1 00:00:00,000 --> 00:00:01,020 2 00:00:01,020 --> 00:00:02,000 Welcome back. 3 00:00:02,000 --> 00:00:04,050 Now let's do some more mechanical advantage problems. 4 00:00:04,050 --> 00:00:06,410 And in this video, we'll focus on pulleys, which is another 5 00:00:06,410 --> 00:00:08,260 form of a simple machine. 6 00:00:08,260 --> 00:00:10,105 And we've done some pulley problems in the past, but now 7 00:00:10,105 --> 00:00:12,200 we'll actually understand what the mechanical advantage 8 00:00:12,200 --> 00:00:14,350 inherent in these machines are. 9 00:00:14,350 --> 00:00:17,370 So let me start with a very simple pulley. 10 00:00:17,370 --> 00:00:19,190 So this is the ceiling up here. 11 00:00:19,190 --> 00:00:23,000 12 00:00:23,000 --> 00:00:24,780 I don't know what they call that part of the pulley. 13 00:00:24,780 --> 00:00:26,540 I should learn my actual terminology. 14 00:00:26,540 --> 00:00:29,840 But let's say I have that little disk where the rope 15 00:00:29,840 --> 00:00:34,170 goes over and it rolls so that the rope can go over it and 16 00:00:34,170 --> 00:00:36,120 move without having a lot of friction. 17 00:00:36,120 --> 00:00:38,520 And let's say I have a rope going over that pulley. 18 00:00:38,520 --> 00:00:42,600 19 00:00:42,600 --> 00:00:44,610 That's my rope. 20 00:00:44,610 --> 00:00:51,740 And at this end, let's say I have a weight, a 10-Newton 21 00:00:51,740 --> 00:00:57,730 weight, and I'm going to pull down on this end to make the 22 00:00:57,730 --> 00:00:59,160 weight to go up. 23 00:00:59,160 --> 00:01:01,410 So my question to you is what is the mechanical advantage of 24 00:01:01,410 --> 00:01:02,480 this system? 25 00:01:02,480 --> 00:01:05,740 What is the force that I have to pull down in order to lift 26 00:01:05,740 --> 00:01:09,770 this weight, this 10-Newton weight in order to produce 10 27 00:01:09,770 --> 00:01:11,620 Newtons of force upwards? 28 00:01:11,620 --> 00:01:14,985 Well, in any pulley situation-- and I don't know 29 00:01:14,985 --> 00:01:17,380 if textbooks cover it this way, but this is how I think 30 00:01:17,380 --> 00:01:19,610 about it, because you don't have to memorize formulas. 31 00:01:19,610 --> 00:01:21,920 I just think about, well, what happens to 32 00:01:21,920 --> 00:01:23,150 the lengths of rope? 33 00:01:23,150 --> 00:01:25,760 Or what is the total distance that the object you're trying 34 00:01:25,760 --> 00:01:27,000 to move travels? 35 00:01:27,000 --> 00:01:29,310 And if you know the distance that it travels versus the 36 00:01:29,310 --> 00:01:31,040 distance that you have to pull, you know 37 00:01:31,040 --> 00:01:32,590 the mechanical advantage. 38 00:01:32,590 --> 00:01:36,880 So in this situation, if I were to hold the rope at that 39 00:01:36,880 --> 00:01:41,670 point, and if I were to pull it down 10 feet or some 40 00:01:41,670 --> 00:01:44,350 arbitrary distance, what happens over here? 41 00:01:44,350 --> 00:01:46,300 Well, this weight is going to move up 42 00:01:46,300 --> 00:01:49,560 exactly the same amount. 