1 00:00:00,282 --> 00:00:01,553 - [Instructor] If you're face to face 2 00:00:01,553 --> 00:00:04,328 with a sophisticated Newton's Second Law problem, 3 00:00:04,328 --> 00:00:06,354 you're gonna need a sophisticated understanding 4 00:00:06,354 --> 00:00:07,521 of Newton's Second Law. 5 00:00:07,521 --> 00:00:08,960 That's what I'm gonna try to provide you with here, 6 00:00:08,960 --> 00:00:11,170 so that no matter what scenario you're faced with 7 00:00:11,170 --> 00:00:13,569 you can apply this law in a correct way. 8 00:00:13,569 --> 00:00:16,458 Most people know Newton's Second Law is F equals MA, 9 00:00:16,458 --> 00:00:18,834 which is fine, it's a simple way to understand it, 10 00:00:18,834 --> 00:00:20,308 and it's fine for simple problems, 11 00:00:20,308 --> 00:00:23,545 if I had an asteroid for instance, of mass m, 12 00:00:23,545 --> 00:00:26,651 out in outer space so there's no air resistance or friction, 13 00:00:26,651 --> 00:00:29,971 and there was only one force on it, a force F, 14 00:00:29,971 --> 00:00:31,388 and that force pointed to the right, 15 00:00:31,388 --> 00:00:34,162 let's say that force was 50 newtons, 16 00:00:34,162 --> 00:00:36,554 well I could plug the 50 newtons into the force, 17 00:00:36,554 --> 00:00:38,156 I could plug the mass of the asteroid, 18 00:00:38,156 --> 00:00:41,661 let's just say it's 10 kilograms, into the mass, 19 00:00:41,661 --> 00:00:43,495 and I'd find the acceleration of the asteroid, 20 00:00:43,495 --> 00:00:45,836 in this case, 50 over 10 would give me five 21 00:00:45,836 --> 00:00:47,914 meters per second squared. 22 00:00:47,914 --> 00:00:50,724 But, what if we had extra forces on this asteroid? 23 00:00:50,724 --> 00:00:52,586 What if there was another force that pointed to the left, 24 00:00:52,586 --> 00:00:54,253 that was 30 newtons? 25 00:00:55,757 --> 00:00:57,740 So let's call, let's name these now, 26 00:00:57,740 --> 00:01:01,011 let's call this F1, this 50 newtons, 27 00:01:01,011 --> 00:01:02,996 let's say that's the magnitude of that force, 28 00:01:02,996 --> 00:01:06,043 let's say F2 was the magnitude of the 30 newton force, 29 00:01:06,043 --> 00:01:09,370 it points to the left, yes, that's the negative direction, 30 00:01:09,370 --> 00:01:10,847 but let's just say these forces here 31 00:01:10,847 --> 00:01:12,260 are just giving the magnitude of it 32 00:01:12,260 --> 00:01:13,903 and then the direction is specified 33 00:01:13,903 --> 00:01:16,096 by the direction of the arrow. 34 00:01:16,096 --> 00:01:17,500 Now what would I do? 35 00:01:17,500 --> 00:01:20,022 Well, to handle this we need to understand 36 00:01:20,022 --> 00:01:22,477 that the left hand side here isn't just force, 37 00:01:22,477 --> 00:01:23,868 it's the net force. 38 00:01:23,868 --> 00:01:26,271 Or, you can call it the sum of the forces. 39 00:01:26,271 --> 00:01:28,758 So to denote the net force, 40 00:01:28,758 --> 00:01:30,956 we often write this Greek letter sigma, 41 00:01:30,956 --> 00:01:33,397 and sigma is a mathematical symbol 42 00:01:33,397 --> 00:01:37,366 that represents the sum of whatever comes after it. 43 00:01:37,366 --> 00:01:40,884 So this is the sum of the forces. 44 00:01:40,884 --> 00:01:42,045 Because F comes afterward. 45 00:01:42,045 --> 00:01:44,229 If I had G it would be the sum of the G's, 46 00:01:44,229 --> 00:01:47,444 and if I had H it would be the sum of the H's. 47 00:01:47,444 --> 00:01:49,028 And this is a little confusing already. 48 00:01:49,028 --> 00:01:51,588 People hear sum of, phonetically, 49 00:01:51,588 --> 00:01:55,891 and they think oh, sometimes they're like oh, so, some of? 50 00:01:55,891 --> 00:01:56,829 Like a few of? 51 00:01:56,829 --> 00:02:00,063 No no no, we mean all of, all of the forces. 