1 00:00:00,270 --> 00:00:01,103 - [Instructor] Today in the gym, 2 00:00:01,103 --> 00:00:02,970 when my wife was doing dumbbell curls, 3 00:00:02,970 --> 00:00:05,400 I started wondering, see, she's putting a force 4 00:00:05,400 --> 00:00:07,200 on that dumbbell upwards, right? 5 00:00:07,200 --> 00:00:09,810 But does that force stay a constant 6 00:00:09,810 --> 00:00:12,450 as she moves the dumbbell up or not? 7 00:00:12,450 --> 00:00:15,090 Does it change? And if it does change, how does it change? 8 00:00:15,090 --> 00:00:17,760 Does it increase, does it decrease? What happens to it? 9 00:00:17,760 --> 00:00:18,593 Guess what. 10 00:00:18,593 --> 00:00:20,520 We can answer this question by the end 11 00:00:20,520 --> 00:00:23,430 of this video using Newton's second law. 12 00:00:23,430 --> 00:00:24,990 So let's start with a simpler example. 13 00:00:24,990 --> 00:00:27,000 We have a ice hockey ground over here, 14 00:00:27,000 --> 00:00:30,304 and there's a puck moving on top of it at some speed. 15 00:00:30,304 --> 00:00:33,540 If there are no frictional forces acting on this, 16 00:00:33,540 --> 00:00:36,750 if you assume that, then the forces acting on this puck 17 00:00:36,750 --> 00:00:40,710 would be balanced because in the horizontal, you can see 18 00:00:40,710 --> 00:00:43,140 that there are no forces because we're ignoring friction. 19 00:00:43,140 --> 00:00:46,380 And in the vertical, the gravitational force, 20 00:00:46,380 --> 00:00:48,210 which is pulling down on it is completely balanced 21 00:00:48,210 --> 00:00:50,790 by the force that the ground is pushing up on it, 22 00:00:50,790 --> 00:00:52,380 the normal force, they balance it out. 23 00:00:52,380 --> 00:00:54,840 And so since there are no unbalanced forces acting 24 00:00:54,840 --> 00:00:56,580 on this puck from Newton's first law, 25 00:00:56,580 --> 00:00:59,400 we know that this thing will continue its state of rest, 26 00:00:59,400 --> 00:01:02,040 or in this particular case, the state of uniform motion. 27 00:01:02,040 --> 00:01:04,800 So it'll continue to move with that same velocity. 28 00:01:04,800 --> 00:01:06,870 But now comes the question, 29 00:01:06,870 --> 00:01:09,330 what if there was an unbalanced force acting on it? 30 00:01:09,330 --> 00:01:11,190 What happens because of that? 31 00:01:11,190 --> 00:01:12,600 Well, let's find out. 32 00:01:12,600 --> 00:01:15,000 For that, let's just whack it with a hockey stick. 33 00:01:15,000 --> 00:01:16,800 No. (instructor laughing) 34 00:01:16,800 --> 00:01:19,860 So if I whack it to the right, let's say in this case, 35 00:01:19,860 --> 00:01:23,490 I will now put an unbalanced force to the right. 36 00:01:23,490 --> 00:01:26,130 What will happen? Well, we can probably guess it. 37 00:01:26,130 --> 00:01:28,110 That puck's velocity will now be higher. 38 00:01:28,110 --> 00:01:29,670 It'll just get blasted off over there. 39 00:01:29,670 --> 00:01:31,590 So its velocity will increase. 40 00:01:31,590 --> 00:01:34,920 In other words, it will accelerate. 41 00:01:34,920 --> 00:01:38,670 Ooh, this means when there's an unbalanced force acting 42 00:01:38,670 --> 00:01:40,404 on a an object, in other words, 43 00:01:40,404 --> 00:01:45,404 if there is a non-zero net force acting on an object, 44 00:01:45,480 --> 00:01:47,880 which is the same thing as saying an unbalanced force, 45 00:01:47,880 --> 00:01:49,710 but whenever this net force acts on an object, 46 00:01:49,710 --> 00:01:50,820 what does it do? 47 00:01:50,820 --> 00:01:52,680 It accelerates our puck. 48 00:01:52,680 --> 00:01:55,983 The puck undergoes, or the object undergoes an acceleration. 