1 00:00:00,196 --> 00:00:02,215 - [Voiceover] Check out this fine looking sneaker 2 00:00:02,215 --> 00:00:04,826 right here, we're gonna use this shoe to illustrate 3 00:00:04,826 --> 00:00:07,220 some more challenging normal force problems 4 00:00:07,220 --> 00:00:09,829 and we're gonna take this as an opportunity to discuss 5 00:00:09,829 --> 00:00:11,935 a lot of the misconceptions that people have about 6 00:00:11,935 --> 00:00:13,129 the normal force. 7 00:00:13,129 --> 00:00:15,312 So one misconception is that people forget 8 00:00:15,312 --> 00:00:17,332 normal force is a contact force. 9 00:00:17,332 --> 00:00:20,317 You only have a normal force when two surfaces 10 00:00:20,317 --> 00:00:22,534 are in contact, so when the shoe's in contact with 11 00:00:22,534 --> 00:00:24,844 the floor, there will be a normal force on the shoe 12 00:00:24,844 --> 00:00:26,529 and a normal force on the floor. 13 00:00:26,529 --> 00:00:28,680 Or if the shoe were in contact with the wall, 14 00:00:28,680 --> 00:00:30,575 there would be a normal force on the wall 15 00:00:30,575 --> 00:00:32,055 and a normal force on the shoe. 16 00:00:32,055 --> 00:00:34,150 But if the shoe were just falling through the air, 17 00:00:34,150 --> 00:00:36,000 here's what happens for a lot of people. 18 00:00:36,000 --> 00:00:37,650 Let's say the shoe's just falling, 19 00:00:37,650 --> 00:00:39,088 and you got a question and the question said, 20 00:00:39,088 --> 00:00:41,230 draw the forces that are exerted on the shoe 21 00:00:41,230 --> 00:00:42,757 while it's falling through the air. 22 00:00:42,757 --> 00:00:44,785 People get so used to having normal forces 23 00:00:44,785 --> 00:00:48,661 that they make a mistake, they do this, they say alright, 24 00:00:48,661 --> 00:00:50,172 let me draw it over here. 25 00:00:50,172 --> 00:00:52,196 They say there's a gravitational force and that's just fine. 26 00:00:52,196 --> 00:00:54,417 There will be a gravitational force, there's always gravity, 27 00:00:54,417 --> 00:00:56,148 the Earth's always pulling down, 28 00:00:56,148 --> 00:00:58,337 and it pulls down with an amount mg. 29 00:00:58,337 --> 00:01:00,734 But they're so used to having normal forces, 30 00:01:00,734 --> 00:01:03,780 I mean normal forces pop up in so many different questions 31 00:01:03,780 --> 00:01:05,769 it's almost just like a reflex, 32 00:01:05,769 --> 00:01:08,435 people just automatically put, whoop, there's a normal force 33 00:01:08,435 --> 00:01:10,068 there's gotta be a normal force, right? 34 00:01:10,068 --> 00:01:11,509 There's always a normal force? 35 00:01:11,509 --> 00:01:13,571 But there isn't always a normal force, if the shoe 36 00:01:13,571 --> 00:01:16,783 is not in contact with the surface, you don't have a normal 37 00:01:16,783 --> 00:01:20,160 force, it's not until this shoe makes it to the ground 38 00:01:20,160 --> 00:01:22,968 or touches another surface that you'll have that 39 00:01:22,968 --> 00:01:25,117 normal force, so if we stick this shoe right here 40 00:01:25,117 --> 00:01:27,429 and we let it rest on the ground, 41 00:01:27,429 --> 00:01:29,465 now you'll have a normal force and that normal force 42 00:01:29,465 --> 00:01:32,676 will point up, and this is what people wanna say 43 00:01:32,676 --> 00:01:35,145 and it's true when the surfaces are in contact 44 00:01:35,145 --> 00:01:36,586 but if they're not in contact, 45 00:01:36,586 --> 00:01:38,149 you don't have a normal force. 46 00:01:38,149 --> 00:01:40,452 And then here's another misconception, 47 00:01:40,452 --> 00:01:43,295 people think the normal force is always equal to mg, 48 00:01:43,295 --> 00:01:45,269 because again, it's equal to mg 49 00:01:45,269 --> 00:01:48,035 in so many different scenarios that people just 50 00:01:48,035 --> 00:01:50,523 wanna say well it's always equal to mg, and again, 51 00:01:50,523 --> 00:01:51,889 it's just like a reaction. 