1 00:00:00,000 --> 00:00:19,449 Well, so now we can do many calculus with forces. 2 00:00:19,449 --> 00:00:29,089 So we can say that at least we have half the problem to understand physical world solved. 3 00:00:29,089 --> 00:00:37,170 However, despite the concept of inertia and the relationship between forces and acceleration 4 00:00:37,170 --> 00:00:39,630 are very important tools. 5 00:00:39,630 --> 00:00:48,810 We cannot find out the speed of a bullet from a gun just by knowing how much powder it had. 6 00:00:48,810 --> 00:00:56,789 Furthermore, we cannot find out the temperature of the bullet when it hits a wall. 7 00:00:56,789 --> 00:01:01,229 So we need another tool, another concept. 8 00:01:01,229 --> 00:01:04,310 Here it is, energy. 9 00:01:04,310 --> 00:01:14,469 is used in ordinary life so we will have a rough idea about energy and I don't mean only 10 00:01:14,469 --> 00:01:24,090 at human level. We will know that we need energy for heating our houses, cooking or washing our 11 00:01:24,090 --> 00:01:33,390 clothes. So we will have an intuitive knowledge about energy as something we need to accomplish 12 00:01:33,390 --> 00:01:43,230 a task make a work. That is, we define energy as the capacity of a system to 13 00:01:43,230 --> 00:01:51,930 make a work. Which kind of work? Well, move something, change the shape of a 14 00:01:51,930 --> 00:02:01,650 solid, compress gas, etc. And this reminds us forces. We know that force can change 15 00:02:01,650 --> 00:02:10,990 the shape of a solid. Force produces acceleration. Thus, if energy is to 16 00:02:10,990 --> 00:02:18,930 produce a work, and work is closely related to forces, then there must be a very 17 00:02:18,930 --> 00:02:25,750 direct relationship between them. We can realize that the man on the 18 00:02:25,750 --> 00:02:34,069 right, that is lifting a weight, would not make the same effort, would not consume the same energy 19 00:02:34,870 --> 00:02:46,229 to lift one pound than to lift 100 pounds, for example. Then work proportional to force makes 20 00:02:46,229 --> 00:02:56,229 sense. On the other hand, the man on the left picture is passing a box, and we can all agree 21 00:02:56,949 --> 00:03:05,270 that the longer distance he's passing that box, the more energy he's spending. And so we conclude 22 00:03:05,270 --> 00:03:12,310 that the force applied along a distance is just the work we are trying to find. 23 00:03:12,310 --> 00:03:20,310 This definition of work as force multiplied by distance deserves a little analysis, 24 00:03:20,310 --> 00:03:28,310 because both force and distance are vectors, but work is scalar, 25 00:03:28,310 --> 00:03:35,310 so this product work is easier to deal with than forces, 26 00:03:35,310 --> 00:03:41,310 but we have to take care that force and distance are aligned 27 00:03:41,310 --> 00:03:51,389 in order to compute the product. Furthermore if distance is null then no 28 00:03:51,389 --> 00:03:59,629 work is performed. For example the man on the right picture is lifting a weight so 29 00:03:59,629 --> 00:04:07,990 when he gets that weight down again the effective work he has performed is zero. 30 00:04:07,990 --> 00:04:23,509 Now, let's generalize the concept of work beyond the effort made by men, not only because we need to understand or calculate the energy required for a machine, 31 00:04:23,509 --> 00:04:33,009 but also to understand the work performed by, for example, gravitational field or a magnet, etc. 32 00:04:33,009 --> 00:04:46,009 And so, we will be able to connect the energy produced in a chemical reaction with the work performed by a car or similar machine. 33 00:04:47,009 --> 00:05:02,009 For example, if the force is just the weight of something, we can easily calculate the work made by the gravitational field of Earth near its surface. 34 00:05:03,009 --> 00:05:14,990 We simply multiply the force of weight by the height that something has fallen, by gravitational attraction. 35 00:05:16,009 --> 00:05:30,149 And conversely, we can tackle this problem to calculate what energy do we need to lift 1 kilogram 5 meters, for example. 36 00:05:30,149 --> 00:05:44,410 So, since nature is symmetric, that energy is the same work that gravitation would produce, downloading 1 kg 5 m. 37 00:05:45,689 --> 00:05:47,290 This is the solution. 