0:00:00.270,0:00:01.103 - [Instructor] Today in the gym, 0:00:01.103,0:00:02.970 when my wife was doing dumbbell curls, 0:00:02.970,0:00:05.400 I started wondering, see,[br]she's putting a force 0:00:05.400,0:00:07.200 on that dumbbell upwards, right? 0:00:07.200,0:00:09.810 But does that force stay a constant 0:00:09.810,0:00:12.450 as she moves the dumbbell up or not? 0:00:12.450,0:00:15.090 Does it change? And if it does[br]change, how does it change? 0:00:15.090,0:00:17.760 Does it increase, does it[br]decrease? What happens to it? 0:00:17.760,0:00:18.593 Guess what. 0:00:18.593,0:00:20.520 We can answer this question by the end 0:00:20.520,0:00:23.430 of this video using Newton's second law. 0:00:23.430,0:00:24.990 So let's start with a simpler example. 0:00:24.990,0:00:27.000 We have a ice hockey ground over here, 0:00:27.000,0:00:30.304 and there's a puck moving[br]on top of it at some speed. 0:00:30.304,0:00:33.540 If there are no frictional[br]forces acting on this, 0:00:33.540,0:00:36.750 if you assume that, then the[br]forces acting on this puck 0:00:36.750,0:00:40.710 would be balanced because in[br]the horizontal, you can see 0:00:40.710,0:00:43.140 that there are no forces[br]because we're ignoring friction. 0:00:43.140,0:00:46.380 And in the vertical,[br]the gravitational force, 0:00:46.380,0:00:48.210 which is pulling down on[br]it is completely balanced 0:00:48.210,0:00:50.790 by the force that the[br]ground is pushing up on it, 0:00:50.790,0:00:52.380 the normal force, they balance it out. 0:00:52.380,0:00:54.840 And so since there are no[br]unbalanced forces acting 0:00:54.840,0:00:56.580 on this puck from Newton's first law, 0:00:56.580,0:00:59.400 we know that this thing will[br]continue its state of rest, 0:00:59.400,0:01:02.040 or in this particular case,[br]the state of uniform motion. 0:01:02.040,0:01:04.800 So it'll continue to move[br]with that same velocity. 0:01:04.800,0:01:06.870 But now comes the question, 0:01:06.870,0:01:09.330 what if there was an[br]unbalanced force acting on it? 0:01:09.330,0:01:11.190 What happens because of that? 0:01:11.190,0:01:12.600 Well, let's find out. 0:01:12.600,0:01:15.000 For that, let's just whack[br]it with a hockey stick. 0:01:15.000,0:01:16.800 No.[br](instructor laughing) 0:01:16.800,0:01:19.860 So if I whack it to the[br]right, let's say in this case, 0:01:19.860,0:01:23.490 I will now put an unbalanced[br]force to the right. 0:01:23.490,0:01:26.130 What will happen? Well,[br]we can probably guess it. 0:01:26.130,0:01:28.110 That puck's velocity will now be higher. 0:01:28.110,0:01:29.670 It'll just get blasted off over there. 0:01:29.670,0:01:31.590 So its velocity will increase. 0:01:31.590,0:01:34.920 In other words, it will accelerate. 0:01:34.920,0:01:38.670 Ooh, this means when there's[br]an unbalanced force acting 0:01:38.670,0:01:40.404 on a an object, in other words, 0:01:40.404,0:01:45.404 if there is a non-zero net[br]force acting on an object, 0:01:45.480,0:01:47.880 which is the same thing as[br]saying an unbalanced force, 0:01:47.880,0:01:49.710 but whenever this net[br]force acts on an object, 0:01:49.710,0:01:50.820 what does it do? 0:01:50.820,0:01:52.680 It accelerates our puck. 0:01:52.680,0:01:55.983 The puck undergoes, or the[br]object undergoes an acceleration. 0:01:56.910,0:02:00.030 This is the essence of[br]Newton's second law. 0:02:00.030,0:02:02.040 Now all we gotta do is[br]analyze the situation 0:02:02.040,0:02:03.000 even more carefully 0:02:03.000,0:02:05.760 and see if we can concretize[br]this relationship. 