49 00:01:56,910 --> 00:02:00,030 This is the essence of Newton's second law. 50 00:02:00,030 --> 00:02:02,040 Now all we gotta do is analyze the situation 51 00:02:02,040 --> 00:02:03,000 even more carefully 52 00:02:03,000 --> 00:02:05,760 and see if we can concretize this relationship. 53 00:02:05,760 --> 00:02:06,930 So let's do that. 54 00:02:06,930 --> 00:02:08,460 The first question we could have is yeah, 55 00:02:08,460 --> 00:02:10,590 so a net force causes an acceleration, 56 00:02:10,590 --> 00:02:13,140 but how long does that acceleration last? 57 00:02:13,140 --> 00:02:14,550 Well, let's see. 58 00:02:14,550 --> 00:02:17,760 When the stick hits the puck, 59 00:02:17,760 --> 00:02:19,440 that's when it starts accelerating, 60 00:02:19,440 --> 00:02:22,770 which means as long as the stick is in contact 61 00:02:22,770 --> 00:02:25,290 with the puck, as long as it's in contact with it, 62 00:02:25,290 --> 00:02:28,500 like right now here, it's during that time 63 00:02:28,500 --> 00:02:30,330 there will be acceleration. 64 00:02:30,330 --> 00:02:33,000 But what happens once it loses contact? 65 00:02:33,000 --> 00:02:35,940 Once it loses contact, again, net force goes to zero. 66 00:02:35,940 --> 00:02:38,640 And now coming back to Newton's first law, 67 00:02:38,640 --> 00:02:43,110 it'll continue moving with that same increased velocity. 68 00:02:43,110 --> 00:02:45,900 This means the acceleration only happened 69 00:02:45,900 --> 00:02:48,450 during this time when the hockey stick 70 00:02:48,450 --> 00:02:49,680 was in contact with it. 71 00:02:49,680 --> 00:02:52,680 In other words, the acceleration lasts as long 72 00:02:52,680 --> 00:02:55,440 as the net force lasts. 73 00:02:55,440 --> 00:02:58,260 Okay, next, let's think about what would happen 74 00:02:58,260 --> 00:03:01,110 if the net force was higher? 75 00:03:01,110 --> 00:03:03,480 For that let's imagine we whacked it harder. 76 00:03:03,480 --> 00:03:04,770 What's gonna happen now? 77 00:03:04,770 --> 00:03:07,770 Or you can imagine it'll get blasted off even more faster, 78 00:03:07,770 --> 00:03:09,030 even faster, right? 79 00:03:09,030 --> 00:03:10,770 Which means it'll have a higher velocity 80 00:03:10,770 --> 00:03:12,330 when it loses contact. 81 00:03:12,330 --> 00:03:15,750 Ooh, that means there'll be bigger acceleration. 82 00:03:15,750 --> 00:03:17,730 So if the net force is larger, 83 00:03:17,730 --> 00:03:19,950 it means you'll have a larger acceleration. 84 00:03:19,950 --> 00:03:22,890 If the net force is smaller, you get a smaller acceleration. 85 00:03:22,890 --> 00:03:26,220 In other words, we see a direct relationship 86 00:03:26,220 --> 00:03:30,390 between acceleration and the net force. 87 00:03:30,390 --> 00:03:32,610 All right, what else can we deduce? 88 00:03:32,610 --> 00:03:35,100 Hey, let's think about the direction. 89 00:03:35,100 --> 00:03:37,620 What is the direction of the acceleration? 90 00:03:37,620 --> 00:03:40,620 Well, in this case, the net force is to the right, 91 00:03:40,620 --> 00:03:42,540 and our puck's velocity 92 00:03:42,540 --> 00:03:45,000 is also increasing towards the right. 93 00:03:45,000 --> 00:03:47,640 So in this case, the acceleration is to the right. 94 00:03:47,640 --> 00:03:49,710 So in this case, if the net force is to the right, 95 00:03:49,710 --> 00:03:51,168 the acceleration is to the right. 