38 00:05:48,110 --> 00:05:49,850 49 joules. 39 00:05:50,930 --> 00:05:56,410 Joule, or julio in Spanish, is the unit for work. 40 00:05:56,730 --> 00:06:00,230 Work for work or energy. 41 00:06:00,230 --> 00:06:07,230 since you are noticing that these two concepts are two faces of the same coin. 42 00:06:07,230 --> 00:06:12,230 The name of the unit for energy in the International System 43 00:06:12,230 --> 00:06:20,230 comes from this scientist, James Joule, whose teacher was Dalton. 44 00:06:20,230 --> 00:06:24,230 You remember him by the atomic model, right? 45 00:06:24,230 --> 00:06:37,930 So James Joule worked on heat, energy, temperatures. In fact, he cooperated with Lord Kelvin, whose scale of temperatures you also know. 46 00:06:37,930 --> 00:06:47,930 Well, Joule was the first man who linked work as force multiplied by distance with heat. 47 00:06:47,930 --> 00:06:56,930 And hence before, everybody understood that heat can produce a mechanical work. 48 00:06:56,930 --> 00:07:03,930 That was the beginning of the industrial revolution 150 years ago. 49 00:07:03,930 --> 00:07:08,930 And that's why we have different units for energy. 50 00:07:08,930 --> 00:07:15,930 The one for the international system, I repeat, is called Joule, or Julio in Spanish. 51 00:07:15,930 --> 00:07:19,870 But we can also use calorie. 52 00:07:19,870 --> 00:07:28,810 Calorie is the energy required to raise one gram of water one Celsius degree of temperature. 53 00:07:28,810 --> 00:07:35,430 Its equivalence with joule is 4.18. 54 00:07:35,430 --> 00:07:37,769 So you have to remember this forever. 55 00:07:37,769 --> 00:07:43,250 One calorie is the same as 4.18 joules. 56 00:07:43,250 --> 00:07:51,009 reason to have so many different units for the same quantity energy is because we have to deal 57 00:07:51,009 --> 00:07:59,730 with it in different fields of physics. So despite you are also guessing that all these kinds of 58 00:07:59,730 --> 00:08:09,810 different energies can be converted one into each other, to solve problems in atomic issues we use 59 00:08:09,810 --> 00:08:19,329 electron volt. To deal with problems of domestic power we use kilowatt. To deal with thermal 60 00:08:19,329 --> 00:08:27,089 problems of course we are using calories and for the rest we'll use always joules. Next year 61 00:08:27,889 --> 00:08:34,289 we'll learn more about devices that can convert one energy into another. Thus far 62 00:08:34,289 --> 00:08:41,309 this table summarizes different sources of energy, not different kinds of energy, 63 00:08:41,309 --> 00:08:49,169 but different sources of energy that we can use for our welfare in industry, at home, 64 00:08:49,169 --> 00:08:59,070 etc. By the way, it would be nice if you can organize this table as a mind map, so then 65 00:08:59,070 --> 00:09:05,490 energy can be transformed into different kinds, but it's always the same stuff. We 66 00:09:05,490 --> 00:09:13,049 understand that a car engine transforms chemical energy from the gasoline into 67 00:09:13,049 --> 00:09:20,009 mechanical energy. Our body transforms food energy into mechanical energy and 68 00:09:20,009 --> 00:09:30,330 and also heat and so energy transformation is a very useful tool because energy is not a vector 69 00:09:30,330 --> 00:09:40,409 so we can add multiply etc but in this point we can ask ourselves which is the origin of all this 70 00:09:40,409 --> 00:09:50,330 energy in our planet, for example? The obvious answer is sun. Life is sustained by the energy 71 00:09:50,330 --> 00:09:58,149 that comes from the sun. But we also know that there are some elements, some stones if you want, 72 00:09:58,149 --> 00:10:08,029 that have a property of radioactivity. So, they produce heat. And also, we know about volcanoes, 73 00:10:08,029 --> 00:10:16,289 earthquakes, even the moon is the source of energy because tides are made because the 74 00:10:16,289 --> 00:10:21,330 moon attracts the water in the ocean. 75 00:10:21,330 --> 00:10:30,169 But please, do not mistake these origins of energy in general with the table we have seen 76 00:10:30,169 --> 00:10:38,009 Before, there is a table with different sources that men have learned to take advantage of 77 00:10:38,009 --> 00:10:44,809 in order to be provided with energy, useful energy in daily life. 78 00:10:45,450 --> 00:10:50,970 Well, let's dig a little bit about this concept of energy transformation. 