52 00:02:00,063 --> 00:02:00,896 That's what this means. 53 00:02:00,896 --> 00:02:03,453 You add up all of the forces, that will equal 54 00:02:03,453 --> 00:02:05,572 the mass times the acceleration. 55 00:02:05,572 --> 00:02:08,209 So in this case, we'd take this 50 newtons, 56 00:02:08,209 --> 00:02:10,850 I can take 50 newtons because it goes to the right, 57 00:02:10,850 --> 00:02:13,074 and, I mean we can call leftward positive 58 00:02:13,074 --> 00:02:15,396 if we really wanted to, if there was a good reason, 59 00:02:15,396 --> 00:02:16,946 but unless otherwise specified, 60 00:02:16,946 --> 00:02:18,675 we're gonna just choose rightward as positive 61 00:02:18,675 --> 00:02:22,420 and upward as positive, so this 50 has to be positive. 62 00:02:22,420 --> 00:02:25,258 And I can't now, by sum of, I add up the forces, 63 00:02:25,258 --> 00:02:27,325 but I have to add them up like vectors. 64 00:02:27,325 --> 00:02:29,413 This force here is a vector. 65 00:02:29,413 --> 00:02:32,259 Forces are vectors, and so I have to add them up as vectors. 66 00:02:32,259 --> 00:02:33,861 This is a vector equation. 67 00:02:33,861 --> 00:02:37,356 I can't just take 50 plus 30 to get the answer, 68 00:02:37,356 --> 00:02:39,068 because vectors that point to the left 69 00:02:39,068 --> 00:02:40,141 we're gonna consider negative, 70 00:02:40,141 --> 00:02:42,284 and vectors that point to the right we'll consider positive, 71 00:02:42,284 --> 00:02:46,167 and so I'll take 50 newtons minus 30 newtons. 72 00:02:46,167 --> 00:02:48,164 That's what's gonna be equal to 73 00:02:48,164 --> 00:02:49,930 the mass times the acceleration, 74 00:02:49,930 --> 00:02:52,762 so I could plug in 10 kilograms if I wanted to, 75 00:02:52,762 --> 00:02:55,268 multiply by A, and in this case I'd get 76 00:02:55,268 --> 00:02:58,312 20 over 10 is two, meters per second squared. 77 00:02:58,312 --> 00:03:00,250 So you have to add these up like vectors, 78 00:03:00,250 --> 00:03:03,626 and if I had more forces it'd be just as easy to deal with, 79 00:03:03,626 --> 00:03:06,478 I can just add them up as vectors, 80 00:03:06,478 --> 00:03:08,852 so if I had another force here that was maybe, 81 00:03:08,852 --> 00:03:12,519 that's maybe 25 newtons, we'll call that F3. 82 00:03:14,595 --> 00:03:17,764 And let's say there's another force that points to the left, 83 00:03:17,764 --> 00:03:21,259 this one's gonna be 40 newtons, so we'll have 84 00:03:21,259 --> 00:03:25,378 40 newtons to the left, we'll call this one F4, 85 00:03:25,378 --> 00:03:26,994 well, I can just keep including these. 86 00:03:26,994 --> 00:03:28,815 I can just add them up as vectors, 87 00:03:28,815 --> 00:03:30,808 the 40 newtons points to the left, 88 00:03:30,808 --> 00:03:31,929 so that's gotta be a negative, 89 00:03:31,929 --> 00:03:34,076 I'll put negative 40 newtons, 90 00:03:34,076 --> 00:03:36,067 and then this 25 points to the right, 91 00:03:36,067 --> 00:03:40,183 I'll make that positive, so positive 25 newtons, 92 00:03:40,183 --> 00:03:42,423 and I can find my total force, my net force, 93 00:03:42,423 --> 00:03:45,083 my sum of the forces, and that would allow me 94 00:03:45,083 --> 00:03:47,010 to figure out the acceleration. 95 00:03:47,010 --> 00:03:49,326 So, there's one problem here though. 96 00:03:49,326 --> 00:03:51,729 A lot of times physicists don't like writing this anymore, 97 00:03:51,729 --> 00:03:53,853 at least physicists that are interested in education 98 00:03:53,853 --> 00:03:57,388 don't like this form of Newton's Second Law as much, 99 00:03:57,388 --> 00:03:58,236 a lot of them don't, 100 00:03:58,236 --> 00:04:01,381 and the reason is, there's a misconception students have. 101 00:04:01,381 --> 00:04:03,490 They think that as they're drawing forces here, 102 00:04:03,490 --> 00:04:06,706 the M times A is also a force. 