1 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 2 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 3 00:00:14,730 --> 00:00:20,740 by free body diagrams. Physical problems -- for example, calculating the force on the bungee 4 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 5 00:00:25,490 --> 00:00:28,430 correct free body diagram. 6 00:00:28,430 --> 00:00:31,820 This video is part of the Representations video series. 7 00:00:31,820 --> 00:00:37,899 Information can be represented in words, through mathematical symbols, graphically, or in 3-D 8 00:00:37,899 --> 00:00:41,699 models. Representations are used to develop a deeper and more flexible understanding of 9 00:00:41,699 --> 00:00:44,760 objects, systems, and processes. 10 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 11 00:00:50,089 --> 00:00:56,420 I'll be talking with you about free body diagrams. Physics uses many different representations 12 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, 13 00:01:02,649 --> 00:01:07,820 thus enhancing our understanding of situations and helping us to solve problems. Studies 14 00:01:07,820 --> 00:01:12,340 have shown that students who understand and use free body diagrams tend to score better 15 00:01:12,340 --> 00:01:17,549 on homework, quizzes, and exams. Such representations can be powerful tools for solving problems, 16 00:01:17,549 --> 00:01:20,158 and remain useful even for physics experts. 17 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 18 00:01:25,420 --> 00:01:29,939 connections between them and the physical situations they represent. I hope you find 19 00:01:29,939 --> 00:01:30,039 it useful. 20 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 21 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 22 00:01:31,859 --> 00:01:36,109 more difficult and detailed problems. Here are some guidelines to remember when drawing 23 00:01:36,109 --> 00:01:41,520 your free-body diagram. Rather than trying to sketch an object in detail, we're always 24 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 25 00:01:47,189 --> 00:01:53,320 only include forces, and not any other vectors or any other quantities. The arrows we draw 26 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 27 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 28 00:02:04,530 --> 00:02:07,319 object's behavior, and leave out any that are negligible. 29 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, 30 00:02:07,509 --> 00:02:07,670 the normal force, tension, hands pushing or pulling, friction, and so forth. We won't 31 00:02:07,670 --> 00:02:07,850 be talking about things like the magnetic force, buoyancy, and so forth, but when you 32 00:02:07,850 --> 00:02:08,030 encounter those in your courses, they can be treated in exactly the same manner as the 33 00:02:08,030 --> 00:02:08,080 forces you'll see today. 34 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 35 00:02:08,288 --> 00:02:08,449 anything to do with circular motion, including torque or centripetal force. Dealing with 36 00:02:08,449 --> 00:02:08,619 torque requires a more complex approach that you'll learn later on in your course. The 37 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. 38 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 39 00:02:09,020 --> 00:02:09,038 well. 40 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 41 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 42 00:02:18,500 --> 00:02:20,940 as we go through the steps. 43 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 44 00:02:27,110 --> 00:02:32,350 with just one force applied: the force of gravity. We're going to... 45 00:02:32,350 --> 00:02:35,000 draw the object as a point, 46 00:02:35,000 --> 00:02:37,829 draw the force of gravity as an arrow, 47 00:02:37,829 --> 00:02:41,490 and label our force. We're done. 48 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. 49 00:02:46,750 --> 00:02:49,590 We need to draw the object as a point, 50 00:02:49,590 --> 00:02:52,960 and draw the force of gravity pulling down on it. 51 00:02:52,960 --> 00:02:58,620 Our block is stationary, which means that it is not accelerating. No acceleration means 52 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 53 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. 54 00:03:08,910 --> 00:03:09,900 Let's draw in the normal force. 55 00:03:09,900 --> 00:03:12,750 If we wanted to have a hand pushing the object... 56 00:03:12,750 --> 00:03:17,870 ...we can adjust our existing diagram to include that. All we need to do is 57 00:03:17,870 --> 00:03:22,390 add an arrow to indicate the force provided by the hand. 58 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 59 00:03:27,880 --> 00:03:33,579 tilt changes the direction of our normal force, but not the force of gravity. 60 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 61 00:03:38,430 --> 00:03:44,460 have a fairly complex diagram that visually represents many different forces on our object. 62 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. 