once again, let us talk about it briefly, quick reminder about how the block and tackle system works. 00:06:51.000 --> 00:06:57.000 Let us say we have got the force of gravity pulling down on this block, Fg, it is pulling down on this block. 00:06:57.000 --> 00:07:10.000 If we want to keep it still, or move it up, say we want to keep it still, we are going to have to pull with the force of gravity here, put that much tension into it, so we have got canceling it out, the force of gravity over here. 00:07:10.000 --> 00:07:13.000 But over here, something weird happens. 00:07:13.000 --> 00:07:20.000 If we pull with a certain tension, then that tension is going to get pulled in here, but it is also going to get pulled in here. 00:07:20.000 --> 00:07:40.000 So we still got that same mg, that same force of gravity, but over here, we are going to have the tension = (1/2)Fg, because if this is (1/2)Fg, and this is (1/2)Fg, then when we put them together, we are going to wind up combining two, one whole force of gravity. 00:07:40.000 --> 00:07:46.000 With the block and tackle system, we are able to distribute our forces over multiple pulleys. 00:07:46.000 --> 00:07:50.000 We are able to distribute the same tension force in multiple places. 00:07:50.000 --> 00:07:54.000 It seems crazy, we are able to get more force for the same original cost. 00:07:54.000 --> 00:07:59.000 How is this possible! This seems like madness. 00:07:59.000 --> 00:08:08.000 The thing to notice here, is that the block and the single pulley system, say we wanted to raise this block 1 m. 00:08:08.000 --> 00:08:11.000 If we wanted to raise the block by 1 m, how much rope would we have to pull? 00:08:11.000 --> 00:08:14.000 We would have to pull 1 m of rope. 00:08:14.000 --> 00:08:17.000 We have to pull, say some force F. 00:08:17.000 --> 00:08:21.000 Over here, we know that we only have to pull at half of that force, F. 00:08:21.000 --> 00:08:23.000 To be able to get that raising happening. 00:08:23.000 --> 00:08:34.000 But, if we want this block to raise up 1 m, we do not just have to get this move by 1 m, if this moves 1 m, we would be lopsided, we have to get this move 1 m as well. 00:08:34.000 --> 00:08:44.000 Both sides of our rope system have to move up a metre, that means we have to get 2 m of motion in our rope. 00:08:44.000 --> 00:08:50.000 Over on the left side, we are able to use 1 m of motion for 1 m of motion. 00:08:50.000 --> 00:08:56.000 Over here, if we want to get that 1 m of lift, we have to put 2 m of distance into our rope. 00:08:56.000 --> 00:09:02.000 Even if we can use half the force, we have to pull double the distance. 00:09:02.000 --> 00:09:07.000 So, our work, the amount of energy in our system is preserved, the force×distance. 00:09:07.000 --> 00:09:15.000 This is force × 1 = F, for work. 00:09:15.000 --> 00:09:28.000 Over here though, we have got, work = (1/2)F × 2 = F, so they wind up being the exact same things, checks out. 00:09:28.000 --> 00:09:36.000 For us to be able to manipulate how the system works, we still have to maintain that conservation of energy, that conservation of work. 00:09:36.000 --> 00:09:45.000 It is equivalent work, because the change in the system, the real change in the system, is how high up we are able to change that block's height. 00:09:45.000 --> 00:09:50.000 If you want to do that, we are going to have to put in the same amount of work, no matter how we go about it. 00:09:50.000 --> 00:09:57.000 Work that goes in, is equal to F in both cases, because you have to pull double the rope. 00:09:57.000 --> 00:10:05.000 And if we had a multiply pulley system, where we were able to have four pulleys, we only have to pull with a quarter of force, we would wind up having to pull 4 times the distance. 00:10:05.000 --> 00:10:10.000 Everything works out, there is nothing magical about it, it makes perfect sense. 00:10:10.000 --> 00:10:13.000 It is the same idea in place with all of our machines. 00:10:13.000 --> 00:10:17.000 Let us look at ramps and levers. 00:10:17.000 --> 00:10:18.000 First we will look at levers. 