103 00:04:06,706 --> 00:04:09,347 They want to draw an extra force on this asteroid, 104 00:04:09,347 --> 00:04:10,863 maybe it points to the right, 105 00:04:10,863 --> 00:04:13,487 that is mass times acceleration. 106 00:04:13,487 --> 00:04:16,486 But mass times acceleration is not a force. 107 00:04:16,486 --> 00:04:18,914 Mass times acceleration is just what the net force 108 00:04:18,914 --> 00:04:20,724 happens to equal. 109 00:04:20,724 --> 00:04:22,891 So if you add up all the net forces, or sorry, 110 00:04:22,891 --> 00:04:25,339 if you add up the net force on an object, 111 00:04:25,339 --> 00:04:28,812 which is adding up as vectors all the forces on the object, 112 00:04:28,812 --> 00:04:32,568 that will just equal MA, it happens to equal MA. 113 00:04:32,568 --> 00:04:35,406 But it is, MA is not a force in and of itself, 114 00:04:35,406 --> 00:04:38,529 so you cannot draw this as a force, 115 00:04:38,529 --> 00:04:40,891 don't draw any of that, that is not a force, 116 00:04:40,891 --> 00:04:43,661 that's just what the sum of the forces happen to equal. 117 00:04:43,661 --> 00:04:46,412 So upon realizing this, physicists were like oh, okay, 118 00:04:46,412 --> 00:04:48,026 this is causing confusion, 119 00:04:48,026 --> 00:04:50,386 so let's just write an equally good form 120 00:04:50,386 --> 00:04:53,193 of Newton's Second Law, in terms of algebra, 121 00:04:53,193 --> 00:04:55,735 but that also makes it so that people 122 00:04:55,735 --> 00:04:58,822 aren't so susceptible to falling into this misconception, 123 00:04:58,822 --> 00:05:00,603 and this alternative version of Newton's Second Law 124 00:05:00,603 --> 00:05:01,610 looks like this. 125 00:05:01,610 --> 00:05:05,777 The acceleration equals the net force divided by the mass. 126 00:05:06,994 --> 00:05:08,546 And you might be like, so what? 127 00:05:08,546 --> 00:05:12,500 We just divided both sides by mass, who really cares? 128 00:05:12,500 --> 00:05:14,009 Well here's why it's better. 129 00:05:14,009 --> 00:05:15,861 Because people are much less like to think 130 00:05:15,861 --> 00:05:18,230 that acceleration itself is a force. 131 00:05:18,230 --> 00:05:20,592 They're much less likely to say oh, 132 00:05:20,592 --> 00:05:22,267 acceleration is a force over here, 133 00:05:22,267 --> 00:05:24,772 I mean people might do that but they're less likely. 134 00:05:24,772 --> 00:05:27,523 So acceleration is not a force, it's a vector, 135 00:05:27,523 --> 00:05:29,160 but it's not a force vector. 136 00:05:29,160 --> 00:05:30,802 And the other reason this equation is nice, 137 00:05:30,802 --> 00:05:32,299 it shows us the relational dependence 138 00:05:32,299 --> 00:05:35,389 of acceleration, it shows us that the net force 139 00:05:35,389 --> 00:05:37,315 is what will give us acceleration, 140 00:05:37,315 --> 00:05:39,212 and the more net force we have, 141 00:05:39,212 --> 00:05:40,588 the bigger the acceleration. 142 00:05:40,588 --> 00:05:44,083 So it shows us that the acceleration is proportional 143 00:05:44,083 --> 00:05:47,075 to the net force, or the sum of the forces. 