WEBVTT 00:00:03.850 --> 00:00:09.040 This is a bungee jumper at the bottom of his trajectory. This is a pack of dogs pulling 00:00:09.040 --> 00:00:14.730 a sled. And this is a golf ball about to be struck. All of these scenarios can be represented 00:00:14.730 --> 00:00:20.740 by free body diagrams. Physical problems -- for example, calculating the force on the bungee 00:00:20.740 --> 00:00:25.490 jumper by the bungee cord -- are much easier to solve once you've drawn a complete and 00:00:25.490 --> 00:00:28.430 correct free body diagram. 00:00:28.430 --> 00:00:31.820 This video is part of the Representations video series. 00:00:31.820 --> 00:00:37.899 Information can be represented in words, through mathematical symbols, graphically, or in 3-D 00:00:37.899 --> 00:00:41.699 models. Representations are used to develop a deeper and more flexible understanding of 00:00:41.699 --> 00:00:44.760 objects, systems, and processes. 00:00:44.760 --> 00:00:50.089 Hello. My name is John Belcher. I am a professor in the physics department at MIT, and today 00:00:50.089 --> 00:00:56.420 I'll be talking with you about free body diagrams. Physics uses many different representations 00:00:56.420 --> 00:01:02.649 to aid with problem solving. Free body diagrams allow us to represent the forces on an object, 00:01:02.649 --> 00:01:07.820 thus enhancing our understanding of situations and helping us to solve problems. Studies 00:01:07.820 --> 00:01:12.340 have shown that students who understand and use free body diagrams tend to score better 00:01:12.340 --> 00:01:17.549 on homework, quizzes, and exams. Such representations can be powerful tools for solving problems, 00:01:17.549 --> 00:01:20.158 and remain useful even for physics experts. 00:01:20.158 --> 00:01:25.420 Our objectives are to improve your skill with free body diagrams and to show some of the 00:01:25.420 --> 00:01:29.939 connections between them and the physical situations they represent. I hope you find 00:01:29.939 --> 00:01:30.039 it useful. 00:01:30.039 --> 00:01:30.979 We're going to assume that you have drawn a few free body diagrams in the past, so this 00:01:30.979 --> 00:01:31.859 video will start with only a short refresher of how to draw them before getting into some 00:01:31.859 --> 00:01:36.109 more difficult and detailed problems. Here are some guidelines to remember when drawing 00:01:36.109 --> 00:01:41.520 your free-body diagram. Rather than trying to sketch an object in detail, we're always 00:01:41.520 --> 00:01:47.189 going to draw it as a single point. We focus on a single moment in time. Our diagram will 00:01:47.189 --> 00:01:53.320 only include forces, and not any other vectors or any other quantities. The arrows we draw 00:01:53.320 --> 00:01:58.320 for the forces will be longer for stronger forces, and we'll always draw them as coming 00:01:58.320 --> 00:02:04.530 from the object. Finally, we'll want to draw only forces with a substantial impact on the 00:02:04.530 --> 00:02:07.319 object's behavior, and leave out any that are negligible. 00:02:07.319 --> 00:02:07.509 The forces we'll consider today are primarily those we see in the world around us: gravity, 00:02:07.509 --> 00:02:07.670 the normal force, tension, hands pushing or pulling, friction, and so forth. We won't 00:02:07.670 --> 00:02:07.850 be talking about things like the magnetic force, buoyancy, and so forth, but when you 00:02:07.850 --> 00:02:08.030 encounter those in your courses, they can be treated in exactly the same manner as the 00:02:08.030 --> 00:02:08.080 forces you'll see today. 00:02:08.080 --> 00:02:08.288 To keep the length of this video down, we've had to leave some things out. The first is 00:02:08.288 --> 00:02:08.449 anything to do with circular motion, including torque or centripetal force. Dealing with 00:02:08.449 --> 00:02:08.619 torque requires a more complex approach that you'll learn later on in your course. The 00:02:08.619 --> 00:02:08.818 second is a complete lesson on how to deal with angles in forces and free body diagrams. 00:02:08.818 --> 00:02:09.020 That is something that you will need to practice on your own in order to really understand 00:02:09.020 --> 00:02:09.038 well. 00:02:09.038 --> 00:02:13.160 Let's do a quick refresher on how to draw free-body diagrams. We'll walk through them 00:02:13.160 --> 00:02:18.500 one step at a time. If you have some paper available you should draw the diagrams yourself 00:02:18.500 --> 00:02:20.940 as we go through the steps. 