96 00:03:51,168 --> 00:03:54,330 What would happen if the net force was to the left? 97 00:03:54,330 --> 00:03:56,790 So let's imagine we whack that puck now 98 00:03:56,790 --> 00:03:59,370 to the left, what would happen? 99 00:03:59,370 --> 00:04:00,750 Well, we can again imagine the puck 100 00:04:00,750 --> 00:04:02,820 would now get blasted off to the left. 101 00:04:02,820 --> 00:04:04,770 But let's look at it carefully. 102 00:04:04,770 --> 00:04:07,950 Since the puck is already moving to the right, if we push it 103 00:04:07,950 --> 00:04:11,280 to the left, now we're gonna slow it down. 104 00:04:11,280 --> 00:04:13,680 The puck will come to a stop first. 105 00:04:13,680 --> 00:04:16,980 It'll happen very quickly that we won't even see it. 106 00:04:16,980 --> 00:04:19,740 But it has to happen before going to the left, right? 107 00:04:19,740 --> 00:04:21,990 Which means when you go from here to here, 108 00:04:21,990 --> 00:04:24,090 notice even though the puck is moving to the right, 109 00:04:24,090 --> 00:04:26,580 it is slowing down, which means the acceleration 110 00:04:26,580 --> 00:04:28,410 is to the left. 111 00:04:28,410 --> 00:04:29,850 So when the net force is to the left, 112 00:04:29,850 --> 00:04:32,130 we're seeing an acceleration is to the left. 113 00:04:32,130 --> 00:04:34,620 After that, its velocity might increase to the left, 114 00:04:34,620 --> 00:04:37,920 which means again, the acceleration is to the left. 115 00:04:37,920 --> 00:04:38,970 Ooh. 116 00:04:38,970 --> 00:04:41,070 So if the net force is to the left, 117 00:04:41,070 --> 00:04:42,390 the acceleration is to the left. 118 00:04:42,390 --> 00:04:43,770 If the net force is to the right, 119 00:04:43,770 --> 00:04:45,300 the acceleration is to the right. 120 00:04:45,300 --> 00:04:48,720 So the acceleration will be in the same direction 121 00:04:48,720 --> 00:04:51,090 as that of the net force. 122 00:04:51,090 --> 00:04:55,530 Okay, is there anything else that affects our acceleration? 123 00:04:55,530 --> 00:04:56,820 Well, let's see. 124 00:04:56,820 --> 00:04:58,140 If you come back over here, 125 00:04:58,140 --> 00:04:59,700 what if you use the same bat, 126 00:04:59,700 --> 00:05:01,440 whacked it with the same force, 127 00:05:01,440 --> 00:05:03,150 but instead of a puck, 128 00:05:03,150 --> 00:05:04,500 let's say there was a bowling ball 129 00:05:04,500 --> 00:05:05,700 moving with the same velocity. 130 00:05:05,700 --> 00:05:07,364 What would happen now? 131 00:05:07,364 --> 00:05:08,250 (instructor laughing) 132 00:05:08,250 --> 00:05:11,400 I'm pretty sure you can feel it in your bones now. 133 00:05:11,400 --> 00:05:14,880 It would be much harder to stop that bowling ball 134 00:05:14,880 --> 00:05:17,190 and make it turn backwards, right? 135 00:05:17,190 --> 00:05:18,630 I mean, the same thing will happen. 136 00:05:18,630 --> 00:05:23,070 You will slow it down, but it'll be much, much harder. 137 00:05:23,070 --> 00:05:26,310 It'll take a much longer time to slow it down, 138 00:05:26,310 --> 00:05:29,100 even though you're putting the same amount of force. 139 00:05:29,100 --> 00:05:30,930 So the net force has stayed the same. 140 00:05:30,930 --> 00:05:33,150 But what has happened to our acceleration? 141 00:05:33,150 --> 00:05:36,450 Since the velocity changed over a much longer time, 142 00:05:36,450 --> 00:05:39,300 the acceleration became smaller. 143 00:05:39,300 --> 00:05:41,850 Hey, why did the acceleration became smaller? 144 00:05:41,850 --> 00:05:43,500 What changed? 145 00:05:43,500 --> 00:05:46,740 From the puck to the bowling ball, the mass changed, 146 00:05:46,740 --> 00:05:48,660 the mass increased. 