[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.71,0:00:01.62,Default,,0000,0000,0000,,- [Voiceover] Oh, it's time.
Dialogue: 0,0:00:01.62,0:00:03.39,Default,,0000,0000,0000,,It's time for the super\Nhot tension problem.
Dialogue: 0,0:00:03.39,0:00:04.84,Default,,0000,0000,0000,,We're about to do this right here.
Dialogue: 0,0:00:04.84,0:00:07.03,Default,,0000,0000,0000,,We've got our super hot can of red peppers
Dialogue: 0,0:00:07.03,0:00:08.82,Default,,0000,0000,0000,,hanging from these strings.
Dialogue: 0,0:00:08.82,0:00:11.76,Default,,0000,0000,0000,,We want to know what the\Ntension is in these ropes.
Dialogue: 0,0:00:11.76,0:00:15.08,Default,,0000,0000,0000,,This is for real now, this\Nis a real tension problem.
Dialogue: 0,0:00:15.08,0:00:16.31,Default,,0000,0000,0000,,And here's the deal.
Dialogue: 0,0:00:16.31,0:00:18.38,Default,,0000,0000,0000,,You might look at this,\Nyou might get frightened.
Dialogue: 0,0:00:18.38,0:00:20.23,Default,,0000,0000,0000,,You might think, I've gotta come up with
Dialogue: 0,0:00:20.23,0:00:22.55,Default,,0000,0000,0000,,a completely new strategy to tackle this.
Dialogue: 0,0:00:22.55,0:00:24.44,Default,,0000,0000,0000,,I've gotta throw away\Neverything I've learned
Dialogue: 0,0:00:24.44,0:00:25.90,Default,,0000,0000,0000,,and just try something new.
Dialogue: 0,0:00:25.90,0:00:27.06,Default,,0000,0000,0000,,And that's a lie.
Dialogue: 0,0:00:27.06,0:00:28.50,Default,,0000,0000,0000,,You should not lie to yourself.
Dialogue: 0,0:00:28.50,0:00:30.44,Default,,0000,0000,0000,,Use the same process.
Dialogue: 0,0:00:30.44,0:00:32.29,Default,,0000,0000,0000,,We're gonna use the same process we used
Dialogue: 0,0:00:32.29,0:00:33.41,Default,,0000,0000,0000,,for the easy tension problems,
Dialogue: 0,0:00:33.41,0:00:35.13,Default,,0000,0000,0000,,because it's gonna lead\Nus to the answer again.
Dialogue: 0,0:00:35.13,0:00:39.17,Default,,0000,0000,0000,,Be careful. Don't stray\Nfrom the strategy here.
Dialogue: 0,0:00:39.17,0:00:40.11,Default,,0000,0000,0000,,The strategy works.
Dialogue: 0,0:00:40.11,0:00:41.65,Default,,0000,0000,0000,,So we're gonna draw our\Nforce diagram first.
Dialogue: 0,0:00:41.65,0:00:43.18,Default,,0000,0000,0000,,That's what we always do.
Dialogue: 0,0:00:43.18,0:00:45.03,Default,,0000,0000,0000,,We're gonna say that the forces are
Dialogue: 0,0:00:45.03,0:00:48.17,Default,,0000,0000,0000,,force of gravity on\Nthis can of red peppers,
Dialogue: 0,0:00:48.17,0:00:50.54,Default,,0000,0000,0000,,which is MG, and if it's 3 kilograms,
Dialogue: 0,0:00:50.54,0:00:52.96,Default,,0000,0000,0000,,we know 3 kilograms times about 10,
Dialogue: 0,0:00:52.96,0:00:55.71,Default,,0000,0000,0000,,we're gonna say, let's\Napproximate G as 10 again
Dialogue: 0,0:00:55.71,0:00:57.42,Default,,0000,0000,0000,,to make the numbers come out nice.
Dialogue: 0,0:00:57.42,0:01:00.82,Default,,0000,0000,0000,,So instead of using 9.8,\Nwe'll say G is about 10,
Dialogue: 0,0:01:00.82,0:01:02.91,Default,,0000,0000,0000,,and so we'll say 3 kilograms
Dialogue: 0,0:01:02.91,0:01:07.08,Default,,0000,0000,0000,,times 10 meters per second\Nsquared is gonna be 30 Newtons.
Dialogue: 0,0:01:09.95,0:01:12.73,Default,,0000,0000,0000,,And so the force of gravity\Ndownward is 30 Newtons.
Dialogue: 0,0:01:12.73,0:01:14.08,Default,,0000,0000,0000,,What other forces do we have?
Dialogue: 0,0:01:14.08,0:01:17.33,Default,,0000,0000,0000,,We've got this T1, remember\Ntension does not push.
Dialogue: 0,0:01:17.33,0:01:20.20,Default,,0000,0000,0000,,Ropes can't push, ropes can only pull,
Dialogue: 0,0:01:20.20,0:01:21.88,Default,,0000,0000,0000,,so T1's gonna pull that way.
Dialogue: 0,0:01:21.88,0:01:23.96,Default,,0000,0000,0000,,So I'm gonna draw T1 coming this way.
Dialogue: 0,0:01:23.96,0:01:25.38,Default,,0000,0000,0000,,So here's our T1.
Dialogue: 0,0:01:26.22,0:01:28.45,Default,,0000,0000,0000,,And then we're gonna have\NT2 pointing this way,
Dialogue: 0,0:01:28.45,0:01:29.63,Default,,0000,0000,0000,,so this is T2.
Dialogue: 0,0:01:29.63,0:01:31.73,Default,,0000,0000,0000,,Again, T2 pulls, just like all tension.
Dialogue: 0,0:01:31.73,0:01:34.02,Default,,0000,0000,0000,,Tension pulls, tension can't push.
Dialogue: 0,0:01:34.02,0:01:37.10,Default,,0000,0000,0000,,So I've got tension 2 going this way.
Dialogue: 0,0:01:39.58,0:01:41.66,Default,,0000,0000,0000,,That's it, that's our force diagram.
