WEBVTT 00:00:00.090 --> 00:00:01.410 - [Lecturer] Let's solve a couple of problems 00:00:01.410 --> 00:00:02.910 on Newton's second law. 00:00:02.910 --> 00:00:03.780 Here's the first one. 00:00:03.780 --> 00:00:05.970 We have an elevator, which is moving up. 00:00:05.970 --> 00:00:07.350 And let's say the mass of the elevator, 00:00:07.350 --> 00:00:11.880 including the passenger inside, is 1,000 kilograms. 00:00:11.880 --> 00:00:14.940 Now the force, the tension force of the cable, 00:00:14.940 --> 00:00:17.400 let's say that's about 7,800 newtons, 00:00:17.400 --> 00:00:20.880 our goal is to figure out what the acceleration 00:00:20.880 --> 00:00:22.710 of this elevator is. 00:00:22.710 --> 00:00:26.070 We're also given that the gravitational force acting 00:00:26.070 --> 00:00:29.310 on that elevator, including the passenger over here, 00:00:29.310 --> 00:00:32.430 is about 9,800 newtons. 00:00:32.430 --> 00:00:33.990 So, how do we figure this out? 00:00:33.990 --> 00:00:35.617 Well, the first thing that comes to my mind is, 00:00:35.617 --> 00:00:37.830 "Hey, we have some forces 00:00:37.830 --> 00:00:40.860 and we have some motion variables like acceleration. 00:00:40.860 --> 00:00:43.440 What connects forces and motion variables? 00:00:43.440 --> 00:00:45.060 What connects forces and motion? 00:00:45.060 --> 00:00:47.490 Newton's second law. 00:00:47.490 --> 00:00:49.140 So, the first thing I try to do 00:00:49.140 --> 00:00:50.880 before applying Newton second law is I try 00:00:50.880 --> 00:00:53.520 to draw a free body diagram. 00:00:53.520 --> 00:00:55.080 So lemme do that. 00:00:55.080 --> 00:00:56.670 What's the way to draw a free body diagram? 00:00:56.670 --> 00:00:58.920 We try to get rid of unnecessary details. 00:00:58.920 --> 00:01:01.350 Use a box to represent your object of interest. 00:01:01.350 --> 00:01:02.910 Our object of interest is this elevator 00:01:02.910 --> 00:01:03.750 and the person over here. 00:01:03.750 --> 00:01:05.490 So, that's our box. 00:01:05.490 --> 00:01:07.020 It's mass is 1,000 kilograms 00:01:07.020 --> 00:01:08.880 and let's draw all the forces acting on it, 00:01:08.880 --> 00:01:09.990 which are the forces acting on it. 00:01:09.990 --> 00:01:12.330 Well, we have an upward force that's tension 00:01:12.330 --> 00:01:15.300 and we have a downward force that's the force of gravity 00:01:15.300 --> 00:01:18.480 and our goal is to calculate what the acceleration is. 00:01:18.480 --> 00:01:19.830 And how do we do that? 00:01:19.830 --> 00:01:20.950 Well, we use Newton second law, 00:01:20.950 --> 00:01:23.190 which says the acceleration 00:01:23.190 --> 00:01:26.310 should equal the net force acting on an object 00:01:26.310 --> 00:01:29.100 divided by its mass. 00:01:29.100 --> 00:01:31.860 And of course, since we're dealing with vectors, 00:01:31.860 --> 00:01:33.990 we can put arrow marks over here. 00:01:33.990 --> 00:01:35.820 The direction of the acceleration will be the same 00:01:35.820 --> 00:01:37.140 as the direction of the net force. 00:01:37.140 --> 00:01:40.350 Okay, now we can calculate the net force from this 00:01:40.350 --> 00:01:42.150 and we can calculate, we know the mass, 00:01:42.150 --> 00:01:43.800 so from that we can calculate the acceleration. 00:01:43.800 --> 00:01:45.240 So why don't you pause the video 00:01:45.240 --> 00:01:46.680 and see if you can plug in the numbers 00:01:46.680 --> 00:01:48.730 and find the acceleration yourself first. 