144 00:05:47,075 --> 00:05:48,346 And it shows us that the acceleration 145 00:05:48,346 --> 00:05:50,720 is inversely proportional to the mass. 146 00:05:50,720 --> 00:05:53,385 So the bigger the mass, the less acceleration you have. 147 00:05:53,385 --> 00:05:54,842 So it's another reason this equation's nice, 148 00:05:54,842 --> 00:05:58,034 shows us what acceleration actually depends on 149 00:05:58,034 --> 00:06:00,348 in terms of net force and mass. 150 00:06:00,348 --> 00:06:02,208 So there's one other problem here. 151 00:06:02,208 --> 00:06:04,083 So this is better, this is already better, 152 00:06:04,083 --> 00:06:06,474 now we know it's net force, now we can write it this way 153 00:06:06,474 --> 00:06:09,998 and not fall into the misconception that MA is a force. 154 00:06:09,998 --> 00:06:10,898 There's a problem though, 155 00:06:10,898 --> 00:06:12,523 what if I introduced another force over here? 156 00:06:12,523 --> 00:06:16,690 Let's say I introduced a force that points downward. 157 00:06:17,619 --> 00:06:20,619 Let's say this force was 28 newtons, 158 00:06:22,819 --> 00:06:26,402 and this is F4, well we did F4, this is F5. 159 00:06:27,475 --> 00:06:29,892 So we have F5, 28 newtons downward, 160 00:06:29,892 --> 00:06:32,359 you might think, oh, I know how to deal with this now, 161 00:06:32,359 --> 00:06:35,213 can't I just sneak this 28 in over here 162 00:06:35,213 --> 00:06:38,704 and write it as a negative 28 because it goes down, 163 00:06:38,704 --> 00:06:40,370 can't I just put negative 28 right there 164 00:06:40,370 --> 00:06:42,098 and it turns out you cannot do that. 165 00:06:42,098 --> 00:06:43,081 That is not allowed, 166 00:06:43,081 --> 00:06:46,871 and the reason is, just like we couldn't take 50 plus 30, 167 00:06:46,871 --> 00:06:48,746 because we're adding these up as vectors, 168 00:06:48,746 --> 00:06:51,667 and leftward meant negative and rightward meant positive, 169 00:06:51,667 --> 00:06:55,050 we can't take a vertical force and just add that magnitude, 170 00:06:55,050 --> 00:06:57,187 or subtract it, from the magnitude 171 00:06:57,187 --> 00:06:59,242 of the horizontal force. 172 00:06:59,242 --> 00:07:00,075 That's not allowed, 173 00:07:00,075 --> 00:07:02,290 a horizontal force and a vertical force added up 174 00:07:02,290 --> 00:07:04,298 will not equal the sum of, 175 00:07:04,298 --> 00:07:07,349 or the difference of, the magnitudes. 176 00:07:07,349 --> 00:07:08,460 What I'm saying is this. 177 00:07:08,460 --> 00:07:11,154 Think about it this way, if you had a certain amount 178 00:07:11,154 --> 00:07:12,934 of force to the right, 179 00:07:12,934 --> 00:07:15,601 and a certain amount of force upward, 180 00:07:15,601 --> 00:07:17,830 to add these up it would not equal 181 00:07:17,830 --> 00:07:20,080 this value plus this value, 182 00:07:20,939 --> 00:07:23,170 you'd have to add them up with the Pythagorean theorem. 183 00:07:23,170 --> 00:07:26,588 To add vectors this way, you'd get this vector right here. 184 00:07:26,588 --> 00:07:28,411 That would be your total vector. 185 00:07:28,411 --> 00:07:32,852 So you'd have to do a squared plus b squared equals 186 00:07:32,852 --> 00:07:36,481 the total force squared over there between those two vectors 187 00:07:36,481 --> 00:07:38,198 and you might be thinking oh great, 188 00:07:38,198 --> 00:07:40,376 I don't want to have to do trigonometry here. 189 00:07:40,376 --> 00:07:43,045 And it turns out you don't have to, not yet at least. 190 00:07:43,045 --> 00:07:45,583 If these are the only forces we have, 191 00:07:45,583 --> 00:07:47,157 we don't have to do it this way, 192 00:07:47,157 --> 00:07:48,869 I'm just trying to show you that you cannot simply 193 00:07:48,869 --> 00:07:52,631 naively add up 50 minus 28 and expect to get 194 00:07:52,631 --> 00:07:54,099 the total answer right. 195 00:07:54,099 --> 00:07:55,324 But here's what you could do. 196 00:07:55,324 --> 00:07:57,545 You could take only horizontal forces, 197 00:07:57,545 --> 00:08:00,583 deal with those in the horizontal direction first. 