Dialogue: 0,0:01:41.66,0:01:42.58,Default,,0000,0000,0000,,There's no other forces.
Dialogue: 0,0:01:42.58,0:01:43.85,Default,,0000,0000,0000,,I don't draw a normal force,
Dialogue: 0,0:01:43.85,0:01:46.28,Default,,0000,0000,0000,,'cause this can isn't in\Ncontact with another surface.
Dialogue: 0,0:01:46.28,0:01:48.96,Default,,0000,0000,0000,,So there's no normal force,\Nyou've got these two tensions,
Dialogue: 0,0:01:48.96,0:01:50.44,Default,,0000,0000,0000,,the force of gravity.
Dialogue: 0,0:01:50.44,0:01:52.16,Default,,0000,0000,0000,,And now we do the same thing we always do.
Dialogue: 0,0:01:52.16,0:01:54.74,Default,,0000,0000,0000,,After our force diagram,\Nwe use Newton's Second Law
Dialogue: 0,0:01:54.74,0:01:56.81,Default,,0000,0000,0000,,in one direction or another.
Dialogue: 0,0:01:56.81,0:01:57.86,Default,,0000,0000,0000,,So let's do it.
Dialogue: 0,0:01:57.86,0:02:00.69,Default,,0000,0000,0000,,Let's say that acceleration\Nis the net force
Dialogue: 0,0:02:00.69,0:02:03.78,Default,,0000,0000,0000,,in a given direction, divided by the mass.
Dialogue: 0,0:02:03.78,0:02:05.83,Default,,0000,0000,0000,,Which direction did we pick again?
Dialogue: 0,0:02:05.83,0:02:08.79,Default,,0000,0000,0000,,It's hard to say, we've\Ngot forces vertical,
Dialogue: 0,0:02:08.79,0:02:10.14,Default,,0000,0000,0000,,we've got forces horizontal.
Dialogue: 0,0:02:10.14,0:02:13.26,Default,,0000,0000,0000,,There's only two directions to\Npick, X or Y in this problem.
Dialogue: 0,0:02:13.26,0:02:15.22,Default,,0000,0000,0000,,We're gonna pick the vertical direction,
Dialogue: 0,0:02:15.22,0:02:17.09,Default,,0000,0000,0000,,even though it doesn't\Nreally matter too much.
Dialogue: 0,0:02:17.09,0:02:19.42,Default,,0000,0000,0000,,But because we know one of\Nthe forces in the vertical
Dialogue: 0,0:02:19.42,0:02:20.91,Default,,0000,0000,0000,,direction, we know the force of gravity.
Dialogue: 0,0:02:20.91,0:02:23.09,Default,,0000,0000,0000,,Force of gravity is 30 Newtons.
Dialogue: 0,0:02:23.09,0:02:25.27,Default,,0000,0000,0000,,Usually that's a guod\Nstrategy, pick the direction
Dialogue: 0,0:02:25.27,0:02:27.77,Default,,0000,0000,0000,,that you know something about at least.
Dialogue: 0,0:02:27.77,0:02:29.53,Default,,0000,0000,0000,,So we're gonna do that here.
Dialogue: 0,0:02:29.53,0:02:31.39,Default,,0000,0000,0000,,We're gonna say that the\Nacceleration vertically
Dialogue: 0,0:02:31.39,0:02:33.90,Default,,0000,0000,0000,,equals to the net force\Nvertically over the mass.
Dialogue: 0,0:02:33.90,0:02:34.97,Default,,0000,0000,0000,,And so now we plug in.
Dialogue: 0,0:02:34.97,0:02:36.78,Default,,0000,0000,0000,,If this can is just sitting here,
Dialogue: 0,0:02:36.78,0:02:39.47,Default,,0000,0000,0000,,if there's no acceleration,\Nif this is in not an elevator
Dialogue: 0,0:02:39.47,0:02:42.56,Default,,0000,0000,0000,,transporting these peppers up or down,
Dialogue: 0,0:02:42.56,0:02:44.45,Default,,0000,0000,0000,,and it's not in a rocket,\Nif it's just sitting here
Dialogue: 0,0:02:44.45,0:02:47.47,Default,,0000,0000,0000,,with no acceleration, our\Nacceleration will be zero.
Dialogue: 0,0:02:47.47,0:02:50.100,Default,,0000,0000,0000,,That's gonna equal the net force\Nand the vertical direction.
Dialogue: 0,0:02:50.100,0:02:52.38,Default,,0000,0000,0000,,So what are we gonna have?
Dialogue: 0,0:02:52.38,0:02:54.20,Default,,0000,0000,0000,,So what are the forces in\Nthe vertical direction here?
Dialogue: 0,0:02:54.20,0:02:57.22,Default,,0000,0000,0000,,One force is this 30\NNewton force of gravity.
Dialogue: 0,0:02:57.22,0:03:00.57,Default,,0000,0000,0000,,This points down, we're gonna\Nassume upward is positive,
Dialogue: 0,0:03:00.57,0:03:02.19,Default,,0000,0000,0000,,that means down in a negative.
Dialogue: 0,0:03:02.19,0:03:03.61,Default,,0000,0000,0000,,So I'll just put -30 Newtons.
Dialogue: 0,0:03:03.61,0:03:05.92,Default,,0000,0000,0000,,I could have written -MG,
Dialogue: 0,0:03:05.92,0:03:07.46,Default,,0000,0000,0000,,but we already knew it was 30 Newtons,
Dialogue: 0,0:03:07.46,0:03:08.92,Default,,0000,0000,0000,,so I'll write -30 Newtons.
Dialogue: 0,0:03:08.92,0:03:10.58,Default,,0000,0000,0000,,Then we've got T1 and T2.
Dialogue: 0,0:03:10.58,0:03:12.26,Default,,0000,0000,0000,,Both of those point up.
Dialogue: 0,0:03:12.26,0:03:13.65,Default,,0000,0000,0000,,But they don't completely point up,
Dialogue: 0,0:03:13.65,0:03:15.00,Default,,0000,0000,0000,,they partially point up.