00:01:49.980 --> 00:01:51.540 All right, let's try. 00:01:51.540 --> 00:01:54.300 So our acceleration would be the net force. 00:01:54.300 --> 00:01:55.890 How do I figure the net force out? 00:01:55.890 --> 00:01:57.000 Well, the total force, 00:01:57.000 --> 00:01:59.430 well they're since in the opposite direction, 00:01:59.430 --> 00:02:00.540 we'll subtract them. 00:02:00.540 --> 00:02:02.400 So, I'll just take the bigger number. 00:02:02.400 --> 00:02:06.000 So 9,800 newtons, which is acting downwards. 00:02:06.000 --> 00:02:08.010 We need to take care of the direction. 00:02:08.010 --> 00:02:10.650 From that, I'll subtract the smaller number, 00:02:10.650 --> 00:02:15.650 that is 7,800 newtons upwards divided by the mass, 00:02:16.350 --> 00:02:18.903 which is 1,000 kilograms. 00:02:20.610 --> 00:02:22.320 And if you simplify, 00:02:22.320 --> 00:02:26.880 we will get 9,800 minus 7,800 is 2,000. 00:02:26.880 --> 00:02:29.640 Nice numbers, 2000 newtons. 00:02:29.640 --> 00:02:31.380 But what direction is it? 00:02:31.380 --> 00:02:34.655 The downward one wins, right? It's bigger. 00:02:34.655 --> 00:02:36.750 So, the net force will be in the downward direction. 00:02:36.750 --> 00:02:41.750 It's divided by 1,000 kilograms and that gives us two. 00:02:42.840 --> 00:02:45.210 So, our acceleration becomes 00:02:45.210 --> 00:02:49.620 two meters per second square downwards. 00:02:49.620 --> 00:02:50.790 Okay, we found our answer, 00:02:50.790 --> 00:02:54.330 but one of the best ways to gain deeper insights is to try 00:02:54.330 --> 00:02:55.890 and see if this kind of makes sense. 00:02:55.890 --> 00:02:58.050 Can you get a feeling for what's going on over here? 00:02:58.050 --> 00:02:59.910 Okay, now the first question 00:02:59.910 --> 00:03:01.830 that we could be having over here is, look, 00:03:01.830 --> 00:03:03.720 the net force is downwards 00:03:03.720 --> 00:03:04.860 because gravity is winning, right? 00:03:04.860 --> 00:03:07.290 So the total force acting on this elevator is downwards 00:03:07.290 --> 00:03:10.080 and yet the elevator is moving up. 00:03:10.080 --> 00:03:11.880 Why is that? (chuckles) 00:03:11.880 --> 00:03:15.090 Well, remember, force does not dictate 00:03:15.090 --> 00:03:17.070 the direction of motion. 00:03:17.070 --> 00:03:20.940 Force tells you the direction of acceleration, okay? 00:03:20.940 --> 00:03:22.020 The elevator could be moving, 00:03:22.020 --> 00:03:24.240 objects can be moving whatever direction it wants. 00:03:24.240 --> 00:03:25.770 When you put a force on it, it tells you 00:03:25.770 --> 00:03:27.210 what direction it should accelerate. 00:03:27.210 --> 00:03:28.170 So that's the key thing. 00:03:28.170 --> 00:03:31.320 So, there is no problem that the force is acting downwards, 00:03:31.320 --> 00:03:32.910 but the elevator is moving upwards. 00:03:32.910 --> 00:03:34.530 Secondly, what does it mean 00:03:34.530 --> 00:03:36.210 that the acceleration is downwards? 00:03:36.210 --> 00:03:38.010 See, if the net force is downwards, 00:03:38.010 --> 00:03:39.060 the acceleration has to be downward. 00:03:39.060 --> 00:03:41.130 But what does it mean the elevator is moving up 00:03:41.130 --> 00:03:42.750 and the acceleration is downwards? 00:03:42.750 --> 00:03:46.560 Ooh, this means since the velocity 00:03:46.560 --> 00:03:48.720 and the acceleration is in the opposite direction, 00:03:48.720 --> 00:03:52.740 this means the elevator is slowing down. 00:03:52.740 --> 00:03:54.090 That's what it means for velocity 00:03:54.090 --> 00:03:55.560 and acceleration to be in the opposite direction. 