00:10:18.000 --> 00:10:27.000 If we want to get some object to move up here, traditionally you have a lever, you stick it under, you got a fulcrum, you got a long lever arm, and you pull, you pry. 00:10:27.000 --> 00:10:32.000 You put a low pressure here, and you get a really strong force here. 00:10:32.000 --> 00:10:34.000 High pressure here, low pressure here. 00:10:34.000 --> 00:10:37.000 How is it being done, it is being done based on work. 00:10:37.000 --> 00:10:43.000 You got that small force over here, small force, but it covers a really long distance. 00:10:43.000 --> 00:10:51.000 On the other side, we get this small distance covered, which means, to be that work to be preserved, it is going to be have to put up a massive force. 00:10:51.000 --> 00:10:54.000 The reason why a lever works, is that the energy is conserved. 00:10:54.000 --> 00:11:03.000 If you put a slight force over a long distance, and the other side has a slight distance, then it is going to need a big force to compensate. 00:11:03.000 --> 00:11:07.000 Force×distance has to be equal in any case. 00:11:07.000 --> 00:11:14.000 Over the lever, if you put that fulcrum really close to one side, we will be able to get a giant force with little distance. 00:11:14.000 --> 00:11:17.000 So, the amount of work is preserved, it makes perfect sense. 00:11:17.000 --> 00:11:19.000 You see the exact same thing with a ramp. 00:11:19.000 --> 00:11:25.000 If we want to get this box up this ramp, then we can push with this little force over this really big distance. 00:11:25.000 --> 00:11:34.000 But, if we want to get this box directly up, then we will have to lift a whole lot harder, but we wind up going a smaller distance. 00:11:34.000 --> 00:11:46.000 The ramp works, because we are able to get a small force over a long distance, whereas if you just want to lift it up with brute strength, we need a really powerful force, but we will be able to save some distance. 00:11:46.000 --> 00:11:49.000 The same idea, force×distance, they are always equal. 00:11:49.000 --> 00:11:55.000 The way that you are going to distribute, how you are going to put it in, what ratio you want to put it in, that is up to you. 00:11:55.000 --> 00:11:59.000 But, it is going to have to come out equal when you multiply the two. 00:11:59.000 --> 00:12:06.000 However you put it in, work is going to be conserved, energy is going to be conserved, the energy that goes into it is going to be the same however you do it. 00:12:06.000 --> 00:12:12.000 Machines do not allow us to break the rules of Physics, they just allow us to take advantage if the resources that we have on hand. 00:12:12.000 --> 00:12:16.000 They allow us to use the rules of Physics on our side. 00:12:16.000 --> 00:12:22.000 If we have a little force, but a lot of distance or time, we can figure out an alternative rather than needing a really big force. 00:12:22.000 --> 00:12:37.000 Like with the ramp, like with the lever, like with the pulley system, you can have that slight force, and then figure out the way to multiply by using more distance, or more force, or both , so you can take advantage of what you have, by being able to use the same amount of energy. 00:12:37.000 --> 00:12:49.000 Same amount of energy will go into the system, same work, but it is up to us to figure how to get that work into it, and that is where the cleverness of machines comes into being, at least simple machines. 00:12:49.000 --> 00:12:51.000 Now we are ready for our examples. 00:12:51.000 --> 00:12:53.000 How much work is going to be involved here? 00:12:53.000 --> 00:12:59.000 50 kg block is pushed along a horizontal surface at a constant velocity by a parallel force 47 N. 00:12:59.000 --> 00:13:01.000 It covers 10 m in 5 s. 00:13:01.000 --> 00:13:03.000 What is the power of the force? 00:13:03.000 --> 00:13:21.000 Lets us draw a quick diagram. 00:13:21.000 --> 00:13:22.000 Do we have to care about the mass? 00:13:22.000 --> 00:13:24.000 We do not have to care about the mass. 00:13:24.000 --> 00:13:27.000 Our power formula is, work/time. 00:13:27.000 --> 00:13:40.000 We can figure out the work, work = F.d = Fdcosθ = Fd (since parallel). 