Dialogue: 0,0:03:15.00,0:03:17.33,Default,,0000,0000,0000,,So part of them points to the right,
Dialogue: 0,0:03:17.33,0:03:19.58,Default,,0000,0000,0000,,part of them points upward.
Dialogue: 0,0:03:19.58,0:03:22.66,Default,,0000,0000,0000,,Only this vertical\Ncomponent, we'll call it T1Y,
Dialogue: 0,0:03:22.66,0:03:25.18,Default,,0000,0000,0000,,is gonna get included\Ninto this calculation,
Dialogue: 0,0:03:25.18,0:03:28.21,Default,,0000,0000,0000,,'cause this calculation\Nonly uses Y directed forces.
Dialogue: 0,0:03:28.21,0:03:30.87,Default,,0000,0000,0000,,And the reason is only Y directed forces,
Dialogue: 0,0:03:30.87,0:03:34.32,Default,,0000,0000,0000,,vertical forces, affect\Nthe vertical acceleration.
Dialogue: 0,0:03:34.32,0:03:36.43,Default,,0000,0000,0000,,So this T1Y points upward,
Dialogue: 0,0:03:36.43,0:03:39.78,Default,,0000,0000,0000,,I'll do plus T1 in the Y direction.
Dialogue: 0,0:03:39.78,0:03:41.68,Default,,0000,0000,0000,,And similarly, this T2.
Dialogue: 0,0:03:41.68,0:03:44.11,Default,,0000,0000,0000,,It doesn't all point vertically,
Dialogue: 0,0:03:44.11,0:03:45.59,Default,,0000,0000,0000,,only part of it points vertically.
Dialogue: 0,0:03:45.59,0:03:49.14,Default,,0000,0000,0000,,So I'll write this as\NT2 in the Y direction.
Dialogue: 0,0:03:49.14,0:03:50.44,Default,,0000,0000,0000,,And that's also upward,
Dialogue: 0,0:03:50.44,0:03:52.60,Default,,0000,0000,0000,,so since that's up, I'll count it
Dialogue: 0,0:03:52.60,0:03:55.31,Default,,0000,0000,0000,,as plus T2 in the Y direction.
Dialogue: 0,0:03:55.31,0:03:57.10,Default,,0000,0000,0000,,And that's it, that's all our forces.
Dialogue: 0,0:03:57.10,0:04:00.48,Default,,0000,0000,0000,,Notice we can't plug in\Nthe total amount T2 in this
Dialogue: 0,0:04:00.48,0:04:02.87,Default,,0000,0000,0000,,formula, 'cause only part of it points up.
Dialogue: 0,0:04:02.87,0:04:05.34,Default,,0000,0000,0000,,Similarly, we have to plug in\Nonly the vertical component
Dialogue: 0,0:04:05.34,0:04:09.03,Default,,0000,0000,0000,,of the T1 force because only\Npart of it points vertically.
Dialogue: 0,0:04:09.03,0:04:13.18,Default,,0000,0000,0000,,And then we divide by the\Nmass, the mass is 3 kilograms.
Dialogue: 0,0:04:13.18,0:04:15.88,Default,,0000,0000,0000,,But we're gonna multiply\Nboth sides by 3 kilograms,
Dialogue: 0,0:04:15.88,0:04:19.67,Default,,0000,0000,0000,,and we're gonna get zero\Nequals all of this right here,
Dialogue: 0,0:04:19.67,0:04:21.06,Default,,0000,0000,0000,,so I'll just copy this right here.
Dialogue: 0,0:04:21.06,0:04:25.23,Default,,0000,0000,0000,,We use this over again,\Nthat comes down right there.
Dialogue: 0,0:04:26.49,0:04:29.33,Default,,0000,0000,0000,,But now there's nothing\Non the bottom here.
Dialogue: 0,0:04:29.33,0:04:30.23,Default,,0000,0000,0000,,So what do we do at this point?
Dialogue: 0,0:04:30.23,0:04:31.56,Default,,0000,0000,0000,,Now you might think we're stuck.
Dialogue: 0,0:04:31.56,0:04:33.52,Default,,0000,0000,0000,,I mean, we've got two unknowns in here.
Dialogue: 0,0:04:33.52,0:04:35.60,Default,,0000,0000,0000,,I can't solve for either one,
Dialogue: 0,0:04:35.60,0:04:36.94,Default,,0000,0000,0000,,I don't know either one of these.
Dialogue: 0,0:04:36.94,0:04:38.62,Default,,0000,0000,0000,,I know they have to add up to 30,
Dialogue: 0,0:04:38.62,0:04:40.92,Default,,0000,0000,0000,,so I'd do fine, if I\Nadded 30 to both sides,
Dialogue: 0,0:04:40.92,0:04:43.13,Default,,0000,0000,0000,,I'd realize that these\Ntwo vertical components
Dialogue: 0,0:04:43.13,0:04:45.10,Default,,0000,0000,0000,,of these tension forces added up
Dialogue: 0,0:04:45.10,0:04:47.31,Default,,0000,0000,0000,,have to add up to 30,\Nand that makes sense.
Dialogue: 0,0:04:47.31,0:04:49.32,Default,,0000,0000,0000,,They have to balance the force downward.
Dialogue: 0,0:04:49.32,0:04:52.66,Default,,0000,0000,0000,,But I don't know either of\Nthem, so how do I solve here?
Dialogue: 0,0:04:52.66,0:04:54.19,Default,,0000,0000,0000,,Well, let's do this.
Dialogue: 0,0:04:54.19,0:04:57.38,Default,,0000,0000,0000,,If you ever get stuck on\None of the force equations
Dialogue: 0,0:04:57.38,0:05:00.09,Default,,0000,0000,0000,,for a single direction, just\Ngo to the next equation.
Dialogue: 0,0:05:00.09,0:05:01.89,Default,,0000,0000,0000,,Let's try A in the X direction.
