1 00:00:01,000 --> 00:00:02,157 - [Instructor] This person right here 2 00:00:02,157 --> 00:00:03,460 is about to play dodgeball. 3 00:00:03,460 --> 00:00:07,003 They're just unfortunately not gonna dodge the ball. 4 00:00:07,003 --> 00:00:09,715 It's gonna fly in, it's gonna bounce off their head. 5 00:00:09,715 --> 00:00:11,665 This may or may not have happened to you. 6 00:00:11,665 --> 00:00:13,046 I think this probably happened to me. 7 00:00:13,046 --> 00:00:14,976 It's been a long time since I played dodgeball. 8 00:00:14,976 --> 00:00:17,018 And although, unfortunate for this person, 9 00:00:17,018 --> 00:00:19,948 it's a wonderful opportunity, scientifically speaking, 10 00:00:19,948 --> 00:00:22,154 to talk about the impulse, momentum, 11 00:00:22,154 --> 00:00:23,965 force, time relationship, 12 00:00:23,965 --> 00:00:24,888 so let's do that. 13 00:00:24,888 --> 00:00:26,110 Let's put some numbers on here. 14 00:00:26,110 --> 00:00:28,194 So, we're gonna need to know the mass of the ball. 15 00:00:28,194 --> 00:00:31,277 Let's say this is a .2 kilogram ball, 16 00:00:33,044 --> 00:00:35,175 and we're gonna need to know some other numbers. 17 00:00:35,175 --> 00:00:36,566 Let's say the ball comes in 18 00:00:36,566 --> 00:00:39,569 at a speed of about 10 meters per second. 19 00:00:39,569 --> 00:00:41,699 So let's say it's comin' in at 10 meters per second 20 00:00:41,699 --> 00:00:44,138 and let's say it leaves at a speed 21 00:00:44,138 --> 00:00:45,682 of five meters per second. 22 00:00:45,682 --> 00:00:46,982 So it's probably gonna recoil 23 00:00:46,982 --> 00:00:49,190 with a little less speed than it came in with. 24 00:00:49,190 --> 00:00:51,029 It comes in with 10, leaves with five, 25 00:00:51,029 --> 00:00:53,628 and let's say that time, time right here, 26 00:00:53,628 --> 00:00:55,231 the time period that it's actually 27 00:00:55,231 --> 00:00:58,275 in contact with the person's face, 28 00:00:58,275 --> 00:00:59,149 let's say the time, 29 00:00:59,149 --> 00:01:01,608 when the ball is getting kind of compressed 30 00:01:01,608 --> 00:01:04,051 and then recoils and expands again, 31 00:01:04,051 --> 00:01:05,646 let's say the time that it's actually 32 00:01:05,646 --> 00:01:09,813 in contact is about .02 seconds, or about 20 milliseconds. 33 00:01:10,822 --> 00:01:12,311 So, knowing this information, 34 00:01:12,311 --> 00:01:14,179 we can ask all kinds of questions. 35 00:01:14,179 --> 00:01:15,278 One of them is: 36 00:01:15,278 --> 00:01:18,899 What was the impulse on the ball from the person? 37 00:01:18,899 --> 00:01:20,548 Now, the definition of impulse, 38 00:01:20,548 --> 00:01:22,573 we use the letter J for impulse, 39 00:01:22,573 --> 00:01:24,376 that always seemed a little weird to me. 40 00:01:24,376 --> 00:01:25,842 There's no J in impulse. 41 00:01:25,842 --> 00:01:27,402 I end up calling it jimpulse, 42 00:01:27,402 --> 00:01:29,284 just so I can remember that it's impulse, 43 00:01:29,284 --> 00:01:30,472 and there's a J for it. 44 00:01:30,472 --> 00:01:32,358 So the jimpulse, or the impulse, 45 00:01:32,358 --> 00:01:36,088 is defined to be the force acting on the object, 46 00:01:36,088 --> 00:01:38,324 multiplied by the time duration 47 00:01:38,324 --> 00:01:40,316 during which that force is acting. 