00:13:40.000 --> 00:13:48.000 So, 47×10 = 470 J of work. 00:13:48.000 --> 00:14:10.000 What is the time? 5 s, so , Power = 470 J / 5s = 94 J/s = 94 W, that is the power of the force. 00:14:10.000 --> 00:14:15.000 It does not change, the power remains the same, because we got a constant velocity. 00:14:15.000 --> 00:14:21.000 Remember, we could have also used, F.v. 00:14:21.000 --> 00:14:47.000 If you wanted to, we could figure out, it travels 10 m in 5 s, means that we got, 2 m/s = v, and F = 47 N, so, power = 47×2 = 94 W, two different ways. 00:14:47.000 --> 00:14:58.000 Example 2: 2 kg watermelon starts at rest, and it is lifted vertically, 9 m. 00:14:58.000 --> 00:15:00.000 It takes time 20 s, and ends at rest. 00:15:00.000 --> 00:15:05.000 Over that lifting, what was the power developed in lifting that watermelon? 00:15:05.000 --> 00:15:09.000 You started at some height, you reached another height, how do we deal with that? 00:15:09.000 --> 00:15:11.000 Potential energy. 00:15:11.000 --> 00:15:13.000 What is the change in energy? 00:15:13.000 --> 00:15:33.000 ΔE = mgΔh = 2×9.8×9 = 176.4 J of work. 00:15:33.000 --> 00:15:52.000 We know that, power = ΔE/t = 176.4 J/20 s = 8.82 W. 00:15:52.000 --> 00:16:10.000 There you go, the change in energy divided by how much time it takes to put it i n there, just like velocity, just like acceleration, it is what you have got already, distance or speed divided by how much it is altered, how much it is being changed by, how much it is being increased by, that tells us how much the power being developed is. 00:16:10.000 --> 00:16:18.000 The power of the system is the change of energy, how much work is going into that system. 00:16:18.000 --> 00:16:27.000 Just like velocity is how much distance is going into an object, whereas the acceleration is how much velocity is going into an object, just a way of thinking how much velocity is going into an object, a way of thinking how much you are putting into a thing. 00:16:27.000 --> 00:16:32.000 S0, 8.82 W is what is put in, in that 20 s. 00:16:32.000 --> 00:16:37.000 Example 3: 20 kg block is initially at rest on a flat frictionless surface. 00:16:37.000 --> 00:16:39.000 Parallel force of 10 N acts on the block. 00:16:39.000 --> 00:16:49.000 What is the work done on the block in (A) the first second (B) the second second (C) the third second (D) the instantaneous power at the end of 3rd second. 00:16:49.000 --> 00:16:55.000 First thing to think about, work = F.d. 00:16:55.000 --> 00:16:56.000 Is this object accelerating? 00:16:56.000 --> 00:17:00.000 It is on a flat frictionless surface, it has got a force acting on it, of course it is accelerating. 00:17:00.000 --> 00:17:03.000 The amount of distance it is going to cover is going to change the entire time. 00:17:03.000 --> 00:17:05.000 It is also going to have a change in velocity. 00:17:05.000 --> 00:17:07.000 Now we have got two different ways of looking at this. 00:17:07.000 --> 00:17:20.000 We can approach this by wither thinking about the distance that it has changed, it is going to be able to give us our work, and from the work, we will be able to get our power. 00:17:20.000 --> 00:17:35.000 But we can also think that the velocity that it has at each time, would be a way to tell us what is the change in energy, and from the change in energy, we can get the amount of power. 00:17:35.000 --> 00:17:40.000 These are both perfectly good ways to do it, and we will do both of them just to be able to understand two different ways to approach this problem. 00:17:40.000 --> 00:17:46.000 First way, we are going to go with distance. 00:17:46.000 --> 00:17:48.000 What is the formula for distance? 00:17:48.000 --> 00:18:02.000 We got, F = ma, 10 N = 20 kg×a, a = (1/2) m/s/s. 00:18:02.000 --> 00:18:04.000 What is the other formula for distance? 00:18:04.000 --> 00:18:27.000 From basic kinematics, d(t) = (1/2)at^2 + v0t + d(0) = (1/2)at^2 = (1/4)t^2, is our distance, (d(0) and v0 are zero). 00:18:27.000 --> 00:18:32.000 Now we have got a distance formula. 00:18:32.000 --> 00:18:42.000 Now we want to find out where is it at 1 s, 2 s and 3 s. 00:18:42.000 --> 00:19:09.000 Plug things in, d(0) = 0, d(1) = (1/4), d(2) = (1/4)×2^2 = 1, d(3) = (1/4)×3^2 = (9/4). 