Dialogue: 0,0:05:01.89,0:05:04.05,Default,,0000,0000,0000,,So for A in the X direction,\Nwe have the net force
Dialogue: 0,0:05:04.05,0:05:06.20,Default,,0000,0000,0000,,in the X direction, over the mass,
Dialogue: 0,0:05:06.20,0:05:09.23,Default,,0000,0000,0000,,again, the acceleration is gonna be zero
Dialogue: 0,0:05:09.23,0:05:11.89,Default,,0000,0000,0000,,if these peppers are not\Naccelerating horizontally.
Dialogue: 0,0:05:11.89,0:05:14.27,Default,,0000,0000,0000,,So unless this thing's in\Na train car or something,
Dialogue: 0,0:05:14.27,0:05:16.44,Default,,0000,0000,0000,,and the whole thing's accelerating,
Dialogue: 0,0:05:16.44,0:05:18.08,Default,,0000,0000,0000,,then you might have\Nhorizontal acceleration.
Dialogue: 0,0:05:18.08,0:05:19.95,Default,,0000,0000,0000,,And if it did, it's\Nnot that big of a deal,
Dialogue: 0,0:05:19.95,0:05:21.64,Default,,0000,0000,0000,,you just plug it in there.
Dialogue: 0,0:05:21.64,0:05:23.34,Default,,0000,0000,0000,,But assuming it's acceleration zero,
Dialogue: 0,0:05:23.34,0:05:24.72,Default,,0000,0000,0000,,because the peppers\Nare just sitting there,
Dialogue: 0,0:05:24.72,0:05:25.77,Default,,0000,0000,0000,,not changing their velocity,\Nwe'll plug in zero.
Dialogue: 0,0:05:25.77,0:05:28.21,Default,,0000,0000,0000,,We'll plug in the forces\Nin the X direction.
Dialogue: 0,0:05:28.21,0:05:31.19,Default,,0000,0000,0000,,These are gonna be T1 in the X.
Dialogue: 0,0:05:31.19,0:05:33.93,Default,,0000,0000,0000,,So part of this T1 points\Nin the X direction.
Dialogue: 0,0:05:33.93,0:05:37.57,Default,,0000,0000,0000,,Similarly, part of T2\Npoints in the X direction.
Dialogue: 0,0:05:37.57,0:05:38.71,Default,,0000,0000,0000,,We'll call this T2X.
Dialogue: 0,0:05:38.71,0:05:40.83,Default,,0000,0000,0000,,We use these as the magnitude.
Dialogue: 0,0:05:40.83,0:05:42.99,Default,,0000,0000,0000,,Let's say T2X is the\Nmagnitude of the force
Dialogue: 0,0:05:42.99,0:05:45.14,Default,,0000,0000,0000,,that T2 pulls with to the left,
Dialogue: 0,0:05:45.14,0:05:49.31,Default,,0000,0000,0000,,and T1 is the magnitude that\NT1 pulls with to the right.
Dialogue: 0,0:05:50.72,0:05:53.08,Default,,0000,0000,0000,,So to plug these in, we've got to decide
Dialogue: 0,0:05:53.08,0:05:55.58,Default,,0000,0000,0000,,whether they should be\Npositive or negative.
Dialogue: 0,0:05:55.58,0:05:57.99,Default,,0000,0000,0000,,So this T1X, since it pulls to the right,
Dialogue: 0,0:05:57.99,0:05:59.70,Default,,0000,0000,0000,,T1X will be positive.
Dialogue: 0,0:05:59.70,0:06:02.84,Default,,0000,0000,0000,,We're gonna consider rightward\Nto be the positive direction,
Dialogue: 0,0:06:02.84,0:06:05.25,Default,,0000,0000,0000,,'cause that's the typical\Nconvention that we're gonna adopt.
Dialogue: 0,0:06:05.25,0:06:08.23,Default,,0000,0000,0000,,And T2X pulls to the left.
Dialogue: 0,0:06:08.23,0:06:10.03,Default,,0000,0000,0000,,That's gonna be a negative contribution,
Dialogue: 0,0:06:10.03,0:06:12.59,Default,,0000,0000,0000,,so minus T2 in the X direction.
Dialogue: 0,0:06:12.59,0:06:14.12,Default,,0000,0000,0000,,'Cause leftward would be negative.
Dialogue: 0,0:06:14.12,0:06:16.60,Default,,0000,0000,0000,,We divided by the mass,\Nthe mass was 3 kilograms,
Dialogue: 0,0:06:16.60,0:06:19.31,Default,,0000,0000,0000,,but again, we'll multiply both sides by 3,
Dialogue: 0,0:06:19.31,0:06:23.31,Default,,0000,0000,0000,,we'll get zero equals,\Nand then we just get T,
Dialogue: 0,0:06:23.31,0:06:24.50,Default,,0000,0000,0000,,the same thing up here,
Dialogue: 0,0:06:24.50,0:06:28.67,Default,,0000,0000,0000,,so we'll just copy this\Nthing here, put it down here.
Dialogue: 0,0:06:30.61,0:06:31.67,Default,,0000,0000,0000,,And again, you might be concerned.
Dialogue: 0,0:06:31.67,0:06:33.53,Default,,0000,0000,0000,,I can't solve this either.
Dialogue: 0,0:06:33.53,0:06:37.13,Default,,0000,0000,0000,,I mean, I can solve for\NT1X, but look at what I get.
Dialogue: 0,0:06:37.13,0:06:40.87,Default,,0000,0000,0000,,If I just multi, or if I\Nadded T2X to both sides,
Dialogue: 0,0:06:40.87,0:06:42.43,Default,,0000,0000,0000,,I'm just gonna get T1 in the X direction
Dialogue: 0,0:06:42.43,0:06:45.35,Default,,0000,0000,0000,,has to equal T2 in the X direction.
Dialogue: 0,0:06:46.22,0:06:47.68,Default,,0000,0000,0000,,And that makes sense.
Dialogue: 0,0:06:47.68,0:06:49.47,Default,,0000,0000,0000,,These two forces have to\Nbe equal and opposite,
Dialogue: 0,0:06:49.47,0:06:52.14,Default,,0000,0000,0000,,because they have to cancel so\Nthat you have no acceleration
Dialogue: 0,0:06:52.14,0:06:53.14,Default,,0000,0000,0000,,in the X direction.