00:03:55.560 --> 00:03:56.460 If they're in the same direction, 00:03:56.460 --> 00:03:57.780 it means they're speeding up. 00:03:57.780 --> 00:04:00.240 So, this means our elevator is going up, 00:04:00.240 --> 00:04:03.150 but it is slowing down, which probably means that, you know, 00:04:03.150 --> 00:04:04.860 it's probably about to stop. 00:04:04.860 --> 00:04:06.990 Maybe this person has probably reached 00:04:06.990 --> 00:04:08.670 his destination or something. 00:04:08.670 --> 00:04:10.560 All right, onto the next problem. 00:04:10.560 --> 00:04:15.120 This time we have a sledge at rest whose is 70 kilograms. 00:04:15.120 --> 00:04:16.620 Our goal is to push it 00:04:16.620 --> 00:04:18.810 and accelerate to six meters per second 00:04:18.810 --> 00:04:20.430 in about two seconds, let's say, 00:04:20.430 --> 00:04:22.110 so that, you know, it can nicely slide down 00:04:22.110 --> 00:04:23.760 and we can enjoy the ride. 00:04:23.760 --> 00:04:26.010 Now, there is going to be some frictional force. 00:04:26.010 --> 00:04:28.140 Even though we're on ice and everything, 00:04:28.140 --> 00:04:29.370 there'll be some frictional force. 00:04:29.370 --> 00:04:30.203 Let's say the friction 00:04:30.203 --> 00:04:32.853 that this ledge will experience is about 200 newtons. 00:04:33.690 --> 00:04:36.840 The question now is what is the force with which we have 00:04:36.840 --> 00:04:39.990 to push on it so as to achieve all of this? 00:04:39.990 --> 00:04:42.060 So how do we figure this out? 00:04:42.060 --> 00:04:43.980 Well, again, the first thing that comes to my mind is 00:04:43.980 --> 00:04:47.010 that look, we're dealing with forces and we have motion. 00:04:47.010 --> 00:04:50.490 What connects forces and motion? Newton's second law. 00:04:50.490 --> 00:04:52.320 So, the first thing I'll do is I'm gonna draw 00:04:52.320 --> 00:04:53.310 a free-body diagram. 00:04:53.310 --> 00:04:56.430 Again, I encourage you to pause the video now 00:04:56.430 --> 00:04:57.600 or anytime later on. 00:04:57.600 --> 00:04:58.710 Whenever you feel more comfortable, 00:04:58.710 --> 00:05:01.050 pause the video and see if you can complete it yourself. 00:05:01.050 --> 00:05:03.120 Okay, so anyways, let's first try 00:05:03.120 --> 00:05:04.230 to draw a free-body diagram. 00:05:04.230 --> 00:05:05.063 How do we do that? 00:05:05.063 --> 00:05:06.780 Well, again, we'll take the object of our interest. 00:05:06.780 --> 00:05:09.510 In this case, the object of our interest is this ledge 00:05:09.510 --> 00:05:12.930 whose mass is 70 kilograms and just make it a square 00:05:12.930 --> 00:05:14.370 and then draw all the forces acting on it. 00:05:14.370 --> 00:05:15.450 What are the forces acting on it? 00:05:15.450 --> 00:05:18.000 I know there's frictional force acting backwards 00:05:18.000 --> 00:05:21.660 of 200 newtons, but then I also have the applied force 00:05:21.660 --> 00:05:23.580 by this person, which I, we need to figure out. 00:05:23.580 --> 00:05:24.810 This is what we need to calculate. 00:05:24.810 --> 00:05:27.780 That is the applied force. What are other forces? 00:05:27.780 --> 00:05:30.600 Well, I know that there's also gravity acting on it 00:05:30.600 --> 00:05:33.150 and then there's a normal force acting on it upwards. 00:05:33.150 --> 00:05:35.220 But we know that these forces are balanced 00:05:35.220 --> 00:05:37.590 and so they're not going to be useful. 