198 00:08:00,583 --> 00:08:03,102 And only vertical forces, and deal with those 199 00:08:03,102 --> 00:08:04,316 in a vertical direction, 200 00:08:04,316 --> 00:08:06,718 so it's the same trick we always play as physicists, 201 00:08:06,718 --> 00:08:08,708 we say alright, we're gonna divide and conquer, 202 00:08:08,708 --> 00:08:10,932 we're gonna take all horizontal forces, 203 00:08:10,932 --> 00:08:12,867 and put those into their own equation 204 00:08:12,867 --> 00:08:15,090 because the horizontal forces should only affect 205 00:08:15,090 --> 00:08:17,267 the horizontal acceleration. 206 00:08:17,267 --> 00:08:20,216 So if I just want horizontal acceleration, 207 00:08:20,216 --> 00:08:23,467 I can take only horizontal forces, add those up, 208 00:08:23,467 --> 00:08:25,557 and get the horizontal acceleration. 209 00:08:25,557 --> 00:08:29,414 Or, I could take only vertical forces. 210 00:08:29,414 --> 00:08:33,458 Add those up, and I'd get the vertical acceleration. 211 00:08:33,458 --> 00:08:35,238 So if I take this, I'll make an equation 212 00:08:35,239 --> 00:08:37,743 for each direction independently, 213 00:08:37,743 --> 00:08:41,772 and I know I can find each component of 214 00:08:41,772 --> 00:08:44,082 the acceleration by just using the forces 215 00:08:44,082 --> 00:08:46,148 in that particular direction. 216 00:08:46,148 --> 00:08:47,372 So this is a nice trick, 217 00:08:47,372 --> 00:08:49,707 we're gonna deal with each direction independently. 218 00:08:49,707 --> 00:08:52,029 And then if we really wanted, say, 219 00:08:52,029 --> 00:08:53,620 say these were acceleration vectors, 220 00:08:53,620 --> 00:08:55,605 say we wanted the total acceleration, 221 00:08:55,605 --> 00:08:56,979 we were talking about forces before, 222 00:08:56,979 --> 00:09:00,300 but all vectors add up the same way. 223 00:09:00,300 --> 00:09:01,727 You can use the Pythagorean theorem. 224 00:09:01,727 --> 00:09:04,300 If you figure out A in the X direction, 225 00:09:04,300 --> 00:09:06,443 the total acceleration in the X direction 226 00:09:06,443 --> 00:09:08,054 and you figure out the total acceleration 227 00:09:08,054 --> 00:09:09,157 in the Y direction, 228 00:09:09,157 --> 00:09:10,675 you could figure out the total acceleration, 229 00:09:10,675 --> 00:09:12,179 the magnitude of it, by again 230 00:09:12,179 --> 00:09:15,133 using the Pythagorean theorem, and so this is just a way, 231 00:09:15,133 --> 00:09:17,182 this is a handy way of dealing with these forces 232 00:09:17,182 --> 00:09:19,191 that point in multiple directions. 233 00:09:19,191 --> 00:09:22,190 Let me stick one more force in here, just because 234 00:09:22,190 --> 00:09:23,391 we should have one that points up 235 00:09:23,391 --> 00:09:25,919 and then we have all possible directions here. 236 00:09:25,919 --> 00:09:30,295 Alright so if this force, F, what are we on, six, 237 00:09:30,295 --> 00:09:33,212 is gonna be, maybe that's about 42, 238 00:09:34,722 --> 00:09:37,441 that's a good number, newtons upward, 239 00:09:37,441 --> 00:09:38,591 how do we deal with this? 240 00:09:38,591 --> 00:09:40,315 Well we already dealt with the X direction. 241 00:09:40,315 --> 00:09:42,939 This was the X direction, this gives us all the forces 242 00:09:42,939 --> 00:09:43,772 in the X direction, 243 00:09:43,772 --> 00:09:46,055 that equals mass times acceleration in the X, 244 00:09:46,055 --> 00:09:47,264 it's not written in this form, 245 00:09:47,264 --> 00:09:49,725 it's just multiplied with the 10 on the right hand side 246 00:09:49,725 --> 00:09:51,913 instead of divided here, but this is the formula 247 00:09:51,913 --> 00:09:54,311 you could use to relate forces in the X direction 248 00:09:54,311 --> 00:09:56,476 to the acceleration in the X direction. 