63 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 64 00:03:55,290 --> 00:04:00,290 a particular time during the jump at which to draw our diagram, because the forces will 65 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 66 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 67 00:04:10,670 --> 00:04:12,350 of his trajectory. 68 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 69 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 70 00:04:23,810 --> 00:04:26,160 -- the jumper. 71 00:04:26,160 --> 00:04:32,350 Gravity is clearly an important force, as is the tension from the bungee cord. To determine 72 00:04:32,350 --> 00:04:38,250 the strength of the tension, we must decide what the acceleration of the jumper is. Pause 73 00:04:38,250 --> 00:04:45,250 the video to consider this. 74 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. 75 00:04:51,780 --> 00:04:58,650 Therefore, we make sure to draw tension as being stronger than the force of gravity. 76 00:04:58,650 --> 00:05:02,240 Looking at the diagram at different points during the fall would give us different amounts 77 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 78 00:05:08,620 --> 00:05:13,160 body diagrams are drawn at a single point in time. 79 00:05:13,160 --> 00:05:16,370 This example involves a dog sled. 80 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. 81 00:05:22,470 --> 00:05:28,550 Here's the sled, "with gravity pulling down, and the normal force pushing upwards. 82 00:05:28,550 --> 00:05:33,200 Here is the force from the dogs, pulling the cart forward. 83 00:05:33,200 --> 00:05:37,770 The sled is moving at constant velocity; therefore the sled has no acceleration. 84 00:05:37,770 --> 00:05:44,560 Therefore, the total force on the sled must be zero. Right now our forces are unbalanced, 85 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. 86 00:05:49,060 --> 00:05:53,960 That's the force of friction between the sled and the snow. 87 00:05:53,960 --> 00:05:57,380 Once we draw that in, we're done. 88 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 89 00:06:01,990 --> 00:06:05,470 zero. 90 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 91 00:06:10,900 --> 00:06:15,490 of the ball just after it loses contact with the ground. 92 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 93 00:06:19,889 --> 00:06:22,400 draw a sketch to help us picture it. 94 00:06:22,400 --> 00:06:26,260 We'll start the diagram with a point representing the ball... 95 00:06:26,260 --> 00:06:29,840 ...and drawing the force of gravity. 96 00:06:29,840 --> 00:06:35,240 The contact force between the ball and the club will be perpendicular to the club, so 97 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 98 00:06:41,470 --> 00:06:46,050 arrow to represent a strong force, because the hit from the club is lifting the ball 99 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 100 00:06:52,840 --> 00:06:55,970 than the force of gravity. 101 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 102 00:07:00,260 --> 00:07:04,510 from the grass. We're all done. 103 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. 104 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 105 00:07:13,590 --> 00:07:19,210 work. Many errors come from breaking the guidelines we set forth earlier, so watch for places 106 00:07:19,210 --> 00:07:22,860 where those are broken as we go through this sequence. 107 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 108 00:07:27,270 --> 00:07:32,180 a red exclamation point in the bottom right corner of the screen. 109 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 110 00:07:36,800 --> 00:07:38,540 to find out what's wrong. 111 00:07:38,540 --> 00:07:44,330 When we correct the diagram, we'll change the exclamation point to a green check-mark. 112 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 113 00:07:49,669 --> 00:07:54,960 after it is thrown. Try to spot the error. 114 00:07:54,960 --> 00:08:00,380 The diagram shows gravity pulling down, and air resistance at work, but a 'throwing force' 115 00:08:00,380 --> 00:08:03,070 is also included. 116 00:08:03,070 --> 00:08:07,830 Because the diagram is intended to be drawn after the ball leaves the pitcher's hand, 117 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 118 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 119 00:08:17,800 --> 00:08:20,120 along all the time. 120 00:08:20,120 --> 00:08:23,270 Now the diagram is correct. 121 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 122 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: 123 00:08:34,828 --> 00:08:40,729 the pushing hand, the normal force, friction, and gravity. 124 00:08:40,729 --> 00:08:47,180 However, there seem to be three gravitational forces at work: one pulling straight down, 125 00:08:47,180 --> 00:08:53,240 one pulling against the normal force, and one pulling down the slope. It seems as if 126 00:08:53,240 --> 00:08:58,980 the gravitational force has been decomposed into x and y components, and then also left 127 00:08:58,980 --> 00:09:05,149 on the diagram. Once a force has been decomposed, the original should be removed. 