00:02:20.940 --> 00:02:27.110 This is very basic example: a falling block. If we ignore air resistance, this is an object 00:02:27.110 --> 00:02:32.350 with just one force applied: the force of gravity. We're going to... 00:02:32.350 --> 00:02:35.000 draw the object as a point, 00:02:35.000 --> 00:02:37.829 draw the force of gravity as an arrow, 00:02:37.829 --> 00:02:41.490 and label our force. We're done. 00:02:41.490 --> 00:02:46.750 Let's build up to a more complex example. Here's the block on a table, stationary. 00:02:46.750 --> 00:02:49.590 We need to draw the object as a point, 00:02:49.590 --> 00:02:52.960 and draw the force of gravity pulling down on it. 00:02:52.960 --> 00:02:58.620 Our block is stationary, which means that it is not accelerating. No acceleration means 00:02:58.620 --> 00:03:03.220 a total force of zero, so we must have at least one more force in place to cancel out 00:03:03.220 --> 00:03:08.910 the force of gravity. In this case, that cancellation is provided by the normal force from the table. 00:03:08.910 --> 00:03:09.900 Let's draw in the normal force. 00:03:09.900 --> 00:03:12.750 If we wanted to have a hand pushing the object... 00:03:12.750 --> 00:03:17.870 ...we can adjust our existing diagram to include that. All we need to do is 00:03:17.870 --> 00:03:22.390 add an arrow to indicate the force provided by the hand. 00:03:22.390 --> 00:03:27.880 We can also tilt the table upwards and push the box up the slope. As you can see, this 00:03:27.880 --> 00:03:33.579 tilt changes the direction of our normal force, but not the force of gravity. 00:03:33.579 --> 00:03:38.430 We could also include friction from the surface if we wanted to be more realistic. Now we 00:03:38.430 --> 00:03:44.460 have a fairly complex diagram that visually represents many different forces on our object. 00:03:44.460 --> 00:03:49.070 Now we're going to show a couple of real-world examples, and show how we would diagram them. 00:03:49.070 --> 00:03:55.290 Here's a bungee jumper. This is a very dynamic situation. It's important for us to choose 00:03:55.290 --> 00:04:00.290 a particular time during the jump at which to draw our diagram, because the forces will 00:04:00.290 --> 00:04:05.530 be very different at different times. We can choose any time we like, but we do have to 00:04:05.530 --> 00:04:10.670 pick just one time. Let's say that we're interested in the time when the jumper is at the bottom 00:04:10.670 --> 00:04:12.350 of his trajectory. 00:04:12.350 --> 00:04:18.509 Again, we start with a dot. We don't draw a stick figure, just a single point. And we 00:04:18.509 --> 00:04:23.810 don't include the rope, even though it is important. We just draw the object in question 00:04:23.810 --> 00:04:26.160 -- the jumper. 00:04:26.160 --> 00:04:32.350 Gravity is clearly an important force, as is the tension from the bungee cord. To determine 00:04:32.350 --> 00:04:38.250 the strength of the tension, we must decide what the acceleration of the jumper is. Pause 00:04:38.250 --> 00:04:45.250 the video to consider this. 00:04:46.590 --> 00:04:51.780 At the bottom of the arc the jumper must be accelerating upwards, so as to bounce up. 00:04:51.780 --> 00:04:58.650 Therefore, we make sure to draw tension as being stronger than the force of gravity. 00:04:58.650 --> 00:05:02.240 Looking at the diagram at different points during the fall would give us different amounts 00:05:02.240 --> 00:05:08.620 of force. Even though we might like to represent that, it doesn't belong on our diagram. Free 00:05:08.620 --> 00:05:13.160 body diagrams are drawn at a single point in time. 00:05:13.160 --> 00:05:16.370 This example involves a dog sled. 00:05:16.370 --> 00:05:22.470 Let's draw a diagram of the sled as the dogs pull it across the snow at constant velocity. 00:05:22.470 --> 00:05:28.550 Here's the sled, "with gravity pulling down, and the normal force pushing upwards. 00:05:28.550 --> 00:05:33.200 Here is the force from the dogs, pulling the cart forward. 00:05:33.200 --> 00:05:37.770 The sled is moving at constant velocity; therefore the sled has no acceleration. 00:05:37.770 --> 00:05:44.560 Therefore, the total force on the sled must be zero. Right now our forces are unbalanced, 00:05:44.560 --> 00:05:49.060 so there must be another force we haven't drawn yet in order to balance out the pull. 00:05:49.060 --> 00:05:53.960 That's the force of friction between the sled and the snow. 00:05:53.960 --> 00:05:57.380 Once we draw that in, we're done. 00:05:57.380 --> 00:06:01.990 Since we know that the sled is moving at constant velocity, the sum of our forces should be 00:06:01.990 --> 00:06:05.470 zero. 00:06:05.470 --> 00:06:10.900 Here's another example: a golf swing. Let's say that we want to draw a free body diagram 00:06:10.900 --> 00:06:15.490 of the ball just after it loses contact with the ground. 