0:02:05.760,0:02:06.930 So let's do that. 0:02:06.930,0:02:08.460 The first question we could have is yeah, 0:02:08.460,0:02:10.590 so a net force causes an acceleration, 0:02:10.590,0:02:13.140 but how long does that acceleration last? 0:02:13.140,0:02:14.550 Well, let's see. 0:02:14.550,0:02:17.760 When the stick hits the puck, 0:02:17.760,0:02:19.440 that's when it starts accelerating, 0:02:19.440,0:02:22.770 which means as long as[br]the stick is in contact 0:02:22.770,0:02:25.290 with the puck, as long as[br]it's in contact with it, 0:02:25.290,0:02:28.500 like right now here, it's during that time 0:02:28.500,0:02:30.330 there will be acceleration. 0:02:30.330,0:02:33.000 But what happens once it loses contact? 0:02:33.000,0:02:35.940 Once it loses contact, again,[br]net force goes to zero. 0:02:35.940,0:02:38.640 And now coming back to Newton's first law, 0:02:38.640,0:02:43.110 it'll continue moving with[br]that same increased velocity. 0:02:43.110,0:02:45.900 This means the acceleration only happened 0:02:45.900,0:02:48.450 during this time when the hockey stick 0:02:48.450,0:02:49.680 was in contact with it. 0:02:49.680,0:02:52.680 In other words, the[br]acceleration lasts as long 0:02:52.680,0:02:55.440 as the net force lasts. 0:02:55.440,0:02:58.260 Okay, next, let's think[br]about what would happen 0:02:58.260,0:03:01.110 if the net force was higher? 0:03:01.110,0:03:03.480 For that let's imagine[br]we whacked it harder. 0:03:03.480,0:03:04.770 What's gonna happen now? 0:03:04.770,0:03:07.770 Or you can imagine it'll get[br]blasted off even more faster, 0:03:07.770,0:03:09.030 even faster, right? 0:03:09.030,0:03:10.770 Which means it'll have a higher velocity 0:03:10.770,0:03:12.330 when it loses contact. 0:03:12.330,0:03:15.750 Ooh, that means there'll[br]be bigger acceleration. 0:03:15.750,0:03:17.730 So if the net force is larger, 0:03:17.730,0:03:19.950 it means you'll have[br]a larger acceleration. 0:03:19.950,0:03:22.890 If the net force is smaller,[br]you get a smaller acceleration. 0:03:22.890,0:03:26.220 In other words, we see[br]a direct relationship 0:03:26.220,0:03:30.390 between acceleration and the net force. 0:03:30.390,0:03:32.610 All right, what else can we deduce? 0:03:32.610,0:03:35.100 Hey, let's think about the direction. 0:03:35.100,0:03:37.620 What is the direction of the acceleration? 0:03:37.620,0:03:40.620 Well, in this case, the[br]net force is to the right, 0:03:40.620,0:03:42.540 and our puck's velocity 0:03:42.540,0:03:45.000 is also increasing towards the right. 0:03:45.000,0:03:47.640 So in this case, the[br]acceleration is to the right. 0:03:47.640,0:03:49.710 So in this case, if the[br]net force is to the right, 0:03:49.710,0:03:51.168 the acceleration is to the right. 0:03:51.168,0:03:54.330 What would happen if the[br]net force was to the left? 0:03:54.330,0:03:56.790 So let's imagine we whack that puck now 0:03:56.790,0:03:59.370 to the left, what would happen? 0:03:59.370,0:04:00.750 Well, we can again imagine the puck 0:04:00.750,0:04:02.820 would now get blasted off to the left. 0:04:02.820,0:04:04.770 But let's look at it carefully. 0:04:04.770,0:04:07.950 Since the puck is already moving[br]to the right, if we push it 0:04:07.950,0:04:11.280 to the left, now we're gonna slow it down. 0:04:11.280,0:04:13.680 The puck will come to a stop first. 0:04:13.680,0:04:16.980 It'll happen very quickly[br]that we won't even see it. 0:04:16.980,0:04:19.740 But it has to happen before[br]going to the left, right? 0:04:19.740,0:04:21.990 Which means when you go from here to here, 0:04:21.990,0:04:24.090 notice even though the puck[br]is moving to the right, 0:04:24.090,0:04:26.580 it is slowing down, which[br]means the acceleration 0:04:26.580,0:04:28.410 is to the left. 0:04:28.410,0:04:29.850 So when the net force is to the left, 0:04:29.850,0:04:32.130 we're seeing an[br]acceleration is to the left. 0:04:32.130,0:04:34.620 After that, its velocity[br]might increase to the left, 0:04:34.620,0:04:37.920 which means again, the[br]acceleration is to the left. 0:04:37.920,0:04:38.970 Ooh. 0:04:38.970,0:04:41.070 So if the net force is to the left, 0:04:41.070,0:04:42.390 the acceleration is to the left. 0:04:42.390,0:04:43.770 If the net force is to the right, 0:04:43.770,0:04:45.300 the acceleration is to the right. 