52 00:01:51,889 --> 00:01:54,602 People see normal force, they just automatically replace it 53 00:01:54,602 --> 00:01:57,116 with mg, and that'll be true in the simple case, 54 00:01:57,116 --> 00:01:59,546 but I'll show you coming up how that's not gonna be true 55 00:01:59,546 --> 00:02:01,438 and what you do if it's not true. 56 00:02:01,438 --> 00:02:03,791 So for instance if we wanted to find what's the normal force 57 00:02:03,791 --> 00:02:06,182 if this shoe has a mass m, 58 00:02:06,182 --> 00:02:08,407 so let's assume that the shoe has a mass m, 59 00:02:08,407 --> 00:02:10,225 what would the normal force be? 60 00:02:10,225 --> 00:02:11,751 We can use Newton's second law, 61 00:02:11,751 --> 00:02:13,854 we can always use Newton's second law, 62 00:02:13,854 --> 00:02:17,901 so we'll say that acceleration equals the net force 63 00:02:17,901 --> 00:02:21,294 divided by the mass, and in this case, 64 00:02:21,294 --> 00:02:23,223 since these are vertical forces, 65 00:02:23,223 --> 00:02:24,867 I'm gonna consider the acceleration 66 00:02:24,867 --> 00:02:26,523 in the vertical direction and the net force 67 00:02:26,523 --> 00:02:28,169 in the vertical direction. 68 00:02:28,169 --> 00:02:30,233 And so what is the acceleration for the shoe vertically 69 00:02:30,233 --> 00:02:33,118 if it's just sitting here in a room, sitting on the ground, 70 00:02:33,118 --> 00:02:35,717 at rest and not changing it's motion, 71 00:02:35,717 --> 00:02:37,807 not changing it's velocity, the acceleration's just gonna 72 00:02:37,807 --> 00:02:40,038 be zero, so the vertical acceleration, 73 00:02:40,038 --> 00:02:42,637 acceleration, excuse me, should be zero. 74 00:02:42,637 --> 00:02:46,219 For the net force, I've got an upward normal force, 75 00:02:46,219 --> 00:02:48,040 so I'm gonna make that positive, 76 00:02:48,040 --> 00:02:50,675 if fn represents the magnitude of the normal force, 77 00:02:50,675 --> 00:02:54,224 this would be positive Fn, I'm just gonna put positive here 78 00:02:54,224 --> 00:02:56,031 even though I don't really need it but to show you 79 00:02:56,031 --> 00:02:58,204 that it's upward, we're gonna consider upward to be positive 80 00:02:58,204 --> 00:03:00,630 and then I've got this downward gravitational force, 81 00:03:00,630 --> 00:03:04,053 and if mg represents the size of the gravitational force, 82 00:03:04,053 --> 00:03:06,737 I'm gonna put a negative here to represent that that 83 00:03:06,737 --> 00:03:09,746 gravitational force is down, and then I divide by 84 00:03:09,746 --> 00:03:13,966 the mass of the shoe and if I do this I get that 85 00:03:13,966 --> 00:03:16,426 these two forces, this net force divided by the mass 86 00:03:16,426 --> 00:03:19,194 has to be zero, according to Newton's second law. 87 00:03:19,194 --> 00:03:22,085 But I can multiply both sides by the mass and if I do that, 88 00:03:22,085 --> 00:03:24,685 the left hand side is still zero, 89 00:03:24,685 --> 00:03:27,609 and I'll get that this is equal to the normal force 90 00:03:27,609 --> 00:03:31,359 minus mg, so I'll have normal force minus mg, 91 00:03:32,978 --> 00:03:35,087 and if I finally solve for the normal force, 92 00:03:35,087 --> 00:03:38,806 I'll get that the normal force is gonna equal mg, 93 00:03:38,806 --> 00:03:42,095 and a lot of people are like yeah I already knew that, duh. 94 00:03:42,095 --> 00:03:45,067 Normal force is always equal to mg, but it's only equal 95 00:03:45,067 --> 00:03:47,298 to mg in this case because those were the only two forces, 96 00:03:47,298 --> 00:03:49,435 look at the assumptions we made. 97 00:03:49,435 --> 00:03:51,829 Only two forces were the normal force and the 98 00:03:51,829 --> 00:03:54,427 gravitational force and we assumed that the acceleration 99 00:03:54,427 --> 00:03:57,270 was zero, if you relax any of those requirements, 100 00:03:57,270 --> 00:04:00,614 normal force is no longer going to be equal to mg. 101 00:04:00,614 --> 00:04:02,679 And it was on a horizontal surface, 102 00:04:02,679 --> 00:04:05,321 if you relax that requirement, again, there's no reason 103 00:04:05,321 --> 00:04:07,584 to think this has to be in the Y direction, 104 00:04:07,584 --> 00:04:09,487 you could have normal forces in the X direction. 