48 00:01:40,316 --> 00:01:41,149 In other words, 49 00:01:41,149 --> 00:01:45,269 the impulse, from a force, is equal to that force, 50 00:01:45,269 --> 00:01:48,703 multiplied by how long that force was acting on the object. 51 00:01:48,703 --> 00:01:50,334 So, if we knew the force on this ball, 52 00:01:50,334 --> 00:01:52,377 we could use this formula to get the impulse, 53 00:01:52,377 --> 00:01:53,287 but we don't. 54 00:01:53,287 --> 00:01:54,581 I don't know the force 55 00:01:54,581 --> 00:01:56,544 that this person's face is exerting on the ball, 56 00:01:56,544 --> 00:01:59,133 so I can't use this formula to solve for the impulse. 57 00:01:59,133 --> 00:02:01,373 But, there's an alternate formula for impulse. 58 00:02:01,373 --> 00:02:04,034 If you're talking about the net impulse, 59 00:02:04,034 --> 00:02:04,938 in other words, 60 00:02:04,938 --> 00:02:08,092 the impulse from all forces on an object, like this ball, 61 00:02:08,092 --> 00:02:10,782 that should just equal the change in momentum 62 00:02:10,782 --> 00:02:11,677 of that object, 63 00:02:11,677 --> 00:02:13,859 like the change in momentum of this ball. 64 00:02:13,859 --> 00:02:16,594 So if we can figure out the change in momentum of this ball, 65 00:02:16,594 --> 00:02:19,806 we can figure out the net impulse on this ball. 66 00:02:19,806 --> 00:02:21,258 And since it's the net impulse, 67 00:02:21,258 --> 00:02:23,132 and this formula appears also true, 68 00:02:23,132 --> 00:02:24,229 this is equivalent, 69 00:02:24,229 --> 00:02:26,278 which is saying that it's the net force, 70 00:02:26,278 --> 00:02:28,746 multiplied by the time duration, 71 00:02:28,746 --> 00:02:30,927 during which that net force is acting. 72 00:02:30,927 --> 00:02:32,424 This is hard for people to remember, 73 00:02:32,424 --> 00:02:35,563 sometimes my students like to remember it as Jape Fat. 74 00:02:35,563 --> 00:02:36,423 So, if you look at this, 75 00:02:36,423 --> 00:02:41,264 it looks like J-A-P, this kinda looks like an E, F-A-T. 76 00:02:41,264 --> 00:02:44,302 So if you need a way, a pneumonic device, to remember this, 77 00:02:44,302 --> 00:02:46,690 Jape Fat is a way to remember how impulse, 78 00:02:46,690 --> 00:02:49,533 change in momentum, force, and time, 79 00:02:49,533 --> 00:02:50,721 are all related. 80 00:02:50,721 --> 00:02:51,624 So let's do it. 81 00:02:51,624 --> 00:02:53,436 We can't use force because we don't know it yet, 82 00:02:53,436 --> 00:02:55,397 but I can figure out the change in momentum 83 00:02:55,397 --> 00:02:56,747 'cause I know the velocities. 84 00:02:56,747 --> 00:02:58,787 So, we know that the change in momentum 85 00:02:58,787 --> 00:03:02,008 is gonna be P final, the final momentum, 86 00:03:02,008 --> 00:03:04,042 minus the initial momentum. 87 00:03:04,042 --> 00:03:05,914 What's my final momentum? 88 00:03:05,914 --> 00:03:07,985 My final momentum is M times V, 89 00:03:07,985 --> 00:03:11,018 so it's gonna be mass times V final, 90 00:03:11,018 --> 00:03:14,049 minus mass times V initial, 91 00:03:14,049 --> 00:03:15,482 and my mass is .2, 92 00:03:15,482 --> 00:03:18,482 so I've got a mass of 0.2 kilograms. 93 00:03:20,088 --> 00:03:21,739 My final velocity is five, 94 00:03:21,739 --> 00:03:25,347 because the ball recoiled to the right with positive five. 95 00:03:25,347 --> 00:03:27,897 Positive five 'cause it's moving to the right. 