43 00:01:49,560 --> 00:01:53,250 Whatever I pull, if I pull a foot down here, this weight 44 00:01:53,250 --> 00:01:57,360 will move up by a foot, so the distance that I pull here is 45 00:01:57,360 --> 00:02:00,130 equivalent to the distance that it pulls up here. 46 00:02:00,130 --> 00:02:02,880 And since we know that the work in has to equal the work 47 00:02:02,880 --> 00:02:06,670 out, we know that the force I'm pulling down has to be the 48 00:02:06,670 --> 00:02:10,080 same as the force or the tension that the rope is 49 00:02:10,080 --> 00:02:11,530 pulling up here. 50 00:02:11,530 --> 00:02:14,920 And we could have done that when we learned about tension, 51 00:02:14,920 --> 00:02:16,740 that the tension in the rope is constant. 52 00:02:16,740 --> 00:02:19,850 I'm producing tension in the rope when I pull here and 53 00:02:19,850 --> 00:02:22,480 that's the same pulling force of the tension on the weight. 54 00:02:22,480 --> 00:02:25,180 So this isn't too interesting of a machine. 55 00:02:25,180 --> 00:02:29,920 All it's doing is I pull down with a force of 10 Newtons and 56 00:02:29,920 --> 00:02:32,480 it will pull up with a force of 10 Newtons, and so the 57 00:02:32,480 --> 00:02:36,550 mechanical advantage is 1, no real mechanical advantage, 58 00:02:36,550 --> 00:02:37,940 although this could be useful. 59 00:02:37,940 --> 00:02:39,590 Maybe it's easier for me to pull down than 60 00:02:39,590 --> 00:02:40,880 for me to pull up. 61 00:02:40,880 --> 00:02:43,810 Or at some point, maybe I can't reach up here, so it's 62 00:02:43,810 --> 00:02:45,930 nice for me to pull down here where I can reach and the 63 00:02:45,930 --> 00:02:48,260 object will keep going up like in a flag pole or 64 00:02:48,260 --> 00:02:49,160 something like that. 65 00:02:49,160 --> 00:02:51,820 So this could still be useful even though its mechanical 66 00:02:51,820 --> 00:02:54,220 advantage is only 1. 67 00:02:54,220 --> 00:02:58,270 So let's see if we can construct a pulley situation 68 00:02:58,270 --> 00:03:03,170 where the mechanical advantage is more than 1. 69 00:03:03,170 --> 00:03:09,810 So let's say over here at the top, I still have the same 70 00:03:09,810 --> 00:03:14,080 pulley that's attached to the ceiling, but I'm going to add 71 00:03:14,080 --> 00:03:16,766 slight variation here. 72 00:03:16,766 --> 00:03:19,700 I have another pulley here. 73 00:03:19,700 --> 00:03:32,315 And now let me do the other pulley down here. 74 00:03:32,315 --> 00:03:36,790 75 00:03:36,790 --> 00:03:40,470 And then let me see if I can draw my rope in a good way. 76 00:03:40,470 --> 00:03:46,010 So my rope starts up going up like that, then it comes back 77 00:03:46,010 --> 00:03:50,820 down, comes around the second pulley, and now this is 78 00:03:50,820 --> 00:03:54,330 attached to the ceiling up here. 79 00:03:54,330 --> 00:03:56,280 The second pulley is actually where the 80 00:03:56,280 --> 00:03:58,660 weight is attached to. 81 00:03:58,660 --> 00:04:00,750 And let's just call it a 10-Newton weight again, 82 00:04:00,750 --> 00:04:02,610 although it doesn't really matter what the weight is. 83 00:04:02,610 --> 00:04:05,030 Let's figure out what the mechanical advantage is. 84 00:04:05,030 --> 00:04:06,430 So the same question. 85 00:04:06,430 --> 00:04:07,930 And this is really the question you always have to 86 00:04:07,930 --> 00:04:08,850 ask yourself. 