147 00:05:48,660 --> 00:05:51,960 So this means mass also affects the acceleration, 148 00:05:51,960 --> 00:05:53,400 but how does it affect it? 149 00:05:53,400 --> 00:05:56,190 Well, we saw that the mass increased right now. 150 00:05:56,190 --> 00:05:58,230 What did that do to the acceleration? 151 00:05:58,230 --> 00:06:01,110 It decreased, and this is kind of intuitive. 152 00:06:01,110 --> 00:06:04,200 The bigger the mass, the harder it is to accelerate, 153 00:06:04,200 --> 00:06:06,660 meaning the smaller the acceleration, 154 00:06:06,660 --> 00:06:11,460 which means acceleration has an inverse relationship 155 00:06:11,460 --> 00:06:13,350 with the mass. 156 00:06:13,350 --> 00:06:16,560 So now, everything that we just analyzed about acceleration, 157 00:06:16,560 --> 00:06:18,630 its direction, its dependency on the net force, 158 00:06:18,630 --> 00:06:19,710 how it depends on the mass, 159 00:06:19,710 --> 00:06:23,250 all of it can be put down in an equation. 160 00:06:23,250 --> 00:06:25,350 And that equation is pretty much right in front of us. 161 00:06:25,350 --> 00:06:29,580 So the acceleration will equal the net force divided 162 00:06:29,580 --> 00:06:31,770 by the mass. 163 00:06:31,770 --> 00:06:36,630 This is our Newton's second law. 164 00:06:36,630 --> 00:06:38,610 And look, the equation is saying the same thing. 165 00:06:38,610 --> 00:06:40,020 Direct relationship between acceleration 166 00:06:40,020 --> 00:06:42,480 and the net force, inverse relationship between acceleration 167 00:06:42,480 --> 00:06:44,640 and the mass and the arrowheads are saying 168 00:06:44,640 --> 00:06:46,710 that acceleration and the net force will always be 169 00:06:46,710 --> 00:06:48,270 in the same direction. 170 00:06:48,270 --> 00:06:50,040 Isn't it amazing that we can pack all 171 00:06:50,040 --> 00:06:53,070 of that information in just one beautiful equation? 172 00:06:53,070 --> 00:06:55,350 And of course, you may have seen this written 173 00:06:55,350 --> 00:06:58,620 as f equals ma in some sources, it's the same thing. 174 00:06:58,620 --> 00:06:59,453 I like to write it this way 175 00:06:59,453 --> 00:07:03,390 because acceleration is caused by the force. 176 00:07:03,390 --> 00:07:06,060 So once we decide the force is and the mass, 177 00:07:06,060 --> 00:07:08,370 then the acceleration gets fixed. 178 00:07:08,370 --> 00:07:12,390 But anyways, what will happen if the net force is zero? 179 00:07:12,390 --> 00:07:15,060 What if we plug in over here zero? 180 00:07:15,060 --> 00:07:18,090 Well, then the acceleration also goes to zero. 181 00:07:18,090 --> 00:07:19,149 What does this mean? 182 00:07:19,149 --> 00:07:22,260 Well, this means we have all the balance forces acting 183 00:07:22,260 --> 00:07:23,093 on an object. 184 00:07:23,093 --> 00:07:25,170 And if the acceleration is zero, it means 185 00:07:25,170 --> 00:07:27,270 that the velocity stays a constant. 186 00:07:27,270 --> 00:07:30,570 In other words, this is Newton's first law, 187 00:07:30,570 --> 00:07:32,730 which says an object continues to stay at rest 188 00:07:32,730 --> 00:07:34,500 or in uniform motion. 189 00:07:34,500 --> 00:07:36,330 That is zero acceleration, right? 