96 00:03:27,897 --> 00:03:30,040 I'm gonna assume rightward is positive. 97 00:03:30,040 --> 00:03:32,790 Then minus, the mass is .2 again, 98 00:03:34,052 --> 00:03:35,469 so 0.2 kilograms. 99 00:03:36,852 --> 00:03:39,320 My initial velocity is not 10. 100 00:03:39,320 --> 00:03:41,476 This is 10 meters per second to the left, 101 00:03:41,476 --> 00:03:44,001 and momentum is a vector, it has direction, 102 00:03:44,001 --> 00:03:46,097 so you have to be careful with negative signs here. 103 00:03:46,097 --> 00:03:47,365 This is the most common mistake. 104 00:03:47,365 --> 00:03:49,862 People just plug in positive 10, then get the wrong answer. 105 00:03:49,862 --> 00:03:51,744 But this ball changed directions, 106 00:03:51,744 --> 00:03:55,122 so the two velocities here have to have two different sides, 107 00:03:55,122 --> 00:03:58,792 so this has to be a negative 10 meters per second, 108 00:03:58,792 --> 00:04:00,985 if I'm assuming rightward is positive. 109 00:04:00,985 --> 00:04:03,807 This leftward velocity, and this leftward initial velocity, 110 00:04:03,807 --> 00:04:05,497 has to be negative 10. 111 00:04:05,497 --> 00:04:06,922 And, if you didn't plug that in, 112 00:04:06,922 --> 00:04:07,958 you'd get a different answer, 113 00:04:07,958 --> 00:04:09,136 so you gotta be careful. 114 00:04:09,136 --> 00:04:11,105 So, what do I get here if I multiply this all out? 115 00:04:11,105 --> 00:04:13,051 I'm gonna get zero, no, sorry, 116 00:04:13,051 --> 00:04:17,442 I'm gonna get one kilogram meters per second, 117 00:04:17,442 --> 00:04:21,442 minus a negative two kilogram meters per second, 118 00:04:22,472 --> 00:04:24,744 and that's gonna give me positive three 119 00:04:24,744 --> 00:04:28,165 kilogram meters per second is the impulse, 120 00:04:28,165 --> 00:04:29,779 and that should make sense. 121 00:04:29,779 --> 00:04:31,286 The impulse was positive. 122 00:04:31,286 --> 00:04:33,958 The direction of the impulse, which is a vector, 123 00:04:33,958 --> 00:04:37,514 is the same direction as the direction of the force. 124 00:04:37,514 --> 00:04:40,316 So, which way did our face exert a force on the ball? 125 00:04:40,316 --> 00:04:43,021 Our face exerted a force on the ball to the right. 126 00:04:43,021 --> 00:04:46,244 That's why the impulse on the ball is to the right. 127 00:04:46,244 --> 00:04:48,669 The impulse on this person's face is to the left, 128 00:04:48,669 --> 00:04:51,863 but the impulse on the ball is to the right, 129 00:04:51,863 --> 00:04:53,715 because the ball was initially going left 130 00:04:53,715 --> 00:04:55,429 and it had a force on it to the right 131 00:04:55,429 --> 00:04:58,409 that made it recoil and bounce back to the right. 132 00:04:58,409 --> 00:05:01,650 That's why this impulse has a positive direction to it. 133 00:05:01,650 --> 00:05:03,123 Now, if you've been paying attention, 134 00:05:03,123 --> 00:05:05,462 you might be like, wait a minute, hold on. 135 00:05:05,462 --> 00:05:06,417 What we really did 136 00:05:06,417 --> 00:05:09,816 was we found the change in momentum of the ball, 137 00:05:09,816 --> 00:05:11,169 and when we do that, 138 00:05:11,169 --> 00:05:14,118 what we're finding is the net impulse on the ball. 139 00:05:14,118 --> 00:05:18,410 In other words, the impulse from all forces on the ball. 140 00:05:18,410 --> 00:05:20,205 But what this question was asking for 141 00:05:20,205 --> 00:05:22,236 was the impulse from a single force. 