128 00:09:05,149 --> 00:09:07,999 That's better. 129 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? 130 00:09:13,790 --> 00:09:20,319 We have gravity, friction, and a force moving the car forward, but this arrows seems to 131 00:09:20,319 --> 00:09:27,279 represent a velocity. It might be useful information, but it's not something that gets included 132 00:09:27,279 --> 00:09:33,600 on a free body diagram. Free body diagrams only include forces. 133 00:09:33,600 --> 00:09:34,879 Let's remove it. 134 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 135 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 136 00:09:46,180 --> 00:09:51,089 in contact with the road, so there must be a normal force. 137 00:09:51,089 --> 00:09:54,399 There we go. Much better. 138 00:09:54,399 --> 00:09:57,550 Here's our final bad example. 139 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 140 00:10:03,360 --> 00:10:08,160 gravity is something we almost always include, and one can understand including air resistance 141 00:10:08,160 --> 00:10:14,550 for a parachute, but this diagram also has gravity from the moon, gravity from the sun, 142 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 143 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 144 00:10:28,720 --> 00:10:35,720 those that apply to the problem at hand. Are all these forces present? Probably, yes. Are 145 00:10:36,639 --> 00:10:39,679 all of them important in your current situation? 146 00:10:39,679 --> 00:10:41,939 Probably not. 147 00:10:41,939 --> 00:10:47,059 Simplification is an important part of physics. The more complex we make things, the harder 148 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 149 00:10:52,379 --> 00:10:55,329 that, and ignore other forces. 150 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 151 00:10:59,709 --> 00:11:04,470 help us refine our understanding of these diagrams. After all, if a free body diagram 152 00:11:04,470 --> 00:11:09,490 is really a representation of what's going on, it should have a strong connection to 153 00:11:09,490 --> 00:11:11,550 a physical situation. 154 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 155 00:11:16,689 --> 00:11:18,100 diagram. 156 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 157 00:11:23,759 --> 00:11:26,809 the forces in our x direction balance. 158 00:11:26,809 --> 00:11:33,369 That means that if we remove or change any of these forces, the car should accelerate. 159 00:11:33,369 --> 00:11:38,240 For instance, if we reduce the force of friction, the car will speed up. 160 00:11:38,240 --> 00:11:43,220 We could also speed up the car by applying more force in the forward direction. 161 00:11:43,220 --> 00:11:47,079 Removing the force that's pushing the car forward results in the opposite effect. 162 00:11:47,079 --> 00:11:49,889 The car will eventually slow to a halt. 163 00:11:49,889 --> 00:11:54,230 Finally, without the normal force, there's nothing to stop gravity from accelerating 164 00:11:54,230 --> 00:11:56,119 the car downward. 165 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 166 00:12:00,600 --> 00:12:02,639 body diagram. 167 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 168 00:12:07,550 --> 00:12:10,029 tool for the job. 169 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 170 00:12:14,160 --> 00:12:18,300 drawing it, especially when you're starting out, but as you become more skilled you may 171 00:12:18,300 --> 00:12:21,209 be able to do without it. 172 00:12:21,209 --> 00:12:26,949 Some situations are better solved with a different approach entirely. This exercise, for example, 173 00:12:26,949 --> 00:12:32,350 calls for the use of a different principle: conservation of energy. A free body diagram 174 00:12:32,350 --> 00:12:35,670 is not likely to shed much light on the problem. 175 00:12:35,670 --> 00:12:42,429 This problem involves rotation and torque. Free body diagrams work best with linear motion. 176 00:12:42,429 --> 00:12:46,410 Even though force is involved, a free body diagram may not help. 177 00:12:46,410 --> 00:12:50,939 However, a more sophisticated diagram may be of assistance. This one shows where the 178 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 179 00:12:56,499 --> 00:13:02,100 see that it is very different from a free body diagram. Free body diagrams are only 180 00:13:02,100 --> 00:13:07,149 one type of representation, and it is important to choose the right representation for your 181 00:13:07,149 --> 00:13:08,699 purpose. 182 00:13:08,699 --> 00:13:12,939 Now you've seen how to represent physical situations with free body diagrams, and gained 183 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 184 00:13:18,509 --> 00:13:24,239 skill that remains useful to physicists and engineers at all levels of experience. Your 185 00:13:24,239 --> 00:13:29,420 expertise with them will improve with practice. I hope this video has helped to improve your 186 00:13:29,420 --> 00:13:36,420 understanding of free body diagrams and their uses.