Dialogue: 0,0:06:53.14,0:06:55.37,Default,,0000,0000,0000,,And this was not drawn\Nproportionately, sorry,
Dialogue: 0,0:06:55.37,0:06:57.45,Default,,0000,0000,0000,,this should be the exact\Nsame size as this force
Dialogue: 0,0:06:57.45,0:06:59.42,Default,,0000,0000,0000,,because they have to cancel,
Dialogue: 0,0:06:59.42,0:07:01.52,Default,,0000,0000,0000,,since there's no horizontal acceleration.
Dialogue: 0,0:07:01.52,0:07:02.82,Default,,0000,0000,0000,,But what do we do?
Dialogue: 0,0:07:02.82,0:07:05.19,Default,,0000,0000,0000,,We can't solve this equation\Nwe got from X direction.
Dialogue: 0,0:07:05.19,0:07:08.64,Default,,0000,0000,0000,,We can't solve this equation\Nwe got from the Y direction.
Dialogue: 0,0:07:08.64,0:07:11.22,Default,,0000,0000,0000,,Whenever this happens,\Nwhen you get two equations,
Dialogue: 0,0:07:11.22,0:07:12.76,Default,,0000,0000,0000,,and you can't solve either
Dialogue: 0,0:07:12.76,0:07:13.100,Default,,0000,0000,0000,,because there's too many unknowns,
Dialogue: 0,0:07:13.100,0:07:16.67,Default,,0000,0000,0000,,you're gonna have to end up\Nplugging one into the other.
Dialogue: 0,0:07:16.67,0:07:18.41,Default,,0000,0000,0000,,But I can't even do that yet.
Dialogue: 0,0:07:18.41,0:07:20.36,Default,,0000,0000,0000,,I've got four different variables here.
Dialogue: 0,0:07:20.36,0:07:22.28,Default,,0000,0000,0000,,T1X, T2X, T1Y, and T2Y,
Dialogue: 0,0:07:24.30,0:07:25.72,Default,,0000,0000,0000,,these are all four different variables,
Dialogue: 0,0:07:25.72,0:07:28.39,Default,,0000,0000,0000,,I've only got two equations,\NI can't solve this.
Dialogue: 0,0:07:28.39,0:07:30.38,Default,,0000,0000,0000,,So the trick, the trick we're gonna use
Dialogue: 0,0:07:30.38,0:07:31.72,Default,,0000,0000,0000,,that a lot of people don't like doing
Dialogue: 0,0:07:31.72,0:07:33.15,Default,,0000,0000,0000,,because it's a little more sophisticated,
Dialogue: 0,0:07:33.15,0:07:37.14,Default,,0000,0000,0000,,now we've gotta put these\Nall in terms of T1 and T2
Dialogue: 0,0:07:37.14,0:07:38.60,Default,,0000,0000,0000,,so that we can solve.
Dialogue: 0,0:07:38.60,0:07:41.86,Default,,0000,0000,0000,,If I put T1Y in terms of the total T1,
Dialogue: 0,0:07:41.86,0:07:44.71,Default,,0000,0000,0000,,and then sines of angles,\Nand cosines of angles,
Dialogue: 0,0:07:44.71,0:07:48.04,Default,,0000,0000,0000,,and I put T2Y in terms of T2 and angles,
Dialogue: 0,0:07:49.58,0:07:51.24,Default,,0000,0000,0000,,and I do the same thing for 1X and 2X,
Dialogue: 0,0:07:51.24,0:07:53.04,Default,,0000,0000,0000,,I'll have two equations,\Nand the only two unknowns
Dialogue: 0,0:07:53.04,0:07:57.50,Default,,0000,0000,0000,,will be T1 and T2, then\Nwe can finally solve.
Dialogue: 0,0:07:57.50,0:07:59.44,Default,,0000,0000,0000,,If that didn't make any\Nsense, here's what I'm saying.
Dialogue: 0,0:07:59.44,0:08:02.75,Default,,0000,0000,0000,,I'm saying figure out what\NT1Y is in terms of T1.
Dialogue: 0,0:08:02.75,0:08:05.63,Default,,0000,0000,0000,,So I know this angle here,\Nlet's figure out these angles.
Dialogue: 0,0:08:05.63,0:08:08.67,Default,,0000,0000,0000,,So these angles here are, if this is 30,
Dialogue: 0,0:08:08.67,0:08:11.20,Default,,0000,0000,0000,,this angle down here has\Nto be 30 because these
Dialogue: 0,0:08:11.20,0:08:13.31,Default,,0000,0000,0000,,are alternate interior angles.
Dialogue: 0,0:08:13.31,0:08:14.70,Default,,0000,0000,0000,,And if you don't believe me,
Dialogue: 0,0:08:14.70,0:08:16.81,Default,,0000,0000,0000,,imagine this big triangle over here,
Dialogue: 0,0:08:16.81,0:08:18.69,Default,,0000,0000,0000,,where this is a right angle.
Dialogue: 0,0:08:18.69,0:08:20.40,Default,,0000,0000,0000,,So this triangle from here\Nto there, down to here,
Dialogue: 0,0:08:20.40,0:08:24.72,Default,,0000,0000,0000,,up to here, if this is 30,\Nthat's 90, this has gotta be 60,
Dialogue: 0,0:08:24.72,0:08:27.21,Default,,0000,0000,0000,,'cause it all adds up\Nto 180 for a triangle.
Dialogue: 0,0:08:27.21,0:08:29.13,Default,,0000,0000,0000,,And if this right angle\Nis 90, and this side's 60,
Dialogue: 0,0:08:29.13,0:08:31.29,Default,,0000,0000,0000,,this side's gotta be 30.
Dialogue: 0,0:08:31.29,0:08:34.10,Default,,0000,0000,0000,,Similarly, this side's a right angle.
Dialogue: 0,0:08:34.10,0:08:36.13,Default,,0000,0000,0000,,Look at this triangle, 60, 90,
Dialogue: 0,0:08:36.13,0:08:37.84,Default,,0000,0000,0000,,that means this would have to be 30.