190 00:07:36,330 --> 00:07:39,150 When there are no unbalanced forces acting on it. 191 00:07:39,150 --> 00:07:42,630 So notice, Newton's first law is just a special case 192 00:07:42,630 --> 00:07:44,910 of Newton's second law, 193 00:07:44,910 --> 00:07:48,900 which means this equation is encompassing both the second 194 00:07:48,900 --> 00:07:50,550 and the first law as well. 195 00:07:50,550 --> 00:07:53,400 And finally, speaking about Newton's first law, 196 00:07:53,400 --> 00:07:56,100 what we also noticed over here is bigger the mass, 197 00:07:56,100 --> 00:07:57,450 smaller the acceleration. 198 00:07:57,450 --> 00:08:01,260 In other words, if the mass is bigger, it is harder 199 00:08:01,260 --> 00:08:02,400 to change its velocity. 200 00:08:02,400 --> 00:08:05,610 It's much harder to do that, which means objects 201 00:08:05,610 --> 00:08:08,940 that have more mass have more inertia. 202 00:08:08,940 --> 00:08:10,845 That's something again we learned in Newton's first law. 203 00:08:10,845 --> 00:08:12,630 Inertia is the property due 204 00:08:12,630 --> 00:08:15,570 to which objects continue to stay at rest 205 00:08:15,570 --> 00:08:18,030 or continue to stay in uniform motion, isn't it? 206 00:08:18,030 --> 00:08:19,007 It can fight acceleration, 207 00:08:19,007 --> 00:08:21,540 and we can now see what inertia depends on. 208 00:08:21,540 --> 00:08:24,000 Inertia is the mass. 209 00:08:24,000 --> 00:08:27,270 More the mass of an object, more than inertia, 210 00:08:27,270 --> 00:08:29,970 harder it is to accelerate. 211 00:08:29,970 --> 00:08:32,023 Newton's second law could arguably be 212 00:08:32,023 --> 00:08:35,640 the most important equation of all of classical physics. 213 00:08:35,640 --> 00:08:37,890 I say classical physics because we now know 214 00:08:37,890 --> 00:08:40,980 that if objects are moving very close to speed of light, 215 00:08:40,980 --> 00:08:42,660 then this breaks down, it doesn't work. 216 00:08:42,660 --> 00:08:43,500 Now we'll have to resort 217 00:08:43,500 --> 00:08:45,420 to Einstein's theory of relativity. 218 00:08:45,420 --> 00:08:46,260 On the other extreme, 219 00:08:46,260 --> 00:08:48,660 if we consider extremely tiny particles, 220 00:08:48,660 --> 00:08:51,240 like subatomic particles like electrons, 221 00:08:51,240 --> 00:08:53,520 protons, and neutrons, well, even over there, 222 00:08:53,520 --> 00:08:55,650 turns out Newton's laws don't work. 223 00:08:55,650 --> 00:08:57,480 So even over there, it breaks down. 224 00:08:57,480 --> 00:08:59,460 But as long as you don't go to such extremes, 225 00:08:59,460 --> 00:09:01,050 this equation will work for us. 226 00:09:01,050 --> 00:09:02,520 So now let's see if we can apply this 227 00:09:02,520 --> 00:09:04,110 to our original question. 228 00:09:04,110 --> 00:09:06,060 When she just started moving the dumbbell, 229 00:09:06,060 --> 00:09:08,250 dumbbell's velocity was increasing. 230 00:09:08,250 --> 00:09:09,930 After that, let's say there was a small phase 231 00:09:09,930 --> 00:09:11,850 during which the velocity was constant, 232 00:09:11,850 --> 00:09:14,490 and finally, when the dumbbell is about to stop, 233 00:09:14,490 --> 00:09:16,230 its velocity is decreasing. 234 00:09:16,230 --> 00:09:18,630 So now the question is how do we figure out what happens 235 00:09:18,630 --> 00:09:20,760 to the force that she's putting on the dumbbell? 236 00:09:20,760 --> 00:09:22,860 Well, let's apply Newton's second law. 237 00:09:22,860 --> 00:09:25,740 For that, let's first think about the acceleration. 238 00:09:25,740 --> 00:09:28,710 Well, over here, we are dealing with increasing velocity. 239 00:09:28,710 --> 00:09:31,350 Therefore, the acceleration is upwards 240 00:09:31,350 --> 00:09:33,510 in the same direction as it's moving. 