0:00:00.090,0:00:01.410 - [Lecturer] Let's solve[br]a couple of problems 0:00:01.410,0:00:02.910 on Newton's second law. 0:00:02.910,0:00:03.780 Here's the first one. 0:00:03.780,0:00:05.970 We have an elevator, which is moving up. 0:00:05.970,0:00:07.350 And let's say the mass of the elevator, 0:00:07.350,0:00:11.880 including the passenger[br]inside, is 1,000 kilograms. 0:00:11.880,0:00:14.940 Now the force, the tension[br]force of the cable, 0:00:14.940,0:00:17.400 let's say that's about 7,800 newtons, 0:00:17.400,0:00:20.880 our goal is to figure[br]out what the acceleration 0:00:20.880,0:00:22.710 of this elevator is. 0:00:22.710,0:00:26.070 We're also given that the[br]gravitational force acting 0:00:26.070,0:00:29.310 on that elevator, including[br]the passenger over here, 0:00:29.310,0:00:32.430 is about 9,800 newtons. 0:00:32.430,0:00:33.990 So, how do we figure this out? 0:00:33.990,0:00:35.617 Well, the first thing[br]that comes to my mind is, 0:00:35.617,0:00:37.830 "Hey, we have some forces 0:00:37.830,0:00:40.860 and we have some motion[br]variables like acceleration. 0:00:40.860,0:00:43.440 What connects forces and motion variables? 0:00:43.440,0:00:45.060 What connects forces and motion? 0:00:45.060,0:00:47.490 Newton's second law. 0:00:47.490,0:00:49.140 So, the first thing I try to do 0:00:49.140,0:00:50.880 before applying Newton second law is I try 0:00:50.880,0:00:53.520 to draw a free body diagram. 0:00:53.520,0:00:55.080 So lemme do that. 0:00:55.080,0:00:56.670 What's the way to draw[br]a free body diagram? 0:00:56.670,0:00:58.920 We try to get rid of unnecessary details. 0:00:58.920,0:01:01.350 Use a box to represent[br]your object of interest. 0:01:01.350,0:01:02.910 Our object of interest is this elevator 0:01:02.910,0:01:03.750 and the person over here. 0:01:03.750,0:01:05.490 So, that's our box. 0:01:05.490,0:01:07.020 It's mass is 1,000 kilograms 0:01:07.020,0:01:08.880 and let's draw all the[br]forces acting on it, 0:01:08.880,0:01:09.990 which are the forces acting on it. 0:01:09.990,0:01:12.330 Well, we have an upward[br]force that's tension 0:01:12.330,0:01:15.300 and we have a downward force[br]that's the force of gravity 0:01:15.300,0:01:18.480 and our goal is to calculate[br]what the acceleration is. 0:01:18.480,0:01:19.830 And how do we do that? 0:01:19.830,0:01:20.950 Well, we use Newton second law, 0:01:20.950,0:01:23.190 which says the acceleration 0:01:23.190,0:01:26.310 should equal the net[br]force acting on an object 0:01:26.310,0:01:29.100 divided by its mass. 0:01:29.100,0:01:31.860 And of course, since we're[br]dealing with vectors, 0:01:31.860,0:01:33.990 we can put arrow marks over here. 0:01:33.990,0:01:35.820 The direction of the[br]acceleration will be the same 0:01:35.820,0:01:37.140 as the direction of the net force. 0:01:37.140,0:01:40.350 Okay, now we can calculate[br]the net force from this 0:01:40.350,0:01:42.150 and we can calculate, we know the mass, 0:01:42.150,0:01:43.800 so from that we can[br]calculate the acceleration. 0:01:43.800,0:01:45.240 So why don't you pause the video 0:01:45.240,0:01:46.680 and see if you can plug in the numbers 0:01:46.680,0:01:48.730 and find the acceleration yourself first. 0:01:49.980,0:01:51.540 All right, let's try. 0:01:51.540,0:01:54.300 So our acceleration[br]would be the net force. 0:01:54.300,0:01:55.890 How do I figure the net force out? 0:01:55.890,0:01:57.000 Well, the total force, 0:01:57.000,0:01:59.430 well they're since in[br]the opposite direction, 0:01:59.430,0:02:00.540 we'll subtract them. 0:02:00.540,0:02:02.400 So, I'll just take the bigger number. 0:02:02.400,0:02:06.000 So 9,800 newtons, which[br]is acting downwards. 0:02:06.000,0:02:08.010 We need to take care of the direction. 0:02:08.010,0:02:10.650 From that, I'll subtract[br]the smaller number, 0:02:10.650,0:02:15.650 that is 7,800 newtons[br]upwards divided by the mass, 0:02:16.350,0:02:18.903 which is 1,000 kilograms. 0:02:20.610,0:02:22.320 And if you simplify, 0:02:22.320,0:02:26.880 we will get 9,800 minus 7,800 is 2,000. 