0:04:45.300,0:04:48.720 So the acceleration will[br]be in the same direction 0:04:48.720,0:04:51.090 as that of the net force. 0:04:51.090,0:04:55.530 Okay, is there anything else[br]that affects our acceleration? 0:04:55.530,0:04:56.820 Well, let's see. 0:04:56.820,0:04:58.140 If you come back over here, 0:04:58.140,0:04:59.700 what if you use the same bat, 0:04:59.700,0:05:01.440 whacked it with the same force, 0:05:01.440,0:05:03.150 but instead of a puck, 0:05:03.150,0:05:04.500 let's say there was a bowling ball 0:05:04.500,0:05:05.700 moving with the same velocity. 0:05:05.700,0:05:07.364 What would happen now? 0:05:07.364,0:05:08.250 (instructor laughing) 0:05:08.250,0:05:11.400 I'm pretty sure you can[br]feel it in your bones now. 0:05:11.400,0:05:14.880 It would be much harder[br]to stop that bowling ball 0:05:14.880,0:05:17.190 and make it turn backwards, right? 0:05:17.190,0:05:18.630 I mean, the same thing will happen. 0:05:18.630,0:05:23.070 You will slow it down, but[br]it'll be much, much harder. 0:05:23.070,0:05:26.310 It'll take a much longer[br]time to slow it down, 0:05:26.310,0:05:29.100 even though you're putting[br]the same amount of force. 0:05:29.100,0:05:30.930 So the net force has stayed the same. 0:05:30.930,0:05:33.150 But what has happened to our acceleration? 0:05:33.150,0:05:36.450 Since the velocity changed[br]over a much longer time, 0:05:36.450,0:05:39.300 the acceleration became smaller. 0:05:39.300,0:05:41.850 Hey, why did the[br]acceleration became smaller? 0:05:41.850,0:05:43.500 What changed? 0:05:43.500,0:05:46.740 From the puck to the bowling[br]ball, the mass changed, 0:05:46.740,0:05:48.660 the mass increased. 0:05:48.660,0:05:51.960 So this means mass also[br]affects the acceleration, 0:05:51.960,0:05:53.400 but how does it affect it? 0:05:53.400,0:05:56.190 Well, we saw that the[br]mass increased right now. 0:05:56.190,0:05:58.230 What did that do to the acceleration? 0:05:58.230,0:06:01.110 It decreased, and this[br]is kind of intuitive. 0:06:01.110,0:06:04.200 The bigger the mass, the[br]harder it is to accelerate, 0:06:04.200,0:06:06.660 meaning the smaller the acceleration, 0:06:06.660,0:06:11.460 which means acceleration[br]has an inverse relationship 0:06:11.460,0:06:13.350 with the mass. 0:06:13.350,0:06:16.560 So now, everything that we just[br]analyzed about acceleration, 0:06:16.560,0:06:18.630 its direction, its[br]dependency on the net force, 0:06:18.630,0:06:19.710 how it depends on the mass, 0:06:19.710,0:06:23.250 all of it can be put down in an equation. 0:06:23.250,0:06:25.350 And that equation is pretty[br]much right in front of us. 0:06:25.350,0:06:29.580 So the acceleration will[br]equal the net force divided 0:06:29.580,0:06:31.770 by the mass. 0:06:31.770,0:06:36.630 This is our Newton's second law. 0:06:36.630,0:06:38.610 And look, the equation[br]is saying the same thing. 0:06:38.610,0:06:40.020 Direct relationship between acceleration 0:06:40.020,0:06:42.480 and the net force, inverse[br]relationship between acceleration 0:06:42.480,0:06:44.640 and the mass and the arrowheads are saying 0:06:44.640,0:06:46.710 that acceleration and the[br]net force will always be 0:06:46.710,0:06:48.270 in the same direction. 0:06:48.270,0:06:50.040 Isn't it amazing that we can pack all 0:06:50.040,0:06:53.070 of that information in just[br]one beautiful equation? 0:06:53.070,0:06:55.350 And of course, you may[br]have seen this written 0:06:55.350,0:06:58.620 as f equals ma in some[br]sources, it's the same thing. 