Dialogue: 0,0:08:37.84,0:08:40.75,Default,,0000,0000,0000,,And so if I come down here,\Nthis angle would have to be 60.
Dialogue: 0,0:08:40.75,0:08:42.33,Default,,0000,0000,0000,,Just like this one,
Dialogue: 0,0:08:43.19,0:08:45.92,Default,,0000,0000,0000,,'cause it's an alternate\Ninterior angle, so that's 60.
Dialogue: 0,0:08:45.92,0:08:49.79,Default,,0000,0000,0000,,So this angle here is 60,\Nthis angle here is 30,
Dialogue: 0,0:08:49.79,0:08:51.93,Default,,0000,0000,0000,,we can figure out what\Nthese components are
Dialogue: 0,0:08:51.93,0:08:53.46,Default,,0000,0000,0000,,in terms of the total vectors.
Dialogue: 0,0:08:53.46,0:08:54.96,Default,,0000,0000,0000,,Once we find those,
Dialogue: 0,0:08:54.96,0:08:56.50,Default,,0000,0000,0000,,we're gonna plug those\Nexpressions into here,
Dialogue: 0,0:08:56.50,0:08:57.75,Default,,0000,0000,0000,,and that will let us solve.
Dialogue: 0,0:08:57.75,0:08:59.36,Default,,0000,0000,0000,,In other words, T1Y is gonna be,
Dialogue: 0,0:08:59.36,0:09:02.11,Default,,0000,0000,0000,,once you do this for awhile you realize,
Dialogue: 0,0:09:02.11,0:09:03.60,Default,,0000,0000,0000,,this is the opposite side.
Dialogue: 0,0:09:03.60,0:09:05.44,Default,,0000,0000,0000,,So this component here is going to be
Dialogue: 0,0:09:05.44,0:09:07.61,Default,,0000,0000,0000,,total T1 times sine of 30.
Dialogue: 0,0:09:09.08,0:09:11.13,Default,,0000,0000,0000,,Because it's the opposite side.
Dialogue: 0,0:09:11.13,0:09:13.78,Default,,0000,0000,0000,,And if that didn't make sense,\Nwe'll derive it right here.
Dialogue: 0,0:09:13.78,0:09:15.96,Default,,0000,0000,0000,,So what we're saying is that sine of 30,
Dialogue: 0,0:09:15.96,0:09:19.21,Default,,0000,0000,0000,,sine of 30 is opposite over hypotenuse,
Dialogue: 0,0:09:21.59,0:09:25.15,Default,,0000,0000,0000,,and in this case, the\Nopposite side is T1Y.
Dialogue: 0,0:09:25.15,0:09:29.15,Default,,0000,0000,0000,,So T1Y over the total T1\Nis equal to sine of 30.
Dialogue: 0,0:09:30.92,0:09:33.28,Default,,0000,0000,0000,,And we can solve this for T1Y now,
Dialogue: 0,0:09:33.28,0:09:36.11,Default,,0000,0000,0000,,we can get the T1Y if I\Nmultiply both sides by T1.
Dialogue: 0,0:09:36.11,0:09:39.27,Default,,0000,0000,0000,,I get that that's T1 times sine of 30.
Dialogue: 0,0:09:40.76,0:09:42.20,Default,,0000,0000,0000,,So that's what I said down here.
Dialogue: 0,0:09:42.20,0:09:45.07,Default,,0000,0000,0000,,T1 is just T, oh sorry, forgot the one.
Dialogue: 0,0:09:45.07,0:09:46.74,Default,,0000,0000,0000,,T1 times sine of 30.
Dialogue: 0,0:09:48.05,0:09:50.51,Default,,0000,0000,0000,,Similarly, if you do the\Nsame thing with cosine 30,
Dialogue: 0,0:09:50.51,0:09:53.51,Default,,0000,0000,0000,,you'll get that T1X is T1 cosine 30,
Dialogue: 0,0:09:55.85,0:09:57.70,Default,,0000,0000,0000,,by the exact same process.
Dialogue: 0,0:09:57.70,0:10:01.15,Default,,0000,0000,0000,,Similarly over here, T2 is going to be,
Dialogue: 0,0:10:01.15,0:10:03.56,Default,,0000,0000,0000,,I'm sorry, T2X is gonna be 2.
Dialogue: 0,0:10:05.00,0:10:09.17,Default,,0000,0000,0000,,So T2 cosine 60, because\Nthis is the adjacent side.
Dialogue: 0,0:10:10.13,0:10:12.97,Default,,0000,0000,0000,,And T2Y is gonna be T2 sine of 60.
Dialogue: 0,0:10:15.07,0:10:16.53,Default,,0000,0000,0000,,And if any of that doesn't make sense,
Dialogue: 0,0:10:16.53,0:10:19.71,Default,,0000,0000,0000,,just go back to the\Ndefinition of sine and cosine,
Dialogue: 0,0:10:19.71,0:10:22.15,Default,,0000,0000,0000,,write what the opposite side is,
Dialogue: 0,0:10:22.15,0:10:25.60,Default,,0000,0000,0000,,the total hypotenuse side,\Nsolve for your expression,
Dialogue: 0,0:10:25.60,0:10:26.72,Default,,0000,0000,0000,,you'll get these.
Dialogue: 0,0:10:26.72,0:10:29.19,Default,,0000,0000,0000,,If you don't believe me on\Nthose, try those out yourselves.
Dialogue: 0,0:10:29.19,0:10:31.49,Default,,0000,0000,0000,,But those are what these components are,
Dialogue: 0,0:10:31.49,0:10:35.97,Default,,0000,0000,0000,,in terms of T2 and the\Nangles T2, T1 and the angles.
Dialogue: 0,0:10:35.97,0:10:37.57,Default,,0000,0000,0000,,And why are we doing this?
Dialogue: 0,0:10:37.57,0:10:39.84,Default,,0000,0000,0000,,We're doing this so that\Nwhen plug in over here,
Dialogue: 0,0:10:39.84,0:10:41.25,Default,,0000,0000,0000,,we'll only have two variables.