00:19:09.000 --> 00:19:17.000 If you wanted to see what the distance covered in that period of time is, that change in distance, we can say what is the distance between 0 and 1? 00:19:17.000 --> 00:19:19.000 That is clearly (1/4). 00:19:19.000 --> 00:19:25.000 What is the distance between 1 and 2? That is (3/4). 00:19:25.000 --> 00:19:31.000 What is the distance between 2 and 3? That is (5/4). 00:19:31.000 --> 00:19:40.000 These three changes in distance, if we want to figure out what the work involved is, we know, work = Fd. 00:19:40.000 --> 00:20:00.000 Then, work that happened from 0 to 1st second is, 10×(1/4) = 2.5 J of work. 00:20:00.000 --> 00:20:09.000 What was the work done between 1 and 2? That is, (3/4)×10 = 7.5 J. 00:20:09.000 --> 00:20:18.000 What is the work from 2 to 3 s? That is, (5/4)×10 = 12.5 J. 00:20:18.000 --> 00:20:28.000 Now, if we want to know how much power, what the average power was, over each one of these, we just go, 2.5 J/1 s = 2.5 W, was the average power in that first second. 00:20:28.000 --> 00:20:37.000 In the 2nd second, 7.5 J/1 s = 7.5 W. 00:20:37.000 --> 00:20:44.000 In the 3rd second, 12.5 J/1 s = 12.5 W. 00:20:44.000 --> 00:20:48.000 Remember, these are going to be the average powers, because this is not going to give us the instantaneous. 00:20:48.000 --> 00:20:57.000 Clearly, the amount of power is changing the faster it goes, because it is getting the chance to cover more distance, and that is how that force being applied more and more, since work = Fd. 00:20:57.000 --> 00:21:04.000 If we want to know what the instantaneous power is, we are going to need to know what its speed is at a given moment. 00:21:04.000 --> 00:21:44.000 Remember, power = F.v, v(3 s) = at = (1/2)×3 = 3/2 is the velocity at the 3rd second. 00:21:44.000 --> 00:22:24.000 If we want to figure out the instantaneous power, Power at the third second, power (3 s) = 10 N × (3/2) = 15 W. (Dot product becomes multiplication because of one dimension, in dot product we are dealing with more dimensions, in more dimensions, we will have to know how to use the dot product, we will have to multiply the first components together, add them to the second components, multiply and add them to the third components, so on and so forth, for as many components you have. You probably will do with only 2 or 3 since you dealing with Physics, but it will work with any.) 00:22:24.000 --> 00:22:38.000 So, the instantaneous power is 15 W for that third second, which makes sense, we see that our average, 2.5, 7.5, 12.5, it continues to go up, so the at the very end of the third second, we got 15 W of instantaneous power. 00:22:38.000 --> 00:22:44.000 Remember, the instantaneous power can change just like your instantaneous velocity can change. 00:22:44.000 --> 00:22:50.000 If you are driving in a car that is accelerating, every instant that you move along, your velocity is getting larger and larger. 00:22:50.000 --> 00:22:54.000 So, if the car is accelerating, you got a larger velocity instant by instant. 00:22:54.000 --> 00:22:58.000 In this case, we got a larger and larger power instant by instant. 00:22:58.000 --> 00:23:02.000 If we have got an alternate method, let us start using it, how will that alternate method work? 00:23:02.000 --> 00:23:10.000 So, we know, we did distance already, we can figure this out using distance, but we can also use velocity to tell us changes in energy. 00:23:10.000 --> 00:23:14.000 Now we are going to do this using velocity. 00:23:14.000 --> 00:23:23.000 If we want to see what its velocity is at 1 s, at 2 s, at 3 s, what is the formula for velocity? 00:23:23.000 --> 00:23:44.000 We know, v(t) = at = (1/2)t, (since previous values still work), makes sense. 00:23:44.000 --> 00:23:51.000 In this case, what will be velocity at 0 s? Zero, it is still. 00:23:51.000 --> 00:24:03.000 v(1 s) = (1/2) m/s, v(2 s) = 1 m/s, and v(3 s) = (3/2) m/s. 00:24:03.000 --> 00:24:33.000 If you want to see what the energy in its movement at that time is, we know, E(0) = (1/2)mv^2 = 0, E(1 s) = (1/2)×20×(1/2)^2 = 2.5. 