00:05:37.590 --> 00:05:41.190 They're not going to affect our situation over here. 00:05:41.190 --> 00:05:42.840 So, I'm just gonna draw them over here. 00:05:42.840 --> 00:05:44.954 They're there, of course, but they're completely balanced. 00:05:44.954 --> 00:05:46.740 They're in the verticals, they're not gonna affect it, 00:05:46.740 --> 00:05:48.150 so we'll not draw it. 00:05:48.150 --> 00:05:50.160 Okay, now that I have my free-body diagram, 00:05:50.160 --> 00:05:52.470 let's go ahead and write down on Newton second law. 00:05:52.470 --> 00:05:57.470 It says acceleration should always equal the net force, 00:05:57.930 --> 00:06:00.420 which let me draw using pink now. 00:06:00.420 --> 00:06:04.920 Net force divided by the mass. 00:06:04.920 --> 00:06:06.510 Divided by the mass. 00:06:06.510 --> 00:06:09.870 Okay, so what do we do next? 00:06:09.870 --> 00:06:12.630 I need to find this applied force. 00:06:12.630 --> 00:06:16.620 So this means if I can calculate the net force, 00:06:16.620 --> 00:06:19.650 then I can figure out what the applied force is, right? 00:06:19.650 --> 00:06:21.150 So, from Newton's second law, 00:06:21.150 --> 00:06:22.770 I just need to figure out what the net force is. 00:06:22.770 --> 00:06:25.470 For that, I ask myself, do I know m? 00:06:25.470 --> 00:06:27.960 I do. I know that m is 70 kilograms. 00:06:27.960 --> 00:06:29.940 Do I know the acceleration? 00:06:29.940 --> 00:06:31.140 Hmm, it's not given directly, 00:06:31.140 --> 00:06:34.740 but wait a second, I know the initial velocity, 00:06:34.740 --> 00:06:36.183 I know the final velocity and I know 00:06:36.183 --> 00:06:38.730 that the change in velocity should happen in two seconds. 00:06:38.730 --> 00:06:39.943 Whoo-hoo! 00:06:39.943 --> 00:06:43.860 That means I can calculate the acceleration from this data. 00:06:43.860 --> 00:06:46.140 I can plug in and from that I can figure out 00:06:46.140 --> 00:06:48.630 what the total force is going to be, 00:06:48.630 --> 00:06:50.070 the net force is going to be. 00:06:50.070 --> 00:06:52.590 And from that we can figure out 00:06:52.590 --> 00:06:54.330 what the applied force should be. 00:06:54.330 --> 00:06:56.280 Okay, so if you haven't done this before, 00:06:56.280 --> 00:06:57.690 why don't you now pause the video 00:06:57.690 --> 00:06:59.430 and see if you can put it all together 00:06:59.430 --> 00:07:01.560 and solve the problem? 00:07:01.560 --> 00:07:03.180 Okay, let's do this. 00:07:03.180 --> 00:07:05.130 So, let me first calculate the acceleration. 00:07:05.130 --> 00:07:06.240 So our acceleration is going 00:07:06.240 --> 00:07:07.620 to be, well how do we figure this out? 00:07:07.620 --> 00:07:11.670 This is the final velocity minus the initial velocity 00:07:11.670 --> 00:07:13.950 divided by the time taken. 00:07:13.950 --> 00:07:15.300 So, that's going to be, in our case, 00:07:15.300 --> 00:07:17.500 the final velocity is six meters per second 00:07:19.260 --> 00:07:21.810 to the right minus... 00:07:21.810 --> 00:07:23.040 What's the initial velocity? 00:07:23.040 --> 00:07:25.650 Well, it's zero, it's at rest. 00:07:25.650 --> 00:07:27.690 So there is no initial velocity divided 00:07:27.690 --> 00:07:30.360 by time is two, two seconds. 00:07:30.360 --> 00:07:31.590 That gives us what? 00:07:31.590 --> 00:07:36.590 That gives us six by two is three meters per second squared 00:07:37.560 --> 00:07:39.870 to the right. 