241 00:09:33,510 --> 00:09:35,280 Then we have a constant velocity, 242 00:09:35,280 --> 00:09:38,160 which means the acceleration is zero. 243 00:09:38,160 --> 00:09:40,530 Finally, we have a decreasing velocity, 244 00:09:40,530 --> 00:09:43,350 since the dumbbell is still going up, decreasing velocity, 245 00:09:43,350 --> 00:09:44,870 which means acceleration must be down 246 00:09:44,870 --> 00:09:47,190 in the opposite direction. 247 00:09:47,190 --> 00:09:49,500 Now, because we know the direction of the acceleration, 248 00:09:49,500 --> 00:09:51,210 we can figure out the direction of the net force. 249 00:09:51,210 --> 00:09:54,360 It has to be exactly the same, upwards here, 250 00:09:54,360 --> 00:09:56,370 zero here, downwards here. 251 00:09:56,370 --> 00:09:57,990 We are applying Newton's second law, 252 00:09:57,990 --> 00:10:00,210 the direction part over here. 253 00:10:00,210 --> 00:10:03,900 Now, finally, this is the direction of the net force. 254 00:10:03,900 --> 00:10:06,330 We want to know what happens to the force 255 00:10:06,330 --> 00:10:07,680 that we are putting on the dumbbell 256 00:10:07,680 --> 00:10:09,570 or she's putting on the dumbbell actually. 257 00:10:09,570 --> 00:10:10,530 How do we do that? 258 00:10:10,530 --> 00:10:13,440 Well, let's look at all the forces acting on the dumbbell. 259 00:10:13,440 --> 00:10:16,110 Well, we know that there's gravitational force acting 260 00:10:16,110 --> 00:10:17,640 on the dumbbell all the time. 261 00:10:17,640 --> 00:10:18,890 That force is a constant, 262 00:10:19,740 --> 00:10:22,350 and therefore, our force is in the opposite direction 263 00:10:22,350 --> 00:10:23,730 of the gravitational force. 264 00:10:23,730 --> 00:10:26,760 Now, in this case, when she's just lifting the dumbbell, 265 00:10:26,760 --> 00:10:30,210 if the net force needs to be upwards, 266 00:10:30,210 --> 00:10:32,790 that means her force must be larger 267 00:10:32,790 --> 00:10:33,810 than the gravitational force. 268 00:10:33,810 --> 00:10:36,000 Only then her force will win out, 269 00:10:36,000 --> 00:10:38,430 giving a net upward force, right? 270 00:10:38,430 --> 00:10:40,440 Okay, what about over here? 271 00:10:40,440 --> 00:10:42,600 We want the net force to be zero over here. 272 00:10:42,600 --> 00:10:44,040 How can that happen? 273 00:10:44,040 --> 00:10:46,890 Ah, her force has to be exactly the same 274 00:10:46,890 --> 00:10:48,330 as gravitational force 275 00:10:48,330 --> 00:10:52,470 because only then the forces get balanced. 276 00:10:52,470 --> 00:10:54,060 Finally, what happens over here? 277 00:10:54,060 --> 00:10:55,650 Well, we want the net force to be downwards, 278 00:10:55,650 --> 00:10:57,570 which means we want gravity to win. 279 00:10:57,570 --> 00:11:00,810 That means her force must be smaller 280 00:11:00,810 --> 00:11:02,220 than the gravitational force. 281 00:11:02,220 --> 00:11:04,560 Look, even though we did simplify it a little bit, 282 00:11:04,560 --> 00:11:05,790 I mean, I'm not really sure 283 00:11:05,790 --> 00:11:07,877 that her dumbbell was moving at a constant velocity, 284 00:11:07,877 --> 00:11:11,970 but once we simplified a little bit, we were able to analyze 285 00:11:11,970 --> 00:11:13,470 what happened to the force 286 00:11:13,470 --> 00:11:14,730 that she was putting on the dumbbell. 287 00:11:14,730 --> 00:11:18,030 It went on decreasing as the dumbbell moved upwards. 288 00:11:18,030 --> 00:11:19,140 Isn't that incredible 289 00:11:19,140 --> 00:11:21,300 how we used Newton's second law do that? 290 00:11:21,300 --> 00:11:22,293 Amazing, isn't it?