249 00:09:56,476 --> 00:09:59,547 We're essentially just taking all of these forces, 250 00:09:59,547 --> 00:10:01,869 plugging them into the net force in the X, 251 00:10:01,869 --> 00:10:03,727 dividing by the mass, and we'd find 252 00:10:03,727 --> 00:10:05,544 the acceleration in the X direction. 253 00:10:05,544 --> 00:10:07,910 For the Y direction, we could say 254 00:10:07,910 --> 00:10:09,688 that acceleration in the Y direction 255 00:10:09,688 --> 00:10:11,679 would be the net force in the Y direction, 256 00:10:11,679 --> 00:10:13,119 so how would we deal with this, 257 00:10:13,119 --> 00:10:15,586 only vertical forces are gonna be affecting 258 00:10:15,586 --> 00:10:17,357 the vertical acceleration, 259 00:10:17,357 --> 00:10:20,486 so I can take this F6 which is 42 newtons, 260 00:10:20,486 --> 00:10:22,772 it points up, we're gonna treat that as positive 261 00:10:22,772 --> 00:10:23,945 because we don't have a good reason 262 00:10:23,945 --> 00:10:25,495 to treat down as positive, 263 00:10:25,495 --> 00:10:28,152 42 up and that's the convention we usually pick, 264 00:10:28,152 --> 00:10:31,559 42 minus 28, 28 points downward, 265 00:10:31,559 --> 00:10:34,862 we typically choose that as the negative direction, 266 00:10:34,862 --> 00:10:36,908 now we can divide by the mass. 267 00:10:36,908 --> 00:10:39,039 We'll divide by 10 kilograms, 268 00:10:39,039 --> 00:10:42,126 this gives us our acceleration in the vertical direction. 269 00:10:42,126 --> 00:10:43,694 And now that we have both of these, 270 00:10:43,694 --> 00:10:46,548 we could if we wanted to do AX squared 271 00:10:46,548 --> 00:10:49,126 plus AY squared equals the total A squared 272 00:10:49,126 --> 00:10:52,534 to find the magnitude of the total acceleration. 273 00:10:52,534 --> 00:10:54,416 Alright, let's step it up one more notch 274 00:10:54,416 --> 00:10:57,782 and see what happens, let's make it one step harder. 275 00:10:57,782 --> 00:10:59,014 We're gonna move this out of the way, 276 00:10:59,014 --> 00:11:00,527 I'm gonna make a little room. 277 00:11:00,527 --> 00:11:02,845 So let's say this 40 newtons is still applied, 278 00:11:02,845 --> 00:11:04,813 but I'm just gonna put it here so it's out of the way. 279 00:11:04,813 --> 00:11:07,286 Let's say there was one more vector involved, 280 00:11:07,286 --> 00:11:09,822 one more vector that points this way, 281 00:11:09,822 --> 00:11:12,729 and let's say the size of that vector, 282 00:11:12,729 --> 00:11:14,646 we'll call this one F7, 283 00:11:15,860 --> 00:11:18,110 let's say F7 is 45 newtons. 284 00:11:20,281 --> 00:11:21,114 Okay. 285 00:11:21,114 --> 00:11:22,858 45 newtons applied at an angle, 286 00:11:22,858 --> 00:11:26,163 let's just say from that point of 30 degrees. 287 00:11:26,163 --> 00:11:27,457 How do you deal with this? 288 00:11:27,457 --> 00:11:29,256 This is an even more sophisticated 289 00:11:29,256 --> 00:11:30,674 Newton's Second Law problem. 