0:06:58.620,0:06:59.453 I like to write it this way 0:06:59.453,0:07:03.390 because acceleration[br]is caused by the force. 0:07:03.390,0:07:06.060 So once we decide the[br]force is and the mass, 0:07:06.060,0:07:08.370 then the acceleration gets fixed. 0:07:08.370,0:07:12.390 But anyways, what will happen[br]if the net force is zero? 0:07:12.390,0:07:15.060 What if we plug in over here zero? 0:07:15.060,0:07:18.090 Well, then the acceleration[br]also goes to zero. 0:07:18.090,0:07:19.149 What does this mean? 0:07:19.149,0:07:22.260 Well, this means we have all[br]the balance forces acting 0:07:22.260,0:07:23.093 on an object. 0:07:23.093,0:07:25.170 And if the acceleration is zero, it means 0:07:25.170,0:07:27.270 that the velocity stays a constant. 0:07:27.270,0:07:30.570 In other words, this[br]is Newton's first law, 0:07:30.570,0:07:32.730 which says an object[br]continues to stay at rest 0:07:32.730,0:07:34.500 or in uniform motion. 0:07:34.500,0:07:36.330 That is zero acceleration, right? 0:07:36.330,0:07:39.150 When there are no unbalanced[br]forces acting on it. 0:07:39.150,0:07:42.630 So notice, Newton's first[br]law is just a special case 0:07:42.630,0:07:44.910 of Newton's second law, 0:07:44.910,0:07:48.900 which means this equation is[br]encompassing both the second 0:07:48.900,0:07:50.550 and the first law as well. 0:07:50.550,0:07:53.400 And finally, speaking[br]about Newton's first law, 0:07:53.400,0:07:56.100 what we also noticed over[br]here is bigger the mass, 0:07:56.100,0:07:57.450 smaller the acceleration. 0:07:57.450,0:08:01.260 In other words, if the mass[br]is bigger, it is harder 0:08:01.260,0:08:02.400 to change its velocity. 0:08:02.400,0:08:05.610 It's much harder to do[br]that, which means objects 0:08:05.610,0:08:08.940 that have more mass have more inertia. 0:08:08.940,0:08:10.845 That's something again we[br]learned in Newton's first law. 0:08:10.845,0:08:12.630 Inertia is the property due 0:08:12.630,0:08:15.570 to which objects continue to stay at rest 0:08:15.570,0:08:18.030 or continue to stay in[br]uniform motion, isn't it? 0:08:18.030,0:08:19.007 It can fight acceleration, 0:08:19.007,0:08:21.540 and we can now see what[br]inertia depends on. 0:08:21.540,0:08:24.000 Inertia is the mass. 0:08:24.000,0:08:27.270 More the mass of an[br]object, more than inertia, 0:08:27.270,0:08:29.970 harder it is to accelerate. 0:08:29.970,0:08:32.023 Newton's second law could arguably be 0:08:32.023,0:08:35.640 the most important equation[br]of all of classical physics. 0:08:35.640,0:08:37.890 I say classical physics[br]because we now know 0:08:37.890,0:08:40.980 that if objects are moving[br]very close to speed of light, 0:08:40.980,0:08:42.660 then this breaks down, it doesn't work. 0:08:42.660,0:08:43.500 Now we'll have to resort 0:08:43.500,0:08:45.420 to Einstein's theory of relativity. 0:08:45.420,0:08:46.260 On the other extreme, 0:08:46.260,0:08:48.660 if we consider extremely tiny particles, 0:08:48.660,0:08:51.240 like subatomic particles like electrons, 0:08:51.240,0:08:53.520 protons, and neutrons,[br]well, even over there, 0:08:53.520,0:08:55.650 turns out Newton's laws don't work. 0:08:55.650,0:08:57.480 So even over there, it breaks down. 0:08:57.480,0:08:59.460 But as long as you don't[br]go to such extremes, 0:08:59.460,0:09:01.050 this equation will work for us. 0:09:01.050,0:09:02.520 So now let's see if we can apply this 0:09:02.520,0:09:04.110 to our original question. 0:09:04.110,0:09:06.060 When she just started moving the dumbbell, 0:09:06.060,0:09:08.250 dumbbell's velocity was increasing. 0:09:08.250,0:09:09.930 After that, let's say[br]there was a small phase 0:09:09.930,0:09:11.850 during which the velocity was constant, 0:09:11.850,0:09:14.490 and finally, when the[br]dumbbell is about to stop, 0:09:14.490,0:09:16.230 its velocity is decreasing. 