79 00:10:51,929 --> 00:10:57,509 We can analyze the mechanical energy transformation. 80 00:10:58,470 --> 00:11:05,429 In fact, a good example is the pendulum. In a pendulum, sometimes when it reaches the streams, 81 00:11:06,070 --> 00:11:16,389 it stops. So the kinetic energy is zero in those stream points. And then it goes down 82 00:11:17,509 --> 00:11:26,309 and increases its speed. And the question is, where has gone that kinetic energy the pendulum has 83 00:11:26,309 --> 00:11:36,629 at the lowest point? Well, the answer is that kinetic energy at the lowest point has transformed 84 00:11:36,629 --> 00:11:43,590 into potential energy at the highest point, where you remember the pendulum stops. 85 00:11:45,029 --> 00:11:55,590 And so mechanical energy can be either potential or kinetic. Kinetic energy has to do with speed. 86 00:11:56,309 --> 00:11:59,750 And potential energy has to do with what? 87 00:12:00,950 --> 00:12:07,230 Well, potential energy is the capacity of a system to produce a work. 88 00:12:08,509 --> 00:12:13,289 And that remembers us the very first slide of this video. 89 00:12:13,690 --> 00:12:21,129 You remember this formula for the potential energy of gravitational field, right? 90 00:12:21,129 --> 00:12:29,730 and we'll know that that potential energy will be transformed into kinetic energy 91 00:12:29,730 --> 00:12:35,169 as soon as the object of mass m drops down. 92 00:12:36,009 --> 00:12:37,909 So, this is the situation. 93 00:12:38,830 --> 00:12:47,909 When the object is upstairs, its energy, its mechanical energy, is just potential energy. 94 00:12:47,909 --> 00:12:55,409 When it drops down it increases its velocity and finally when it gets on 95 00:12:55,409 --> 00:13:03,590 ground the total energy it has is kinetic energy. Its value is this one. 96 00:13:03,590 --> 00:13:14,190 Half the product of mass multiplied by the speed squared. By the way, if the 97 00:13:14,190 --> 00:13:21,330 object is elastic, like a ball for football for example, then you know it 98 00:13:21,330 --> 00:13:28,309 will rebound from ground so it will reverse the process. It will change now 99 00:13:28,309 --> 00:13:35,230 kinetic energy into potential energy because it will go up gaining potential 100 00:13:35,230 --> 00:13:43,009 energy. So the situation is similar to the pendulum we have seen before. Let's 101 00:13:43,009 --> 00:13:46,850 Let's perform this virtual experiment. 102 00:13:46,850 --> 00:14:01,309 The skateboard girl or boy going downhill or uphill, I would like you to pay attention 103 00:14:01,309 --> 00:14:15,080 to the record of kinetic and potential energy at the square of the right. 104 00:14:15,080 --> 00:14:21,919 We can appreciate that the total energy, in other words, adding kinetic and potential 105 00:14:21,919 --> 00:14:30,559 energy remains invariable, it's a constant. So this happens for any mechanical problem, 106 00:14:31,200 --> 00:14:39,679 the pendulum, something that falls down or whatever. The total mechanical energy is constant. 107 00:14:40,720 --> 00:14:49,679 So we can compare the two extreme situations when the object is on ground and when the object 108 00:14:49,679 --> 00:14:57,279 is at the highest position. If the energy is the same at both situations then we can write 109 00:14:58,240 --> 00:15:06,000 and so we can calculate the speed of something that's falling down from a given height 110 00:15:06,000 --> 00:15:13,039 or conversely with the speed that we need to impulse something up to reach 111 00:15:13,039 --> 00:15:22,659 a given altitude or simply calculate the altitude if we know the initial speed of 112 00:15:22,659 --> 00:15:30,659 something we launch up. So now we can easily compute the altitude the object 113 00:15:30,659 --> 00:15:40,879 will reach if its initial speed is 44.3 meters per second. Please check the 114 00:15:40,879 --> 00:15:49,080 result. Besides, you can find out the speed at ground of something that is 115 00:15:49,080 --> 00:15:58,519 dropped from 100 meters. And finally, just notice that the speed or height is 116 00:15:58,519 --> 00:16:08,659 independent of the mass of the object.