87 00:04:08,850 --> 00:04:15,150 If I were take a point on this rope and if I were to pull it 88 00:04:15,150 --> 00:04:18,399 2 feet down, so let's see I take this point and I move it 89 00:04:18,399 --> 00:04:23,970 2 feet down, what essentially happens to the rope? 90 00:04:23,970 --> 00:04:26,480 Well, every point on the rope's going to move 91 00:04:26,480 --> 00:04:29,720 2 feet to the right. 92 00:04:29,720 --> 00:04:31,640 I guess you can view it this way if you view that motion is 93 00:04:31,640 --> 00:04:33,330 to the right. 94 00:04:33,330 --> 00:04:37,780 But if this length of rope is getting 2 feet shorter, what 95 00:04:37,780 --> 00:04:39,740 is this length of rope getting? 96 00:04:39,740 --> 00:04:42,410 Well, this entire length of rope is also going to get 2 97 00:04:42,410 --> 00:04:46,530 feet shorter, this entire length of rope right here. 98 00:04:46,530 --> 00:04:49,940 But this entire length of rope is split between this side-- 99 00:04:49,940 --> 00:04:53,882 let me do it in different color-- between this 100 00:04:53,882 --> 00:04:58,050 side and this side. 101 00:04:58,050 --> 00:05:02,420 So if I make this side of the rope shorter-- I mean, the 102 00:05:02,420 --> 00:05:05,660 rope goes through the whole thing, but if I take this side 103 00:05:05,660 --> 00:05:08,080 of the rope and I pull down by 2 feet, 104 00:05:08,080 --> 00:05:10,080 what is going to happen? 105 00:05:10,080 --> 00:05:13,590 Well, this is going to get 1 foot shorter. 106 00:05:13,590 --> 00:05:15,840 This rope is going to get 1 foot shorter. 107 00:05:15,840 --> 00:05:18,960 This is going to go 1 foot shorter and this length of the 108 00:05:18,960 --> 00:05:20,590 rope is going to get 1 foot shorter. 109 00:05:20,590 --> 00:05:21,440 And how do I know that? 110 00:05:21,440 --> 00:05:23,070 Well, this is all the same rope. 111 00:05:23,070 --> 00:05:25,070 And if this is getting 1 foot shorter, and this is one 112 00:05:25,070 --> 00:05:26,950 getting 1 foot shorter, it makes sense this whole thing 113 00:05:26,950 --> 00:05:28,510 is getting 2 feet shorter. 114 00:05:28,510 --> 00:05:30,520 But the important thing to realize, if each of these are 115 00:05:30,520 --> 00:05:33,200 getting 1 foot shorter, then this weight is 116 00:05:33,200 --> 00:05:35,110 only moving up 1 foot. 117 00:05:35,110 --> 00:05:38,050 118 00:05:38,050 --> 00:05:42,440 So when I pull the rope down 2 feet here, this weight only 119 00:05:42,440 --> 00:05:43,850 moves up 1 foot. 120 00:05:43,850 --> 00:05:46,320 So what is the work that I'm doing? 121 00:05:46,320 --> 00:05:48,560 Well, the work in is the same as the work out, and we know 122 00:05:48,560 --> 00:05:49,960 what the work out is. 123 00:05:49,960 --> 00:05:53,100 The work out is going to be the force that this 124 00:05:53,100 --> 00:05:55,530 contraption or this machine is pulling upwards with, and 125 00:05:55,530 --> 00:06:01,070 that's 10 Newtons, so the workout is equal to 10 Newtons 126 00:06:01,070 --> 00:06:03,255 times the distance that the force is 127 00:06:03,255 --> 00:06:05,730 pulling in, times 1 foot. 128 00:06:05,730 --> 00:06:06,750 Oh, why did I do feet? 129 00:06:06,750 --> 00:06:08,000 I should do meters. 130 00:06:08,000 --> 00:06:10,920 131 00:06:10,920 --> 00:06:12,565 That's not a good thing for me to do. 132 00:06:12,565 --> 00:06:15,170 That should be meters. 