0:09:16.230,0:09:18.630 So now the question is how[br]do we figure out what happens 0:09:18.630,0:09:20.760 to the force that she's[br]putting on the dumbbell? 0:09:20.760,0:09:22.860 Well, let's apply Newton's second law. 0:09:22.860,0:09:25.740 For that, let's first think[br]about the acceleration. 0:09:25.740,0:09:28.710 Well, over here, we are dealing[br]with increasing velocity. 0:09:28.710,0:09:31.350 Therefore, the acceleration is upwards 0:09:31.350,0:09:33.510 in the same direction as it's moving. 0:09:33.510,0:09:35.280 Then we have a constant velocity, 0:09:35.280,0:09:38.160 which means the acceleration is zero. 0:09:38.160,0:09:40.530 Finally, we have a decreasing velocity, 0:09:40.530,0:09:43.350 since the dumbbell is still[br]going up, decreasing velocity, 0:09:43.350,0:09:44.870 which means acceleration must be down 0:09:44.870,0:09:47.190 in the opposite direction. 0:09:47.190,0:09:49.500 Now, because we know the[br]direction of the acceleration, 0:09:49.500,0:09:51.210 we can figure out the[br]direction of the net force. 0:09:51.210,0:09:54.360 It has to be exactly[br]the same, upwards here, 0:09:54.360,0:09:56.370 zero here, downwards here. 0:09:56.370,0:09:57.990 We are applying Newton's second law, 0:09:57.990,0:10:00.210 the direction part over here. 0:10:00.210,0:10:03.900 Now, finally, this is the[br]direction of the net force. 0:10:03.900,0:10:06.330 We want to know what happens to the force 0:10:06.330,0:10:07.680 that we are putting on the dumbbell 0:10:07.680,0:10:09.570 or she's putting on the dumbbell actually. 0:10:09.570,0:10:10.530 How do we do that? 0:10:10.530,0:10:13.440 Well, let's look at all the[br]forces acting on the dumbbell. 0:10:13.440,0:10:16.110 Well, we know that there's[br]gravitational force acting 0:10:16.110,0:10:17.640 on the dumbbell all the time. 0:10:17.640,0:10:18.890 That force is a constant, 0:10:19.740,0:10:22.350 and therefore, our force is[br]in the opposite direction 0:10:22.350,0:10:23.730 of the gravitational force. 0:10:23.730,0:10:26.760 Now, in this case, when she's[br]just lifting the dumbbell, 0:10:26.760,0:10:30.210 if the net force needs to be upwards, 0:10:30.210,0:10:32.790 that means her force must be larger 0:10:32.790,0:10:33.810 than the gravitational force. 0:10:33.810,0:10:36.000 Only then her force will win out, 0:10:36.000,0:10:38.430 giving a net upward force, right? 0:10:38.430,0:10:40.440 Okay, what about over here? 0:10:40.440,0:10:42.600 We want the net force[br]to be zero over here. 0:10:42.600,0:10:44.040 How can that happen? 0:10:44.040,0:10:46.890 Ah, her force has to be exactly the same 0:10:46.890,0:10:48.330 as gravitational force 0:10:48.330,0:10:52.470 because only then the forces get balanced. 0:10:52.470,0:10:54.060 Finally, what happens over here? 0:10:54.060,0:10:55.650 Well, we want the net[br]force to be downwards, 0:10:55.650,0:10:57.570 which means we want gravity to win. 0:10:57.570,0:11:00.810 That means her force must be smaller 0:11:00.810,0:11:02.220 than the gravitational force. 0:11:02.220,0:11:04.560 Look, even though we did[br]simplify it a little bit, 0:11:04.560,0:11:05.790 I mean, I'm not really sure 0:11:05.790,0:11:07.877 that her dumbbell was moving[br]at a constant velocity, 0:11:07.877,0:11:11.970 but once we simplified a little[br]bit, we were able to analyze 0:11:11.970,0:11:13.470 what happened to the force 0:11:13.470,0:11:14.730 that she was putting on the dumbbell. 0:11:14.730,0:11:18.030 It went on decreasing as[br]the dumbbell moved upwards. 0:11:18.030,0:11:19.140 Isn't that incredible 0:11:19.140,0:11:21.300 how we used Newton's second law do that? 0:11:21.300,0:11:22.293 Amazing, isn't it?