00:06:15.490 --> 00:06:19.889 You can see that the photo is not at a great angle for us to see what's going on, so let's 00:06:19.889 --> 00:06:22.400 draw a sketch to help us picture it. 00:06:22.400 --> 00:06:26.260 We'll start the diagram with a point representing the ball... 00:06:26.260 --> 00:06:29.840 ...and drawing the force of gravity. 00:06:29.840 --> 00:06:35.240 The contact force between the ball and the club will be perpendicular to the club, so 00:06:35.240 --> 00:06:41.470 we need to be careful to make sure our angles match. We also need to draw a fairly long 00:06:41.470 --> 00:06:46.050 arrow to represent a strong force, because the hit from the club is lifting the ball 00:06:46.050 --> 00:06:52.840 off the ground. We need to make sure that the vertical part of the club's force is stronger 00:06:52.840 --> 00:06:55.970 than the force of gravity. 00:06:55.970 --> 00:07:00.260 Since the ball is no longer in contact with the ground, there will be no normal force 00:07:00.260 --> 00:07:04.510 from the grass. We're all done. 00:07:04.510 --> 00:07:08.500 Now we're going to look at some typical mistakes that people make when drawing free-body diagrams. 00:07:08.500 --> 00:07:13.590 This is to help you catch errors in your own work, as well as to assist others during group 00:07:13.590 --> 00:07:19.210 work. Many errors come from breaking the guidelines we set forth earlier, so watch for places 00:07:19.210 --> 00:07:22.860 where those are broken as we go through this sequence. 00:07:22.860 --> 00:07:27.270 The diagrams we'll show here each have issues with them. To remind you of this, we'll put 00:07:27.270 --> 00:07:32.180 a red exclamation point in the bottom right corner of the screen. 00:07:32.180 --> 00:07:36.800 If you're watching this on your own, pause the video when a new example appears, to try 00:07:36.800 --> 00:07:38.540 to find out what's wrong. 00:07:38.540 --> 00:07:44.330 When we correct the diagram, we'll change the exclamation point to a green check-mark. 00:07:44.330 --> 00:07:49.669 Here's a diagram with a problem. In this situation we're trying to show the forces on the ball 00:07:49.669 --> 00:07:54.960 after it is thrown. Try to spot the error. 00:07:54.960 --> 00:08:00.380 The diagram shows gravity pulling down, and air resistance at work, but a 'throwing force' 00:08:00.380 --> 00:08:03.070 is also included. 00:08:03.070 --> 00:08:07.830 Because the diagram is intended to be drawn after the ball leaves the pitcher's hand, 00:08:07.830 --> 00:08:12.949 that force has already done its job. There's no need to include it here. Newton's First 00:08:12.949 --> 00:08:17.800 Law tells us that the ball will keep moving; it doesn't need an extra force pushing it 00:08:17.800 --> 00:08:20.120 along all the time. 00:08:20.120 --> 00:08:23.270 Now the diagram is correct. 00:08:23.270 --> 00:08:28.320 Here's our example of a block on a tilted table from before. We've drawn in a coordinate 00:08:28.320 --> 00:08:34.828 system to show the x and y directions. We can see that there are several forces at work: 00:08:34.828 --> 00:08:40.729 the pushing hand, the normal force, friction, and gravity. 00:08:40.729 --> 00:08:47.180 However, there seem to be three gravitational forces at work: one pulling straight down, 00:08:47.180 --> 00:08:53.240 one pulling against the normal force, and one pulling down the slope. It seems as if 00:08:53.240 --> 00:08:58.980 the gravitational force has been decomposed into x and y components, and then also left 00:08:58.980 --> 00:09:05.149 on the diagram. Once a force has been decomposed, the original should be removed. 00:09:05.149 --> 00:09:07.999 That's better. 00:09:07.999 --> 00:09:13.790 Here's a diagram of a car driving on the highway. Can you tell what's wrong here? 00:09:13.790 --> 00:09:20.319 We have gravity, friction, and a force moving the car forward, but this arrows seems to 00:09:20.319 --> 00:09:27.279 represent a velocity. It might be useful information, but it's not something that gets included 00:09:27.279 --> 00:09:33.600 on a free body diagram. Free body diagrams only include forces. 00:09:33.600 --> 00:09:34.879 Let's remove it. 00:09:34.879 --> 00:09:40.510 That's better. But we're not done yet. According to the diagram, this car is accelerating downward 00:09:40.510 --> 00:09:46.180 -- it's falling through the road." "We need a force to balance out gravity. The car is 00:09:46.180 --> 00:09:51.089 in contact with the road, so there must be a normal force. 00:09:51.089 --> 00:09:54.399 There we go. Much better. 00:09:54.399 --> 00:09:57.550 Here's our final bad example. 