0:02:26.880,0:02:29.640 Nice numbers, 2000 newtons. 0:02:29.640,0:02:31.380 But what direction is it? 0:02:31.380,0:02:34.655 The downward one wins, right? It's bigger. 0:02:34.655,0:02:36.750 So, the net force will be[br]in the downward direction. 0:02:36.750,0:02:41.750 It's divided by 1,000 kilograms[br]and that gives us two. 0:02:42.840,0:02:45.210 So, our acceleration becomes 0:02:45.210,0:02:49.620 two meters per second square downwards. 0:02:49.620,0:02:50.790 Okay, we found our answer, 0:02:50.790,0:02:54.330 but one of the best ways to[br]gain deeper insights is to try 0:02:54.330,0:02:55.890 and see if this kind of makes sense. 0:02:55.890,0:02:58.050 Can you get a feeling for[br]what's going on over here? 0:02:58.050,0:02:59.910 Okay, now the first question 0:02:59.910,0:03:01.830 that we could be having[br]over here is, look, 0:03:01.830,0:03:03.720 the net force is downwards 0:03:03.720,0:03:04.860 because gravity is winning, right? 0:03:04.860,0:03:07.290 So the total force acting on[br]this elevator is downwards 0:03:07.290,0:03:10.080 and yet the elevator is moving up. 0:03:10.080,0:03:11.880 Why is that? (chuckles) 0:03:11.880,0:03:15.090 Well, remember, force does not dictate 0:03:15.090,0:03:17.070 the direction of motion. 0:03:17.070,0:03:20.940 Force tells you the direction[br]of acceleration, okay? 0:03:20.940,0:03:22.020 The elevator could be moving, 0:03:22.020,0:03:24.240 objects can be moving[br]whatever direction it wants. 0:03:24.240,0:03:25.770 When you put a force on it, it tells you 0:03:25.770,0:03:27.210 what direction it should accelerate. 0:03:27.210,0:03:28.170 So that's the key thing. 0:03:28.170,0:03:31.320 So, there is no problem that[br]the force is acting downwards, 0:03:31.320,0:03:32.910 but the elevator is moving upwards. 0:03:32.910,0:03:34.530 Secondly, what does it mean 0:03:34.530,0:03:36.210 that the acceleration is downwards? 0:03:36.210,0:03:38.010 See, if the net force is downwards, 0:03:38.010,0:03:39.060 the acceleration has to be downward. 0:03:39.060,0:03:41.130 But what does it mean[br]the elevator is moving up 0:03:41.130,0:03:42.750 and the acceleration is downwards? 0:03:42.750,0:03:46.560 Ooh, this means since the velocity 0:03:46.560,0:03:48.720 and the acceleration is[br]in the opposite direction, 0:03:48.720,0:03:52.740 this means the elevator is slowing down. 0:03:52.740,0:03:54.090 That's what it means for velocity 0:03:54.090,0:03:55.560 and acceleration to be in[br]the opposite direction. 0:03:55.560,0:03:56.460 If they're in the same direction, 0:03:56.460,0:03:57.780 it means they're speeding up. 0:03:57.780,0:04:00.240 So, this means our elevator is going up, 0:04:00.240,0:04:03.150 but it is slowing down, which[br]probably means that, you know, 0:04:03.150,0:04:04.860 it's probably about to stop. 0:04:04.860,0:04:06.990 Maybe this person has probably reached 0:04:06.990,0:04:08.670 his destination or something. 0:04:08.670,0:04:10.560 All right, onto the next problem. 0:04:10.560,0:04:15.120 This time we have a sledge at[br]rest whose is 70 kilograms. 0:04:15.120,0:04:16.620 Our goal is to push it 0:04:16.620,0:04:18.810 and accelerate to six meters per second 0:04:18.810,0:04:20.430 in about two seconds, let's say, 0:04:20.430,0:04:22.110 so that, you know, it[br]can nicely slide down 0:04:22.110,0:04:23.760 and we can enjoy the ride. 0:04:23.760,0:04:26.010 Now, there is going to[br]be some frictional force. 0:04:26.010,0:04:28.140 Even though we're on ice and everything, 0:04:28.140,0:04:29.370 there'll be some frictional force. 0:04:29.370,0:04:30.203 Let's say the friction 0:04:30.203,0:04:32.853 that this ledge will experience[br]is about 200 newtons. 0:04:33.690,0:04:36.840 The question now is what is[br]the force with which we have 0:04:36.840,0:04:39.990 to push on it so as to[br]achieve all of this? 0:04:39.990,0:04:42.060 So how do we figure this out? 0:04:42.060,0:04:43.980 Well, again, the first thing[br]that comes to my mind is 0:04:43.980,0:04:47.010 that look, we're dealing with[br]forces and we have motion. 