00:07:39.870 --> 00:07:42.390 So I know my acceleration has to be 00:07:42.390 --> 00:07:44.610 to the right, which is good news. (chuckles) 00:07:44.610 --> 00:07:45.660 It has to be to the right. 00:07:45.660 --> 00:07:46.920 We want this ledge to move to the right. 00:07:46.920 --> 00:07:47.753 So, that makes sense. 00:07:47.753 --> 00:07:49.440 So, we are on the right track over here. 00:07:49.440 --> 00:07:50.730 Okay, now, I can plug in 00:07:50.730 --> 00:07:52.560 and figure out what the net force is going to be. 00:07:52.560 --> 00:07:56.100 So, if I just simplify that, so net force is going to be, 00:07:56.100 --> 00:07:58.770 if I rearrange this equation multiply by m on both sides. 00:07:58.770 --> 00:08:02.223 So I get net force to be mass times the acceleration. 00:08:03.240 --> 00:08:06.060 And so now I can plug in for mass and acceleration. 00:08:06.060 --> 00:08:09.150 What do I get? Well I get 70 kilograms. 00:08:09.150 --> 00:08:10.530 That's the mass, 00:08:10.530 --> 00:08:14.160 times the acceleration is three meters per second squared, 00:08:14.160 --> 00:08:15.620 70 times three, seven times these 21. 00:08:15.620 --> 00:08:18.090 So, this is 210. 00:08:18.090 --> 00:08:21.910 So, I get that my net force is 210 newtons 00:08:23.606 --> 00:08:25.230 to the right of this, 00:08:25.230 --> 00:08:27.210 this acceleration was to the right. 00:08:27.210 --> 00:08:30.660 So, this will also be to the right. 00:08:30.660 --> 00:08:34.740 So, now that I've found my net force, so my net force, 00:08:34.740 --> 00:08:37.860 the total force will be to the right 00:08:37.860 --> 00:08:40.020 and that is 210 newtons. 00:08:40.020 --> 00:08:44.070 From that, can I calculate the applied force? Yes. 00:08:44.070 --> 00:08:45.030 So now, first of all, 00:08:45.030 --> 00:08:47.550 I know my applied force should be bigger. 00:08:47.550 --> 00:08:48.660 It has to be bigger 00:08:48.660 --> 00:08:51.510 because my total force should be towards the right, 00:08:51.510 --> 00:08:54.030 which means if I subtract the two from this, 00:08:54.030 --> 00:08:57.030 if I subtract this number, I should get this number. 00:08:57.030 --> 00:08:58.530 That's the net force, all right? 00:08:58.530 --> 00:09:00.390 So now, now that I know all the directions 00:09:00.390 --> 00:09:02.070 and everything, I can just subtract the numbers. 00:09:02.070 --> 00:09:04.530 So I can now say, "Hey, my net force 00:09:04.530 --> 00:09:08.640 that is 210 newtons should equal this bigger number, 00:09:08.640 --> 00:09:13.443 the bigger force minus 200 newtons. 00:09:14.610 --> 00:09:17.850 Now, to get applied force, I just add 200 on both sides 00:09:17.850 --> 00:09:20.283 so that I can get rid of this. 00:09:22.050 --> 00:09:27.050 And look, the applied force becomes 210 plus 200. 00:09:27.150 --> 00:09:31.170 That is 410 newtons. 00:09:31.170 --> 00:09:32.880 And I already know it's to the right, 00:09:32.880 --> 00:09:34.440 so I know it's direction. 00:09:34.440 --> 00:09:37.110 So if I were to write down its direction, 00:09:37.110 --> 00:09:39.115 it's going to be, oops. (chuckles) 00:09:39.115 --> 00:09:39.990 Okay. Okay. 00:09:39.990 --> 00:09:42.990 I mean, okay, not the most organized board over here, 00:09:42.990 --> 00:09:45.420 but let me just write it down a little bit more neatly. 00:09:45.420 --> 00:09:49.410 So 410 newtons to the right. 00:09:49.410 --> 00:09:51.390 That's how much force we need to apply 00:09:51.390 --> 00:09:53.013 for all of this to happen.