Dialogue: 0,0:10:41.25,0:10:45.01,Default,,0000,0000,0000,,In other words, if I plug\NT1Y, this expression here,
Dialogue: 0,0:10:45.01,0:10:48.76,Default,,0000,0000,0000,,T1 sine 30 in for T1Y,\Nsimilarly if I plug in
Dialogue: 0,0:10:49.70,0:10:53.87,Default,,0000,0000,0000,,T2Y is T2 sine 60 into\Nthis expression right there
Dialogue: 0,0:10:55.36,0:10:57.41,Default,,0000,0000,0000,,for T2Y, look at what I'll get.
Dialogue: 0,0:10:57.41,0:10:58.99,Default,,0000,0000,0000,,I'll get zero equals.
Dialogue: 0,0:10:58.99,0:11:01.65,Default,,0000,0000,0000,,So I'll get negative 30 Newtons,
Dialogue: 0,0:11:02.71,0:11:06.80,Default,,0000,0000,0000,,and then I'll get plus\NT1Y was T1 sine 30, so T1,
Dialogue: 0,0:11:08.50,0:11:11.14,Default,,0000,0000,0000,,and then sine 30, we can\Nclean this up a little bit.
Dialogue: 0,0:11:11.14,0:11:12.33,Default,,0000,0000,0000,,Sine 30 is just a half.
Dialogue: 0,0:11:12.33,0:11:15.94,Default,,0000,0000,0000,,So I'll just write T1 over 2, and then
Dialogue: 0,0:11:15.94,0:11:17.87,Default,,0000,0000,0000,,'cause sine 30 is just one half.
Dialogue: 0,0:11:17.87,0:11:20.87,Default,,0000,0000,0000,,And then T2Y is gonna be T2 sine 60,
Dialogue: 0,0:11:23.73,0:11:26.65,Default,,0000,0000,0000,,and sine 60 is just root 3 over 2.
Dialogue: 0,0:11:26.65,0:11:30.82,Default,,0000,0000,0000,,So I'll write this as plus T2\Nover 2, and then times root 3.
Dialogue: 0,0:11:33.09,0:11:35.52,Default,,0000,0000,0000,,And you might think this is no better.
Dialogue: 0,0:11:35.52,0:11:37.48,Default,,0000,0000,0000,,I mean this is still a\Nhorrible mess right here.
Dialogue: 0,0:11:37.48,0:11:40.99,Default,,0000,0000,0000,,But, look at. This is\Nin terms of T1 and T2.
Dialogue: 0,0:11:40.99,0:11:42.27,Default,,0000,0000,0000,,That's what I'm gonna do over here.
Dialogue: 0,0:11:42.27,0:11:44.24,Default,,0000,0000,0000,,I'm gonna put these in terms of T1 and T2,
Dialogue: 0,0:11:44.24,0:11:45.50,Default,,0000,0000,0000,,and then we can solve.
Dialogue: 0,0:11:45.50,0:11:48.56,Default,,0000,0000,0000,,So T1X is T1 over cosine 30,
Dialogue: 0,0:11:48.56,0:11:52.80,Default,,0000,0000,0000,,so I'm gonna write this\Nas T1 times cosine 30,
Dialogue: 0,0:11:52.80,0:11:55.38,Default,,0000,0000,0000,,and cosine 30 is root 3 over 2,
Dialogue: 0,0:11:56.57,0:11:59.58,Default,,0000,0000,0000,,so this is T1 over 2 times root 3.
Dialogue: 0,0:11:59.58,0:12:02.91,Default,,0000,0000,0000,,And that should equal T2X is right here,
Dialogue: 0,0:12:03.94,0:12:07.35,Default,,0000,0000,0000,,That's T2 cosine 60, cosine 60 is a half.
Dialogue: 0,0:12:08.22,0:12:10.64,Default,,0000,0000,0000,,So T2X is gonna be T2 over 2.
Dialogue: 0,0:12:12.35,0:12:13.95,Default,,0000,0000,0000,,So T2 over 2.
Dialogue: 0,0:12:13.95,0:12:16.14,Default,,0000,0000,0000,,So what I'm doing is, if\Nthis doesn't make sense,
Dialogue: 0,0:12:16.14,0:12:18.87,Default,,0000,0000,0000,,I'm just substituting\Nwhat these components are
Dialogue: 0,0:12:18.87,0:12:22.75,Default,,0000,0000,0000,,in terms of the total\Nmagnitude in the angle.
Dialogue: 0,0:12:22.75,0:12:25.27,Default,,0000,0000,0000,,And I do this, because\Nlook at what I have now,
Dialogue: 0,0:12:25.27,0:12:26.68,Default,,0000,0000,0000,,I have got one equation with T1 and T2.
Dialogue: 0,0:12:26.68,0:12:28.66,Default,,0000,0000,0000,,I've got another equation with T1 and T2.
Dialogue: 0,0:12:28.66,0:12:30.93,Default,,0000,0000,0000,,So what I'm gonna do to solve these,
Dialogue: 0,0:12:30.93,0:12:32.84,Default,,0000,0000,0000,,when we have two equations\Nand two unknowns,
Dialogue: 0,0:12:32.84,0:12:34.92,Default,,0000,0000,0000,,you have to solve for\None of these variables,
Dialogue: 0,0:12:34.92,0:12:37.20,Default,,0000,0000,0000,,and then substitute it\Ninto the other equation.
Dialogue: 0,0:12:37.20,0:12:40.13,Default,,0000,0000,0000,,That way you'll get one\Nequation with one unknown.
Dialogue: 0,0:12:40.13,0:12:42.22,Default,,0000,0000,0000,,And you try to get the math right,
Dialogue: 0,0:12:42.22,0:12:43.20,Default,,0000,0000,0000,,and you'll get the problem.
Dialogue: 0,0:12:43.20,0:12:44.92,Default,,0000,0000,0000,,So I'm gonna solve this one is easier,
Dialogue: 0,0:12:44.92,0:12:47.57,Default,,0000,0000,0000,,so I'm gonna solve this\None for, let's just say T2.