142 00:05:22,236 --> 00:05:24,984 The impulse from just the person's face. 143 00:05:24,984 --> 00:05:27,625 Now, aren't there other forces on this ball? 144 00:05:27,625 --> 00:05:29,321 Isn't there a force of gravity? 145 00:05:29,321 --> 00:05:30,466 And if there is, 146 00:05:30,466 --> 00:05:32,767 doesn't that mean what we really found here 147 00:05:32,767 --> 00:05:34,626 wasn't the impulse from just our face, 148 00:05:34,626 --> 00:05:36,649 but the impulse from the person's face 149 00:05:36,649 --> 00:05:39,212 and the force of gravity during this time period? 150 00:05:39,212 --> 00:05:43,034 And the answer is no, not really, for a few reasons. 151 00:05:43,034 --> 00:05:44,768 Most important reason being that, 152 00:05:44,768 --> 00:05:48,942 what I gave you up here was the initial horizontal velocity. 153 00:05:48,942 --> 00:05:52,477 This 10 meters per second was in the X direction, 154 00:05:52,477 --> 00:05:54,148 and this five meters per second, 155 00:05:54,148 --> 00:05:56,666 I'm assuming is also in the X direction. 156 00:05:56,666 --> 00:05:58,856 'Cause if I'm taking the initial velocity in the X, 157 00:05:58,856 --> 00:06:00,560 and the final velocity in the X, 158 00:06:00,560 --> 00:06:02,258 and I take the difference in momentum, 159 00:06:02,258 --> 00:06:04,124 what I really found was the change in momentum 160 00:06:04,124 --> 00:06:05,790 in the X direction. 161 00:06:05,790 --> 00:06:06,852 When I do that, 162 00:06:06,852 --> 00:06:10,151 I'm finding the net impulse in the X direction, 163 00:06:10,151 --> 00:06:13,569 and there was only one X directed force during this time 164 00:06:13,569 --> 00:06:15,448 and that was our face on the ball, 165 00:06:15,448 --> 00:06:17,023 pushing it to the right. 166 00:06:17,023 --> 00:06:18,662 There was a force of gravity. 167 00:06:18,662 --> 00:06:20,550 That force of gravity was downward. 168 00:06:20,550 --> 00:06:22,076 But what that force of gravity does, 169 00:06:22,076 --> 00:06:25,502 it doesn't add or subtract any impulse in the X direction. 170 00:06:25,502 --> 00:06:28,607 It tries to add impulse in the downward direction, 171 00:06:28,607 --> 00:06:29,856 in the Y direction, 172 00:06:29,856 --> 00:06:32,781 so it tries to add vertical component of velocity downward, 173 00:06:32,781 --> 00:06:35,329 and so we're not even considering that over here. 174 00:06:35,329 --> 00:06:36,721 We're just gonna consider that we're lookin' 175 00:06:36,721 --> 00:06:38,671 at the horizontal components of velocity. 176 00:06:38,671 --> 00:06:41,488 How much velocity does it add vertically, gravity? 177 00:06:41,488 --> 00:06:43,623 Typically, not much during the situation, 178 00:06:43,623 --> 00:06:46,204 because the time period during which 179 00:06:46,204 --> 00:06:48,218 this collision acted is very small 180 00:06:48,218 --> 00:06:50,423 and the weight of this ball, 181 00:06:50,423 --> 00:06:52,270 compared to the force that our face 182 00:06:52,270 --> 00:06:53,726 is acting on the ball with, 183 00:06:53,726 --> 00:06:55,514 the weight is typically much smaller 184 00:06:55,514 --> 00:06:57,431 than this collision force. 