00:24:33.000 --> 00:24:55.000 E(2 s) = (1/2)×20×1 =10, and E(3 s) = (1/2)×20×(3/2)^2 = 22.5. 00:24:55.000 --> 00:25:00.000 So, we have got, 2.5 J, 10 J, 22.5 J. 00:25:00.000 --> 00:25:14.000 If we want to figure out what the change in energy is, because we are working towards figuring out what the work is in each of these seconds, change in energy = work, work = ΔE. 00:25:14.000 --> 00:25:43.000 ΔE(0 to 1) = 2.5 - 0 = 2.5 J, ΔE(1 to 2) = 10 - 2.5 = 7.5 J, ΔE(2 to 3) = 22.5 - 10 = 12.5 J, it is the exact same thing that we saw by doing it the other way. 00:25:43.000 --> 00:25:48.000 Figuring out through the work, figuring out through the change in energy, of course they are going to give the same answer because they are the same thing. 00:25:48.000 --> 00:25:59.000 If we want to figure what the power developed at the 3rd second was, we just do the exact same thing we did previously, so we can skip that, because we are just figuring out instantaneous power, and we discussed that on the last slide. 00:25:59.000 --> 00:26:03.000 But, it is kind of cool to be able to see that we have got two different ways of approaching it. 00:26:03.000 --> 00:26:07.000 So, whichever way that makes more sense to you, is the way you want to do it. 00:26:07.000 --> 00:26:17.000 The important thing to think is, "Okay, great! I have got lots of methods, I have got lots of ways I can attempt a problem." Figure out what is the best for you, what is the best possible way to approach a problem, and then do it. 00:26:17.000 --> 00:26:23.000 There are lots of tools for any given job, and it is up to you to figure out what tool to use. 00:26:23.000 --> 00:26:25.000 Last example: This one is a fun one. 00:26:25.000 --> 00:26:35.000 We have got a race car of mass 1500 kg, and it has an engine capable of putting out 700 hp ~ 5.22×10^5 W of power. 00:26:35.000 --> 00:26:48.000 Neglecting air friction, and friction on the ground, the air drag, the car begins at rest, and we assume that the car puts out its maximum amount of power, how long will it take the car to accelerate to 50 m/s on flat ground? 00:26:48.000 --> 00:26:52.000 In this case, what do we want to use, what power formula are we going to use? 00:26:52.000 --> 00:26:55.000 Do we know what the work is? Do we know what the forces involved are? 00:26:55.000 --> 00:26:56.000 We do not really. 00:26:56.000 --> 00:26:58.000 Do we know what the change in energy is? 00:26:58.000 --> 00:26:59.000 We do know what the change in energy is. 00:26:59.000 --> 00:27:03.000 It starts at a stop, it stops going at 50 m/s. 00:27:03.000 --> 00:27:05.000 Do we know what its instantaneous velocity is? 00:27:05.000 --> 00:27:09.000 No, because that is going to change depending. 00:27:09.000 --> 00:27:19.000 So, we do not really want to go with that one, because that will give us the force, and the force is not really useful, so the best choice for this one is, power = ΔE/t. 00:27:19.000 --> 00:28:01.000 We know what the time is, can we figure out what is the change in energy? 00:28:01.000 --> 00:28:06.000 We do not know what the time is, we are solving for the time. 00:28:06.000 --> 00:28:22.000 But we do know what the change in energy is, we do know what the power is, so we are good to go. 00:28:22.000 --> 00:28:45.000 That gives us, t= ΔE/power = (1/2)mv^2/power = (1/2)×1500×(50)^2/(5.22×10^5) = 3.59 s, that tells us how long it will take us for that car to accelerate form a dead stop, to going at 50 m/s, and that is equivalent to 110 miles/h. 00:28:45.000 --> 00:28:52.000 3.59 s to get to 110 miles/h, or 50 m/s, that is pretty darn good, that explains why race cars are so powerful. 00:28:52.000 --> 00:28:59.000 Hope you enjoyed this lesson, hope power made sense, just think of it as the change in work, the change in energy, and how long it took to get there. 00:28:59.000 --> 00:29:12.000 There is a great analog between speed and velocity and energy and power, it is the same thing. 00:29:12.000 --> 00:29:16.000 How fast are we changing, how much are we changing from moment to moment. 00:29:16.000 --> 00:28:54.000 Hope you enjoyed this.