133 00:06:15,170 --> 00:06:17,360 I shouldn't mix English and metric system. 134 00:06:17,360 --> 00:06:23,840 So 10 Newtons times 1 meter, so it equals 10 joules. 135 00:06:23,840 --> 00:06:25,310 And this has to be the work that I've put 136 00:06:25,310 --> 00:06:26,330 into it, too, right? 137 00:06:26,330 --> 00:06:32,350 So the work in also has to be 10 joules. 138 00:06:32,350 --> 00:06:33,890 Well, I know the distance that I pulled down. 139 00:06:33,890 --> 00:06:36,280 I know I pulled down 2 meters. 140 00:06:36,280 --> 00:06:39,100 So I pulled down 2 meters, so this has to equal the force 141 00:06:39,100 --> 00:06:39,890 times the distance. 142 00:06:39,890 --> 00:06:42,360 So the force, which I don't know, times the distance, 143 00:06:42,360 --> 00:06:45,420 which is 2 meters, is equal to 10 joules. 144 00:06:45,420 --> 00:06:48,090 So divide both sides by 2, so the force that I pulled down 145 00:06:48,090 --> 00:06:51,270 with is 5 Newtons. 146 00:06:51,270 --> 00:06:54,940 So I pulled down 5 Newtons for 2 meters, and it pulls up a 147 00:06:54,940 --> 00:06:57,100 10-Newton weight for 1 meter. 148 00:06:57,100 --> 00:06:59,780 Force times distance is equal to force times distance. 149 00:06:59,780 --> 00:07:01,800 So what was the input force? 150 00:07:01,800 --> 00:07:07,050 The input force is equal to 5 Newtons and the output force 151 00:07:07,050 --> 00:07:09,280 of this machine is equal to 10 Newtons. 152 00:07:09,280 --> 00:07:12,650 Mechanical advantage is the output over the input, so the 153 00:07:12,650 --> 00:07:16,110 mechanical advantage is equal to the force output by the 154 00:07:16,110 --> 00:07:20,400 force input, which equals 10/5, which equals 2. 155 00:07:20,400 --> 00:07:23,970 And that makes sense, because I have to pull twice as much 156 00:07:23,970 --> 00:07:32,280 for this thing to move up half of that distance. 157 00:07:32,280 --> 00:07:36,520 Let's see if we can do another mechanical advantage problem. 158 00:07:36,520 --> 00:07:39,410 Actually, let's do a really simple one that we've really 159 00:07:39,410 --> 00:07:41,690 been working with a long time. 160 00:07:41,690 --> 00:07:45,050 Let's say that I have a wedge. 161 00:07:45,050 --> 00:07:48,760 A wedge is actually considered a machine, which it took me a 162 00:07:48,760 --> 00:07:52,220 little while to get my mind around that, but 163 00:07:52,220 --> 00:07:53,940 a wedge is a machine. 164 00:07:53,940 --> 00:07:55,200 And why is a wedge a machine? 165 00:07:55,200 --> 00:07:57,670 Because it gives you mechanical advantage. 166 00:07:57,670 --> 00:07:59,770 So if I have this wedge here. 167 00:07:59,770 --> 00:08:05,580 And this is a 30-degree angle, if this distance up here, 168 00:08:05,580 --> 00:08:09,260 let's call this distance D, what is this 169 00:08:09,260 --> 00:08:11,630 distance going to be? 170 00:08:11,630 --> 00:08:13,530 Well, it's going to be D sine of 30. 171 00:08:13,530 --> 00:08:15,540 And we know that the sine of 30 degrees, hopefully by this 172 00:08:15,540 --> 00:08:19,520 point, is 1/2, so this is going to be 1/2D. 173 00:08:19,520 --> 00:08:21,190 You might want to review the trigonometry a little bit if 174 00:08:21,190 --> 00:08:23,800 that doesn't completely ring a bell for you. 175 00:08:23,800 --> 00:08:27,020 So if I take an object, if I take a box-- and let's assume 176 00:08:27,020 --> 00:08:28,280 it has no friction. 