290 00:11:30,674 --> 00:11:32,431 Here's where it starts to frighten people, 291 00:11:32,431 --> 00:11:33,698 they don't know what to do, 292 00:11:33,698 --> 00:11:35,173 a lot of times they try to just throw 293 00:11:35,173 --> 00:11:38,486 this 45 newtons into one of the equations, 294 00:11:38,486 --> 00:11:40,031 they think the 45 maybe should go 295 00:11:40,031 --> 00:11:42,243 in the X equation because it points to the left, 296 00:11:42,243 --> 00:11:45,841 that's horizontal, that's X, but it also points vertical, 297 00:11:45,841 --> 00:11:47,468 sometimes they throw the whole 45 298 00:11:47,468 --> 00:11:51,670 into the vertical equation, maybe they do plus 45 over here, 299 00:11:51,670 --> 00:11:53,452 but that's wrong, you can't do that, 300 00:11:53,452 --> 00:11:56,736 and you can't do that because only vertical forces 301 00:11:56,736 --> 00:11:57,764 and components of forces 302 00:11:57,764 --> 00:11:59,588 can go in this vertical equation, 303 00:11:59,588 --> 00:12:02,525 and only horizontal forces and horizontal components 304 00:12:02,525 --> 00:12:05,909 of forces can go into this horizontal equation. 305 00:12:05,909 --> 00:12:07,366 So what we have to do at this point, 306 00:12:07,366 --> 00:12:08,250 I think you know what we have to do, 307 00:12:08,250 --> 00:12:09,475 we have to break this up. 308 00:12:09,475 --> 00:12:11,273 So we have to take this 45 newtons, 309 00:12:11,273 --> 00:12:12,812 that points up and to the left, 310 00:12:12,812 --> 00:12:14,849 we have to break this up into how much of this force 311 00:12:14,849 --> 00:12:17,996 points left, how much of this force points upward. 312 00:12:17,996 --> 00:12:20,603 So we're gonna have to figure out what is this component 313 00:12:20,603 --> 00:12:23,557 of this force that way, in the X direction, 314 00:12:23,557 --> 00:12:25,810 what is this component in the vertical direction, 315 00:12:25,810 --> 00:12:28,893 I'll call this F7 in the Y direction, 316 00:12:30,709 --> 00:12:35,266 and this component here would be F7 in the X direction, 317 00:12:35,266 --> 00:12:37,675 it's getting a little cluttered there, sorry about that. 318 00:12:37,675 --> 00:12:39,382 We have to figure out what these components are, 319 00:12:39,382 --> 00:12:40,548 and once we figure out what those are, 320 00:12:40,548 --> 00:12:43,590 I can associate the F7 X into the X equation, 321 00:12:43,590 --> 00:12:46,005 and the F7 Y into the Y equation, 322 00:12:46,005 --> 00:12:48,902 but I can't put the whole 45 into either equation 323 00:12:48,902 --> 00:12:51,924 because all 45 newtons is not directed vertically 324 00:12:51,924 --> 00:12:54,573 or horizontally, only part of it is. 325 00:12:54,573 --> 00:12:56,634 So we have to figure out with more trigonometry, 326 00:12:56,634 --> 00:12:58,532 we're gonna use this same rule or the same idea 327 00:12:58,532 --> 00:13:02,323 over here, but instead of the Pythagorean theorem, 328 00:13:02,323 --> 00:13:04,656 we're gonna take this 45 newtons 329 00:13:04,656 --> 00:13:06,543 and break it up into components, 330 00:13:06,543 --> 00:13:07,470 and the way we do that 331 00:13:07,470 --> 00:13:09,821 is with the definition of sine and cosine. 332 00:13:09,821 --> 00:13:12,429 So if this is, I'm just gonna make it bigger over here, 333 00:13:12,429 --> 00:13:15,679 45 newtons, if this side is 45 newtons, 334 00:13:17,845 --> 00:13:22,644 then this side would be the adjacent to this 30 degrees, 335 00:13:22,644 --> 00:13:25,228 this F7 in the X direction, 336 00:13:25,228 --> 00:13:28,525 and this side would be the opposite to that 30 degrees, 337 00:13:28,525 --> 00:13:31,192 so that's F7 in the Y direction. 338 00:13:32,050 --> 00:13:33,525 Now we use sine and cosine, 339 00:13:33,525 --> 00:13:35,654 let's use the definition of cosine. 340 00:13:35,654 --> 00:13:40,247 The definition of cosine, theta, is gonna be the adjacent 341 00:13:40,247 --> 00:13:41,958 over the hypotenuse. 342 00:13:41,958 --> 00:13:43,693 So the adjacent to this 30 degrees 343 00:13:43,693 --> 00:13:47,666 is the side touching that angle, which is F7 X. 344 00:13:47,666 --> 00:13:51,190 So F7 in the X direction, over the hypotenuse 345 00:13:51,190 --> 00:13:54,080 is the total magnitude of this force vector 346 00:13:54,080 --> 00:13:56,412 which is 45 newtons. 