00:09:57.550 --> 00:10:03.360 It looks like whoever drew this was trying to list every force they could think of. Earth's 00:10:03.360 --> 00:10:08.160 gravity is something we almost always include, and one can understand including air resistance 00:10:08.160 --> 00:10:14.550 for a parachute, but this diagram also has gravity from the moon, gravity from the sun, 00:10:14.550 --> 00:10:21.550 a buoyant force, force from the wind, aerodynamic lift, and whatever this F-Z is! We're practically 00:10:21.949 --> 00:10:28.720 out of space. One key to drawing a free body diagram is narrowing down your forces to just 00:10:28.720 --> 00:10:35.720 those that apply to the problem at hand. Are all these forces present? Probably, yes. Are 00:10:36.639 --> 00:10:39.679 all of them important in your current situation? 00:10:39.679 --> 00:10:41.939 Probably not. 00:10:41.939 --> 00:10:47.059 Simplification is an important part of physics. The more complex we make things, the harder 00:10:47.059 --> 00:10:52.379 our problems will be to solve. If our problem tells us to keep air resistance, we'll use 00:10:52.379 --> 00:10:55.329 that, and ignore other forces. 00:10:55.329 --> 00:10:59.709 Now we're going to look into what our diagrams tell us about a physical setup. This will 00:10:59.709 --> 00:11:04.470 help us refine our understanding of these diagrams. After all, if a free body diagram 00:11:04.470 --> 00:11:09.490 is really a representation of what's going on, it should have a strong connection to 00:11:09.490 --> 00:11:11.550 a physical situation. 00:11:11.550 --> 00:11:16.689 Here's a car on the highway. This animation will help us understand the changes in our 00:11:16.689 --> 00:11:18.100 diagram. 00:11:18.100 --> 00:11:23.759 We can tell that this car is not accelerating. The forces in our y direction balance, and 00:11:23.759 --> 00:11:26.809 the forces in our x direction balance. 00:11:26.809 --> 00:11:33.369 That means that if we remove or change any of these forces, the car should accelerate. 00:11:33.369 --> 00:11:38.240 For instance, if we reduce the force of friction, the car will speed up. 00:11:38.240 --> 00:11:43.220 We could also speed up the car by applying more force in the forward direction. 00:11:43.220 --> 00:11:47.079 Removing the force that's pushing the car forward results in the opposite effect. 00:11:47.079 --> 00:11:49.889 The car will eventually slow to a halt. 00:11:49.889 --> 00:11:54.230 Finally, without the normal force, there's nothing to stop gravity from accelerating 00:11:54.230 --> 00:11:56.119 the car downward. 00:11:56.119 --> 00:12:00.600 You can see how any change in the physical forces applied can be represented on the free 00:12:00.600 --> 00:12:02.639 body diagram. 00:12:02.639 --> 00:12:07.550 As useful as they are, there are some situations in which a free body diagram is not the right 00:12:07.550 --> 00:12:10.029 tool for the job. 00:12:10.029 --> 00:12:14.160 Some situations are so simple that they may not warrant a diagram. There's no harm in 00:12:14.160 --> 00:12:18.300 drawing it, especially when you're starting out, but as you become more skilled you may 00:12:18.300 --> 00:12:21.209 be able to do without it. 00:12:21.209 --> 00:12:26.949 Some situations are better solved with a different approach entirely. This exercise, for example, 00:12:26.949 --> 00:12:32.350 calls for the use of a different principle: conservation of energy. A free body diagram 00:12:32.350 --> 00:12:35.670 is not likely to shed much light on the problem. 00:12:35.670 --> 00:12:42.429 This problem involves rotation and torque. Free body diagrams work best with linear motion. 00:12:42.429 --> 00:12:46.410 Even though force is involved, a free body diagram may not help. 00:12:46.410 --> 00:12:50.939 However, a more sophisticated diagram may be of assistance. This one shows where the 00:12:50.939 --> 00:12:56.499 forces are applied to the bar, and can be used in the calculation of torques. You can 00:12:56.499 --> 00:13:02.100 see that it is very different from a free body diagram. Free body diagrams are only 00:13:02.100 --> 00:13:07.149 one type of representation, and it is important to choose the right representation for your 00:13:07.149 --> 00:13:08.699 purpose. 00:13:08.699 --> 00:13:12.939 Now you've seen how to represent physical situations with free body diagrams, and gained 00:13:12.939 --> 00:13:18.509 some greater insight into their use. The ability to use and analyze free body diagrams is a 00:13:18.509 --> 00:13:24.239 skill that remains useful to physicists and engineers at all levels of experience. Your 00:13:24.239 --> 00:13:29.420 expertise with them will improve with practice. I hope this video has helped to improve your 00:13:29.420 --> 00:13:36.420 understanding of free body diagrams and their uses.