185 00:06:57,431 --> 00:06:59,568 So that's why, in these collision problems, 186 00:06:59,568 --> 00:07:02,020 we typically ignore the force of gravity. 187 00:07:02,020 --> 00:07:03,698 So, we don't have to worry about that here. 188 00:07:03,698 --> 00:07:06,191 That's not actually posing much of a problem. 189 00:07:06,191 --> 00:07:08,949 We did find the net impulse in the X direction 190 00:07:08,949 --> 00:07:11,935 since our face was the only X directed force, 191 00:07:11,935 --> 00:07:15,661 this had to be the impulse our face exerted on the ball. 192 00:07:15,661 --> 00:07:17,115 Now, let's solve one more problem. 193 00:07:17,115 --> 00:07:18,419 Let's say we wanted to know: 194 00:07:18,419 --> 00:07:19,874 What was the average force 195 00:07:19,874 --> 00:07:22,584 on this person's face from the ball? 196 00:07:22,584 --> 00:07:24,937 Well, we know the net impulse on the ball, 197 00:07:24,937 --> 00:07:28,292 that means we can figure out the net force on the ball, 198 00:07:28,292 --> 00:07:30,593 because I can use this relationship now. 199 00:07:30,593 --> 00:07:32,703 Since I know that the net impulse 200 00:07:32,703 --> 00:07:34,625 on the ball in the X direction 201 00:07:34,625 --> 00:07:37,507 should just equal the net force on the ball 202 00:07:37,507 --> 00:07:38,835 in the X direction, 203 00:07:38,835 --> 00:07:40,953 multiplied by the time interval 204 00:07:40,953 --> 00:07:42,775 during which the force was applied, 205 00:07:42,775 --> 00:07:45,050 I can say that the net impulse on the ball 206 00:07:45,050 --> 00:07:48,905 was three kilogram meters per second, 207 00:07:48,905 --> 00:07:52,413 and that should equal the net force on the ball 208 00:07:52,413 --> 00:07:53,700 in the X direction, 209 00:07:53,700 --> 00:07:56,887 which was supplied by, unfortunately, this person's face, 210 00:07:56,887 --> 00:07:58,741 multiplied by the time interval, 211 00:07:58,741 --> 00:08:01,260 which is 0.02, 20 milliseconds. 212 00:08:01,260 --> 00:08:02,771 So, now I can solve. 213 00:08:02,771 --> 00:08:05,390 The force, the net force on the ball, 214 00:08:05,390 --> 00:08:07,826 during this time interval in the X direction, 215 00:08:07,826 --> 00:08:09,993 was three, divided by .02. 216 00:08:11,377 --> 00:08:14,624 If I take three kilogram meters per second 217 00:08:14,624 --> 00:08:16,957 and I divide by .02 seconds, 218 00:08:18,062 --> 00:08:23,047 I'm gonna get 150 Newtons was the net force on the ball. 219 00:08:23,047 --> 00:08:25,174 We got a positive number, and that makes sense, 220 00:08:25,174 --> 00:08:27,428 because this person's face exerted 221 00:08:27,428 --> 00:08:29,842 a positive force on this ball, 222 00:08:29,842 --> 00:08:32,145 'cause the force was exerted to the right. 