177 00:08:28,280 --> 00:08:29,970 We're not going to go into the whole normal 178 00:08:29,970 --> 00:08:31,240 force and all that. 179 00:08:31,240 --> 00:08:37,200 If I take a box, and I push it with some force all the way up 180 00:08:37,200 --> 00:08:42,200 here, what is the mechanical advantage of this system? 181 00:08:42,200 --> 00:08:44,670 Well, when the box is up here, we know what its 182 00:08:44,670 --> 00:08:46,220 potential energy is. 183 00:08:46,220 --> 00:08:49,820 Its potential energy is going to be the weight of the box. 184 00:08:49,820 --> 00:08:54,510 So let's say this is a 10-Newton box. 185 00:08:54,510 --> 00:08:56,790 The potential energy at this point is going to be 10 186 00:08:56,790 --> 00:08:59,750 Newtons times its height. 187 00:08:59,750 --> 00:09:03,540 So potential energy at this point has to equal 10 Newtons 188 00:09:03,540 --> 00:09:07,870 times the height, which is going to be 5 joules. 189 00:09:07,870 --> 00:09:11,380 And that's also the amount of work one has to put into the 190 00:09:11,380 --> 00:09:14,530 system in order to get it into this state, in order to get it 191 00:09:14,530 --> 00:09:16,380 this high in the air. 192 00:09:16,380 --> 00:09:20,090 So we know that we would have to put 5 joules of work in 193 00:09:20,090 --> 00:09:23,260 order to get the box up to this point. 194 00:09:23,260 --> 00:09:25,490 So what is the force that we had to apply? 195 00:09:25,490 --> 00:09:28,490 Well, it's that force, that input force, times this 196 00:09:28,490 --> 00:09:31,310 distance has to equal 5 joules. 197 00:09:31,310 --> 00:09:33,850 198 00:09:33,850 --> 00:09:36,810 So this input force-- oh, sorry, this is going to be-- 199 00:09:36,810 --> 00:09:38,610 sorry, this isn't 5 joules. 200 00:09:38,610 --> 00:09:41,700 It's 10 times 1/2 times the distance. 201 00:09:41,700 --> 00:09:43,820 It's 5D joules. 202 00:09:43,820 --> 00:09:47,480 This isn't some kind of units. 203 00:09:47,480 --> 00:09:49,720 It's 10 Newtons times the distance that we're up, and 204 00:09:49,720 --> 00:09:52,610 that's 1/2D, so it's 5D joules. 205 00:09:52,610 --> 00:09:53,860 Sorry for confusing you. 206 00:09:53,860 --> 00:09:56,510 207 00:09:56,510 --> 00:10:00,030 And so the force I'm pushing here times this distance has 208 00:10:00,030 --> 00:10:04,220 to also equal to 5D joules. 209 00:10:04,220 --> 00:10:05,500 I just remembered, I just used D as a 210 00:10:05,500 --> 00:10:06,820 variable the whole time. 211 00:10:06,820 --> 00:10:08,710 Dividing both sides by D, what do I get? 212 00:10:08,710 --> 00:10:14,780 The input force had to be equal to 5 Newtons. 213 00:10:14,780 --> 00:10:17,370 I'm dividing both sides by D meters. 214 00:10:17,370 --> 00:10:21,650 So I inputted 5 Newtons of force and I was able to lift 215 00:10:21,650 --> 00:10:24,370 essentially a 10-Newton object. 216 00:10:24,370 --> 00:10:26,410 So what is the mechanical advantage? 217 00:10:26,410 --> 00:10:29,390 Well, it's the force output, 10 Newtons, divided by the 218 00:10:29,390 --> 00:10:31,195 force input, 5 Newtons. 219 00:10:31,195 --> 00:00:00,000 The mechanical advantage is 2.