105 00:04:09,487 --> 00:04:12,407 So let's slowly, one point at a time, 106 00:04:12,407 --> 00:04:14,687 try to relax some of these requirements and see what 107 00:04:14,687 --> 00:04:16,999 that does to the normal force. 108 00:04:16,999 --> 00:04:19,935 In other words, what if we just added another force? 109 00:04:19,935 --> 00:04:22,205 What if we let the shoe sit here on the ground 110 00:04:22,205 --> 00:04:23,888 and I push down on it? 111 00:04:23,888 --> 00:04:26,899 So I'm pushing down on this shoe, I'm gonna say I'm pushing 112 00:04:26,899 --> 00:04:31,656 down with a force, I'll just call it F1, so a force 113 00:04:31,656 --> 00:04:34,586 of magnitude, F1, and it's pointing downward, 114 00:04:34,586 --> 00:04:36,574 how would that change this now? 115 00:04:36,574 --> 00:04:38,297 So this is, we're stepping it up, this is gonna be a little 116 00:04:38,297 --> 00:04:40,649 harder, what do we do? 117 00:04:40,649 --> 00:04:42,863 Well the acceleration is still zero, let's say it's still 118 00:04:42,863 --> 00:04:45,292 just sitting there, so we don't have to do anything 119 00:04:45,292 --> 00:04:47,019 with the left hand side that's still zero, 120 00:04:47,019 --> 00:04:49,081 multiplying by m still makes that zero, 121 00:04:49,081 --> 00:04:50,817 but now up here in this force up here, 122 00:04:50,817 --> 00:04:53,119 I'm gonna have another force, I'm gonna have F1, 123 00:04:53,119 --> 00:04:55,639 that points down so in my force diagram 124 00:04:55,639 --> 00:04:58,862 I'd have another force that points down, F1, 125 00:04:58,862 --> 00:05:01,465 that means I'd have to subtract it when I find 126 00:05:01,465 --> 00:05:03,574 the net vertical force, I'd have F1, 127 00:05:03,574 --> 00:05:06,473 this would be a negative F1 right here, 128 00:05:06,473 --> 00:05:09,482 and when I solve for Fn I'd add mg to both sides 129 00:05:09,482 --> 00:05:12,331 to cancel it and then I'd add F1 to both sides 130 00:05:12,331 --> 00:05:14,769 to cancel this F1, this negative F1, 131 00:05:14,769 --> 00:05:16,686 and I'd get mg plus F1. 132 00:05:17,653 --> 00:05:19,600 So I get the normal force is gonna be bigger, 133 00:05:19,600 --> 00:05:22,319 bigger by an amount F2 and that makes sense, 134 00:05:22,319 --> 00:05:25,043 if you push down on a, oh no F2, wow, 135 00:05:25,043 --> 00:05:28,873 F1, sorry about that, it's gonna be bigger by an amount F1, 136 00:05:28,873 --> 00:05:32,309 so if I push down with an extra 10 Newtons of force, 137 00:05:32,309 --> 00:05:34,161 there's more pressure, right? 138 00:05:34,161 --> 00:05:36,306 That makes sense, the pressure between the ground 139 00:05:36,306 --> 00:05:37,877 and the shoe is gonna be greater, you're squashing 140 00:05:37,877 --> 00:05:40,556 these two surfaces together with greater force, 141 00:05:40,556 --> 00:05:42,535 so the ground's gotta push up to keep the shoe 142 00:05:42,535 --> 00:05:45,789 out of the surface, that's what this normal force does, 143 00:05:45,789 --> 00:05:48,058 it exerts a force to keep the object out of the surface, 144 00:05:48,058 --> 00:05:51,390 to keep the object from penetrating that surface, 145 00:05:51,390 --> 00:05:54,975 so if I push down on an object, into a surface, 146 00:05:54,975 --> 00:05:57,904 that normal force increases and it increases by the amount 147 00:05:57,904 --> 00:06:00,005 you're pushing down, so that makes sense. 