0:04:47.010,0:04:50.490 What connects forces and[br]motion? Newton's second law. 0:04:50.490,0:04:52.320 So, the first thing I'll[br]do is I'm gonna draw 0:04:52.320,0:04:53.310 a free-body diagram. 0:04:53.310,0:04:56.430 Again, I encourage you[br]to pause the video now 0:04:56.430,0:04:57.600 or anytime later on. 0:04:57.600,0:04:58.710 Whenever you feel more comfortable, 0:04:58.710,0:05:01.050 pause the video and see if[br]you can complete it yourself. 0:05:01.050,0:05:03.120 Okay, so anyways, let's first try 0:05:03.120,0:05:04.230 to draw a free-body diagram. 0:05:04.230,0:05:05.063 How do we do that? 0:05:05.063,0:05:06.780 Well, again, we'll take[br]the object of our interest. 0:05:06.780,0:05:09.510 In this case, the object of[br]our interest is this ledge 0:05:09.510,0:05:12.930 whose mass is 70 kilograms[br]and just make it a square 0:05:12.930,0:05:14.370 and then draw all the forces acting on it. 0:05:14.370,0:05:15.450 What are the forces acting on it? 0:05:15.450,0:05:18.000 I know there's frictional[br]force acting backwards 0:05:18.000,0:05:21.660 of 200 newtons, but then I[br]also have the applied force 0:05:21.660,0:05:23.580 by this person, which I,[br]we need to figure out. 0:05:23.580,0:05:24.810 This is what we need to calculate. 0:05:24.810,0:05:27.780 That is the applied force.[br]What are other forces? 0:05:27.780,0:05:30.600 Well, I know that there's[br]also gravity acting on it 0:05:30.600,0:05:33.150 and then there's a normal[br]force acting on it upwards. 0:05:33.150,0:05:35.220 But we know that these forces are balanced 0:05:35.220,0:05:37.590 and so they're not going to be useful. 0:05:37.590,0:05:41.190 They're not going to affect[br]our situation over here. 0:05:41.190,0:05:42.840 So, I'm just gonna draw them over here. 0:05:42.840,0:05:44.954 They're there, of course, but[br]they're completely balanced. 0:05:44.954,0:05:46.740 They're in the verticals,[br]they're not gonna affect it, 0:05:46.740,0:05:48.150 so we'll not draw it. 0:05:48.150,0:05:50.160 Okay, now that I have[br]my free-body diagram, 0:05:50.160,0:05:52.470 let's go ahead and write[br]down on Newton second law. 0:05:52.470,0:05:57.470 It says acceleration should[br]always equal the net force, 0:05:57.930,0:06:00.420 which let me draw using pink now. 0:06:00.420,0:06:04.920 Net force divided by the mass. 0:06:04.920,0:06:06.510 Divided by the mass. 0:06:06.510,0:06:09.870 Okay, so what do we do next? 0:06:09.870,0:06:12.630 I need to find this applied force. 0:06:12.630,0:06:16.620 So this means if I can[br]calculate the net force, 0:06:16.620,0:06:19.650 then I can figure out what[br]the applied force is, right? 0:06:19.650,0:06:21.150 So, from Newton's second law, 0:06:21.150,0:06:22.770 I just need to figure out[br]what the net force is. 0:06:22.770,0:06:25.470 For that, I ask myself, do I know m? 0:06:25.470,0:06:27.960 I do. I know that m is 70 kilograms. 0:06:27.960,0:06:29.940 Do I know the acceleration? 0:06:29.940,0:06:31.140 Hmm, it's not given directly, 0:06:31.140,0:06:34.740 but wait a second, I know[br]the initial velocity, 0:06:34.740,0:06:36.183 I know the final velocity and I know 0:06:36.183,0:06:38.730 that the change in velocity[br]should happen in two seconds. 0:06:38.730,0:06:39.943 Whoo-hoo! 0:06:39.943,0:06:43.860 That means I can calculate the[br]acceleration from this data. 0:06:43.860,0:06:46.140 I can plug in and from[br]that I can figure out 0:06:46.140,0:06:48.630 what the total force is going to be, 0:06:48.630,0:06:50.070 the net force is going to be. 0:06:50.070,0:06:52.590 And from that we can figure out 0:06:52.590,0:06:54.330 what the applied force should be. 0:06:54.330,0:06:56.280 Okay, so if you haven't done this before, 0:06:56.280,0:06:57.690 why don't you now pause the video 0:06:57.690,0:06:59.430 and see if you can put it all together 0:06:59.430,0:07:01.560 and solve the problem? 0:07:01.560,0:07:03.180 Okay, let's do this. 0:07:03.180,0:07:05.130 So, let me first calculate[br]the acceleration. 