223 00:08:32,145 --> 00:08:33,515 So, these were positive, 224 00:08:33,515 --> 00:08:36,179 and the impulse from the face on the ball 225 00:08:36,179 --> 00:08:37,626 should be going the same direction 226 00:08:37,626 --> 00:08:40,349 as the force from the face on the ball. 227 00:08:40,350 --> 00:08:43,547 So, this is the force on the ball by the person's face, 228 00:08:43,547 --> 00:08:45,688 but notice this question is asking: 229 00:08:45,688 --> 00:08:49,870 What was the average force on the person's face 230 00:08:49,870 --> 00:08:50,856 from the ball? 231 00:08:50,856 --> 00:08:53,407 Not on the ball by the face. 232 00:08:53,407 --> 00:08:55,587 You might think, oh no, we gotta start all over, 233 00:08:55,587 --> 00:08:57,334 we solved for the wrong question, 234 00:08:57,334 --> 00:08:58,293 but we're in luck. 235 00:08:58,293 --> 00:09:01,082 Newton's third law says that the force 236 00:09:01,082 --> 00:09:05,399 on the face from the ball should be equal and opposite. 237 00:09:05,399 --> 00:09:07,551 So, this force on the face from the ball 238 00:09:07,551 --> 00:09:10,205 has got to be equal and opposite 239 00:09:10,205 --> 00:09:12,672 to the force on the ball from the face, 240 00:09:12,672 --> 00:09:13,954 so that's what we found here, 241 00:09:13,954 --> 00:09:16,126 the force on the ball from the face, 242 00:09:16,126 --> 00:09:18,712 that means the force on the face from the ball 243 00:09:18,712 --> 00:09:20,302 is gonna have the same size. 244 00:09:20,302 --> 00:09:22,160 It's gonna be 150 Newtons. 245 00:09:22,160 --> 00:09:24,948 It's just gonna be directed in the leftward direction, 246 00:09:24,948 --> 00:09:26,923 that means it's gonna be a negative force, 247 00:09:26,923 --> 00:09:28,487 so technically, you could say, 248 00:09:28,487 --> 00:09:31,194 this would be negative 150 Newtons on the face 249 00:09:31,194 --> 00:09:32,269 from the ball. 250 00:09:32,269 --> 00:09:36,304 So, to recap, the impulse, from an individual force, 251 00:09:36,304 --> 00:09:38,255 is defined to be that force, 252 00:09:38,255 --> 00:09:39,923 multiplied by the time interval 253 00:09:39,923 --> 00:09:41,987 during which that force is applied. 254 00:09:41,987 --> 00:09:44,239 And if you're talkin' about the net force 255 00:09:44,239 --> 00:09:45,406 in a given direction, 256 00:09:45,406 --> 00:09:47,137 multiplied by the time interval, 257 00:09:47,137 --> 00:09:50,397 you'd be finding the net impulse in that direction, 258 00:09:50,397 --> 00:09:53,567 and this also happens to equal the change in momentum 259 00:09:53,567 --> 00:09:54,740 in that direction. 260 00:09:54,740 --> 00:09:55,867 So, in other words, 261 00:09:55,867 --> 00:09:58,328 if there is a net impulse in a given direction, 262 00:09:58,328 --> 00:10:00,456 there's gotta be a change in momentum 263 00:10:00,456 --> 00:10:03,457 in that direction by the same amount. 264 00:10:03,457 --> 00:10:06,670 And one convenient way to remember how are these related, 265 00:10:06,670 --> 00:10:10,214 is you could use the pneumonic device, Jape Fat. 266 00:10:10,214 --> 00:10:12,198 I have no idea what Jape Fat means, 267 00:10:12,198 --> 00:10:14,785 but it helped me remember that the net impulse 268 00:10:14,785 --> 00:10:16,561 equals the change in momentum, 269 00:10:16,561 --> 00:10:18,607 and that also equals the net force, 270 00:10:18,607 --> 00:10:20,534 multiplied by the time interval, 271 00:10:20,534 --> 00:10:22,879 during which that force was applied. 272 00:10:22,879 --> 00:10:25,334 And finally, remember that during these collisions, 273 00:10:25,334 --> 00:10:28,349 there's always an equal and opposite force exerted 274 00:10:28,349 --> 00:00:00,000 on the two objects participating in the collision.