148 00:06:00,005 --> 00:06:01,984 If you had an upward force, let's say you had an 149 00:06:01,984 --> 00:06:04,289 upward force, someone's pulling up on the shoe 150 00:06:04,289 --> 00:06:06,892 while you push down, you're fighting over the shoe, 151 00:06:06,892 --> 00:06:09,331 you're wrestling over it with somebody because they just, 152 00:06:09,331 --> 00:06:12,343 they love the shoe, they recognize the beauty of the shoe, 153 00:06:12,343 --> 00:06:15,475 well crafted shoe, so if there's an F2 pointing up, 154 00:06:15,475 --> 00:06:17,491 we now have another force in our diagram, 155 00:06:17,491 --> 00:06:20,303 that force would point up, we would call this F2, 156 00:06:20,303 --> 00:06:22,323 over here how would this change? 157 00:06:22,323 --> 00:06:24,009 Again, still acceleration to zero, 158 00:06:24,009 --> 00:06:26,078 but I'd have an upward force now so I'd have to add 159 00:06:26,078 --> 00:06:29,505 F2 vertically because that's another force, 160 00:06:29,505 --> 00:06:31,531 I'd have a plus F2 right here, 161 00:06:31,531 --> 00:06:34,007 and then over here when I solve for this, 162 00:06:34,007 --> 00:06:37,229 I add mg to both sides, I add F1 to both sides, 163 00:06:37,229 --> 00:06:40,291 and I have to subtract F2 from both sides 164 00:06:40,291 --> 00:06:43,791 so now I'd have Fn is mg plus F1 minus F2, 165 00:06:44,719 --> 00:06:47,973 this also makes sense, if you pull up on a shoe, 166 00:06:47,973 --> 00:06:50,980 you're relieving some of the pressure between the shoe 167 00:06:50,980 --> 00:06:53,245 and the other surface, the shoe and the floor. 168 00:06:53,245 --> 00:06:56,627 So if I pull up with 20 Newtons I'm gonna reduce 169 00:06:56,627 --> 00:06:58,899 the normal force by 20 Newtons because I'm relieving 170 00:06:58,899 --> 00:07:01,781 some of that pressure between the shoe and the floor. 171 00:07:01,781 --> 00:07:03,510 Let's make it even harder. 172 00:07:03,510 --> 00:07:06,064 Let's make this thing scary, sometimes you get really 173 00:07:06,064 --> 00:07:08,871 crazy problems and you don't know what to do, let's say, 174 00:07:08,871 --> 00:07:12,051 we have another force, let's say this force is gonna be 175 00:07:12,051 --> 00:07:15,968 a diagonal force, so we're gonna pull this way. 176 00:07:17,624 --> 00:07:21,541 That was not a well drawn force, let me draw it like this. 177 00:07:21,541 --> 00:07:24,016 So we got a force this way at an angle. 178 00:07:24,016 --> 00:07:26,516 Now we're talking, this is F3. 179 00:07:28,182 --> 00:07:32,677 F3, at an angle of, we'll call it Fi, so the angle from 180 00:07:32,677 --> 00:07:35,344 this horizontal line here is Fi. 181 00:07:37,131 --> 00:07:38,830 Now what do we do? 182 00:07:38,830 --> 00:07:41,384 So I've got this crooked angle in here, now this F3 is 183 00:07:41,384 --> 00:07:44,845 gonna be pointing this way, so I'll add another force 184 00:07:44,845 --> 00:07:48,183 to my force diagram, and I can figure out how to include 185 00:07:48,183 --> 00:07:53,018 this into my vertical force version of Newton's second law, 186 00:07:53,018 --> 00:07:56,106 I can't include the entire F3 force, here's a mistake 187 00:07:56,106 --> 00:07:58,914 people make, they wanna just add F3 or subtract F3, 188 00:07:58,914 --> 00:08:02,126 but I can't do that, this is the vertical form of 189 00:08:02,126 --> 00:08:04,608 Newton's second law, this is only applying to the vertical 190 00:08:04,608 --> 00:08:07,791 direction, the Y direction, but F3 is pointing both 191 00:08:07,791 --> 00:08:09,776 vertically and horizontally. 192 00:08:09,776 --> 00:08:12,656 So I have to only include the vertical part of F3 193 00:08:12,656 --> 00:08:15,146 in this formula so what I have to do is say that alright 194 00:08:15,146 --> 00:08:17,197 F3 is gonna have a vertical component, 195 00:08:17,197 --> 00:08:20,620 that vertical component, I'll call it F3 Y, 196 00:08:20,620 --> 00:08:22,779 for F3 in the vertical direction. 