0:07:05.130,0:07:06.240 So our acceleration is going 0:07:06.240,0:07:07.620 to be, well how do we figure this out? 0:07:07.620,0:07:11.670 This is the final velocity[br]minus the initial velocity 0:07:11.670,0:07:13.950 divided by the time taken. 0:07:13.950,0:07:15.300 So, that's going to be, in our case, 0:07:15.300,0:07:17.500 the final velocity is[br]six meters per second 0:07:19.260,0:07:21.810 to the right minus... 0:07:21.810,0:07:23.040 What's the initial velocity? 0:07:23.040,0:07:25.650 Well, it's zero, it's at rest. 0:07:25.650,0:07:27.690 So there is no initial velocity divided 0:07:27.690,0:07:30.360 by time is two, two seconds. 0:07:30.360,0:07:31.590 That gives us what? 0:07:31.590,0:07:36.590 That gives us six by two is[br]three meters per second squared 0:07:37.560,0:07:39.870 to the right. 0:07:39.870,0:07:42.390 So I know my acceleration has to be 0:07:42.390,0:07:44.610 to the right, which is[br]good news. (chuckles) 0:07:44.610,0:07:45.660 It has to be to the right. 0:07:45.660,0:07:46.920 We want this ledge to move to the right. 0:07:46.920,0:07:47.753 So, that makes sense. 0:07:47.753,0:07:49.440 So, we are on the right track over here. 0:07:49.440,0:07:50.730 Okay, now, I can plug in 0:07:50.730,0:07:52.560 and figure out what the[br]net force is going to be. 0:07:52.560,0:07:56.100 So, if I just simplify that,[br]so net force is going to be, 0:07:56.100,0:07:58.770 if I rearrange this equation[br]multiply by m on both sides. 0:07:58.770,0:08:02.223 So I get net force to be[br]mass times the acceleration. 0:08:03.240,0:08:06.060 And so now I can plug in[br]for mass and acceleration. 0:08:06.060,0:08:09.150 What do I get? Well I get 70 kilograms. 0:08:09.150,0:08:10.530 That's the mass, 0:08:10.530,0:08:14.160 times the acceleration is three[br]meters per second squared, 0:08:14.160,0:08:15.620 70 times three, seven times these 21. 0:08:15.620,0:08:18.090 So, this is 210. 0:08:18.090,0:08:21.910 So, I get that my net force is 210 newtons 0:08:23.606,0:08:25.230 to the right of this, 0:08:25.230,0:08:27.210 this acceleration was to the right. 0:08:27.210,0:08:30.660 So, this will also be to the right. 0:08:30.660,0:08:34.740 So, now that I've found my[br]net force, so my net force, 0:08:34.740,0:08:37.860 the total force will be to the right 0:08:37.860,0:08:40.020 and that is 210 newtons. 0:08:40.020,0:08:44.070 From that, can I calculate[br]the applied force? Yes. 0:08:44.070,0:08:45.030 So now, first of all, 0:08:45.030,0:08:47.550 I know my applied force should be bigger. 0:08:47.550,0:08:48.660 It has to be bigger 0:08:48.660,0:08:51.510 because my total force[br]should be towards the right, 0:08:51.510,0:08:54.030 which means if I subtract[br]the two from this, 0:08:54.030,0:08:57.030 if I subtract this number,[br]I should get this number. 0:08:57.030,0:08:58.530 That's the net force, all right? 0:08:58.530,0:09:00.390 So now, now that I know all the directions 0:09:00.390,0:09:02.070 and everything, I can[br]just subtract the numbers. 0:09:02.070,0:09:04.530 So I can now say, "Hey, my net force 0:09:04.530,0:09:08.640 that is 210 newtons should[br]equal this bigger number, 0:09:08.640,0:09:13.443 the bigger force minus 200 newtons. 0:09:14.610,0:09:17.850 Now, to get applied force,[br]I just add 200 on both sides 0:09:17.850,0:09:20.283 so that I can get rid of this. 0:09:22.050,0:09:27.050 And look, the applied[br]force becomes 210 plus 200. 0:09:27.150,0:09:31.170 That is 410 newtons. 0:09:31.170,0:09:32.880 And I already know it's to the right, 0:09:32.880,0:09:34.440 so I know it's direction. 0:09:34.440,0:09:37.110 So if I were to write down its direction, 0:09:37.110,0:09:39.115 it's going to be, oops. (chuckles) 0:09:39.115,0:09:39.990 Okay. Okay. 0:09:39.990,0:09:42.990 I mean, okay, not the most[br]organized board over here, 0:09:42.990,0:09:45.420 but let me just write it down[br]a little bit more neatly. 0:09:45.420,0:09:49.410 So 410 newtons to the right. 0:09:49.410,0:09:51.390 That's how much force we need to apply 0:09:51.390,0:09:53.013 for all of this to happen.