347 00:13:56,412 --> 00:13:59,044 So I can solve now for F7 in the X direction, 348 00:13:59,044 --> 00:14:02,711 F7 in the X direction is gonna be 45 newtons 349 00:14:03,638 --> 00:14:05,888 times cosine of 30 degrees. 350 00:14:07,768 --> 00:14:09,603 Now I can take this F7 in the X direction, 351 00:14:09,603 --> 00:14:10,915 I can take this, whatever it is, 352 00:14:10,915 --> 00:14:12,852 this is just a number, you can calculate it if you want, 353 00:14:12,852 --> 00:14:15,019 and I'm gonna take this and I'm gonna plug this 354 00:14:15,019 --> 00:14:17,519 straight into the X direction, 355 00:14:18,740 --> 00:14:20,829 I'm gonna put it right into here, as, let's see, 356 00:14:20,829 --> 00:14:22,557 should it be positive or negative? 357 00:14:22,557 --> 00:14:23,883 Here's where it's tricky. 358 00:14:23,883 --> 00:14:27,764 The F7 Y points up, the F7 X points left, 359 00:14:27,764 --> 00:14:30,378 this is the X component, so it's the leftward 360 00:14:30,378 --> 00:14:31,897 that we care about, the fact that it points up 361 00:14:31,897 --> 00:14:33,699 doesn't matter in terms of X, 362 00:14:33,699 --> 00:14:35,223 but this component points left 363 00:14:35,223 --> 00:14:39,539 so we have to include it as a negative 45 newtons 364 00:14:39,539 --> 00:14:41,122 times cosine of 30. 365 00:14:42,006 --> 00:14:42,932 And now for the Y direction 366 00:14:42,932 --> 00:14:45,622 we can use the definition of sine of theta. 367 00:14:45,622 --> 00:14:49,047 Sine of theta is F7 in the Y direction, 368 00:14:49,047 --> 00:14:50,499 which is the opposite, 369 00:14:50,499 --> 00:14:53,604 because sine is opposite over hypotenuse. 370 00:14:53,604 --> 00:14:56,844 So in this case the opposite is F7 in the Y direction, 371 00:14:56,844 --> 00:14:59,705 over the hypotenuse, the hypotenuse is the total vector 372 00:14:59,705 --> 00:15:02,228 which is 45 newtons, the magnitude of the total vector, 373 00:15:02,228 --> 00:15:05,127 so, we get that F7 in the Y direction 374 00:15:05,127 --> 00:15:09,127 is gonna be 45 newtons times sine of 30 degrees. 375 00:15:11,188 --> 00:15:14,072 So I can take this, this is the Y component, 376 00:15:14,072 --> 00:15:17,852 I can plug this over into, how am I gonna get there 377 00:15:17,852 --> 00:15:19,468 without crossing a line? 378 00:15:19,468 --> 00:15:22,563 I'm gonna take this and plug it, 379 00:15:22,563 --> 00:15:23,396 over here. 380 00:15:24,895 --> 00:15:27,021 Right into this Y directed equation. 381 00:15:27,021 --> 00:15:28,739 Should it be positive or negative? 382 00:15:28,739 --> 00:15:30,458 The Y component points up, so it's gonna be 383 00:15:30,458 --> 00:15:34,375 plus 45 newtons times sine of 30 degrees, whew. 384 00:15:36,710 --> 00:15:39,002 Okay, so, Newton's Second Law, 385 00:15:39,002 --> 00:15:40,929 now you're equipped, you know how to use it, 386 00:15:40,929 --> 00:15:43,963 these forces might not be asteroid forces, 387 00:15:43,963 --> 00:15:46,767 maybe they're tension or gravity or normal forces 388 00:15:46,767 --> 00:15:48,892 or frictions, maybe there's forces 389 00:15:48,892 --> 00:15:49,881 in all different directions, 390 00:15:49,881 --> 00:15:53,277 but these rules still apply no matter what the force, 391 00:15:53,277 --> 00:15:56,619 whether it's up, down, left, right, or diagonal, 392 00:15:56,619 --> 00:15:58,151 now you know how you can figure out 393 00:15:58,151 --> 00:15:59,674 how to use Newton's Second Law 394 00:15:59,674 --> 00:00:00,000 no matter what direction the force is pointed in.