197 00:08:22,779 --> 00:08:24,965 And it's also gonna have a horizontal component. 198 00:08:24,965 --> 00:08:29,338 I'll just call that F3 X for F3 in the horizontal direction. 199 00:08:29,338 --> 00:08:32,671 So if I wanna solve for F3 Y, I'll just use the definition 200 00:08:32,671 --> 00:08:35,589 of sign and I know to use sign because this side is 201 00:08:35,589 --> 00:08:38,144 the opposite to this angle, I know sign 202 00:08:38,144 --> 00:08:40,818 relates opposite side, so I'm gonna write this as 203 00:08:40,818 --> 00:08:45,232 sign of Fi is gonna equal the opposite side is F3 Y 204 00:08:45,232 --> 00:08:48,982 so F3 in the Y direction divided by F3 total, 205 00:08:50,416 --> 00:08:53,916 the total magnitude of F3, and if I solve this for F3 Y, 206 00:08:53,916 --> 00:08:58,083 I get F3 in the Y direction is gonna equal F3 times sign 207 00:08:59,808 --> 00:09:03,561 of Fi, now I can include this in my force, my net force, 208 00:09:03,561 --> 00:09:07,572 because this points upward, so since it points up, 209 00:09:07,572 --> 00:09:10,095 this vertical component's gonna add a plus, 210 00:09:10,095 --> 00:09:14,341 F3 sin theta over here, or sorry not theta, 211 00:09:14,341 --> 00:09:18,508 it's gonna be F3 sin Fi, and I'll have a plus F3 sin fi 212 00:09:20,447 --> 00:09:24,883 right here, and when we subtract this F3 sin fi from the 213 00:09:24,883 --> 00:09:27,476 other side to get it over to here, 214 00:09:27,476 --> 00:09:31,141 we're gonna get minus F3 sign fi and that makes sense 215 00:09:31,141 --> 00:09:34,860 because if we pull up, we know we're reducing some 216 00:09:34,860 --> 00:09:37,510 of the pressure, we'll reduce the normal force, 217 00:09:37,510 --> 00:09:39,812 so this component, look at this component points up, 218 00:09:39,812 --> 00:09:41,709 it's reducing some of the pressure 219 00:09:41,709 --> 00:09:44,266 on the bottom of the shoe, the normal force goes down, 220 00:09:44,266 --> 00:09:47,523 and so we subtract the F3 sin fi. 221 00:09:47,523 --> 00:09:50,454 And one more way to step this problem up to the next level 222 00:09:50,454 --> 00:09:53,258 would be to say that this room isn't really just a room, 223 00:09:53,258 --> 00:09:54,905 maybe it's an elevator, 224 00:09:54,905 --> 00:09:56,926 and this elevator is accelerating upward 225 00:09:56,926 --> 00:10:00,132 with some acceleration A zero, in that case, 226 00:10:00,132 --> 00:10:02,564 nothing would change on this right hand side. 227 00:10:02,564 --> 00:10:04,914 Sometimes people think if there's acceleration, 228 00:10:04,914 --> 00:10:07,807 there's gonna be some new force, but if these are the forces 229 00:10:07,807 --> 00:10:10,741 those are the forces, the only thing that changes over here 230 00:10:10,741 --> 00:10:13,334 if this was in an elevator that's accelerating up, 231 00:10:13,334 --> 00:10:16,543 is that instead of zero, you'd replace this with a zero 232 00:10:16,543 --> 00:10:19,391 or whatever the acceleration is, that's it, 233 00:10:19,391 --> 00:10:21,529 that's the only change, you could still solve for fn 234 00:10:21,529 --> 00:10:23,958 the same way, when you multiply by m it wouldn't be 235 00:10:23,958 --> 00:10:26,767 zero on the left anymore, you'd have a m a zero, 236 00:10:26,767 --> 00:10:30,394 and then a plus m a zero when you solve 237 00:10:30,394 --> 00:10:32,255 for the normal force. 238 00:10:32,255 --> 00:10:34,569 Alright, I think we've pretty much exhausted 239 00:10:34,569 --> 00:10:36,875 this example of a shoe on the floor, 240 00:10:36,875 --> 00:10:39,222 it's probably harder than any example you'll see 241 00:10:39,222 --> 00:10:41,367 but now you know how to handle any type of force 242 00:10:41,367 --> 00:00:00,000 you might meet or acceleration.