Dialogue: 0,0:12:47.57,0:12:48.98,Default,,0000,0000,0000,,So if we solve this for T2,
Dialogue: 0,0:12:48.98,0:12:52.24,Default,,0000,0000,0000,,I get that T2 equals, well, I can multiply
Dialogue: 0,0:12:52.24,0:12:56.58,Default,,0000,0000,0000,,both sides by 2, and\NI'll get T1 times root 3.
Dialogue: 0,0:12:56.58,0:13:00.95,Default,,0000,0000,0000,,So T1 times root 3, because\Nthe 2 here cancels with this 2,
Dialogue: 0,0:13:00.95,0:13:04.18,Default,,0000,0000,0000,,or when I multiply both\Nsides by 2 it cancels out.
Dialogue: 0,0:13:04.18,0:13:07.94,Default,,0000,0000,0000,,So we get that T2 equals\NT1 root 3. This is great.
Dialogue: 0,0:13:07.94,0:13:12.10,Default,,0000,0000,0000,,I can substitute T2 as T1\Nroot 3 into here for T2.
Dialogue: 0,0:13:13.100,0:13:15.43,Default,,0000,0000,0000,,And the reason I do that,
Dialogue: 0,0:13:15.43,0:13:17.66,Default,,0000,0000,0000,,is I'll get one equation with one unknown.
Dialogue: 0,0:13:17.66,0:13:19.54,Default,,0000,0000,0000,,I'll only have T1 in that equation now.
Dialogue: 0,0:13:19.54,0:13:23.17,Default,,0000,0000,0000,,So if I do this, I'll\Nget zero equals negative,
Dialogue: 0,0:13:23.17,0:13:25.12,Default,,0000,0000,0000,,you know what, let's\Njust move the -30 over.
Dialogue: 0,0:13:25.12,0:13:26.69,Default,,0000,0000,0000,,This is kind of annoying here.
Dialogue: 0,0:13:26.69,0:13:28.32,Default,,0000,0000,0000,,Just add 30 to both sides,
Dialogue: 0,0:13:28.32,0:13:30.80,Default,,0000,0000,0000,,then take this calculation here.
Dialogue: 0,0:13:30.80,0:13:35.33,Default,,0000,0000,0000,,We get plus 30 equals,\Nand then we're gonna have
Dialogue: 0,0:13:35.33,0:13:38.41,Default,,0000,0000,0000,,T1 over 2, from this T1, so T1 over 2
Dialogue: 0,0:13:39.49,0:13:42.57,Default,,0000,0000,0000,,plus, I've got plus, T2 is T1 root 3.
Dialogue: 0,0:13:44.89,0:13:48.38,Default,,0000,0000,0000,,So when I plug T1 root 3 in for T2,
Dialogue: 0,0:13:48.38,0:13:52.29,Default,,0000,0000,0000,,what I'm gonna get is,\NI'm gonna get T1 root 3,
Dialogue: 0,0:13:55.09,0:13:56.89,Default,,0000,0000,0000,,and then times another route 3,
Dialogue: 0,0:13:56.89,0:13:59.56,Default,,0000,0000,0000,,because T2 itself was T1 root 3.
Dialogue: 0,0:14:00.94,0:14:02.45,Default,,0000,0000,0000,,So I'm taking this expression here,
Dialogue: 0,0:14:02.45,0:14:05.52,Default,,0000,0000,0000,,plugging it in for T2, but\NI still have to multiply
Dialogue: 0,0:14:05.52,0:14:08.58,Default,,0000,0000,0000,,that T2 by a root 3 and divide by 2.
Dialogue: 0,0:14:08.58,0:14:10.43,Default,,0000,0000,0000,,And so, what do we get?
Dialogue: 0,0:14:10.43,0:14:13.23,Default,,0000,0000,0000,,Root 3 times root 3 is just 3.
Dialogue: 0,0:14:13.23,0:14:16.98,Default,,0000,0000,0000,,So we have T2 times 3\Nhalves, plus T1 over 2.
Dialogue: 0,0:14:18.13,0:14:19.94,Default,,0000,0000,0000,,So I'll get 30 equals,
Dialogue: 0,0:14:19.94,0:14:24.23,Default,,0000,0000,0000,,and then I get T1 over 2,\Nwe're almost there, I promise.
Dialogue: 0,0:14:24.23,0:14:29.12,Default,,0000,0000,0000,,T1 over 2, plus, and this is\Ngonna be T1 times 3 over 2,
Dialogue: 0,0:14:29.12,0:14:33.77,Default,,0000,0000,0000,,so it's gonna be 3 T1 over\N2, or what does that equal?
Dialogue: 0,0:14:33.77,0:14:37.44,Default,,0000,0000,0000,,T1 over 2 plus 3 T1\Nover 2 is just 4 halves.
Dialogue: 0,0:14:39.04,0:14:42.37,Default,,0000,0000,0000,,So that's just 2 T1. So\Nthis cleaned up beautifully.
Dialogue: 0,0:14:42.37,0:14:45.93,Default,,0000,0000,0000,,So this is just 2 times T1,\Nand now we can solve for T1.
Dialogue: 0,0:14:45.93,0:14:49.35,Default,,0000,0000,0000,,We get that T1 is simply 30 divided by 2.
Dialogue: 0,0:14:51.13,0:14:54.50,Default,,0000,0000,0000,,If I divide both sides,\Nthis left hand side by 2,
Dialogue: 0,0:14:54.50,0:14:56.51,Default,,0000,0000,0000,,and this side here, this right side by 2,
Dialogue: 0,0:14:56.51,0:14:59.01,Default,,0000,0000,0000,,I get T1 is 30 over 2 Newtons,
Dialogue: 0,0:15:00.04,0:15:02.40,Default,,0000,0000,0000,,which is just, these should be Newtons,
Dialogue: 0,0:15:02.40,0:15:06.56,Default,,0000,0000,0000,,I should have units on these,\Nwhich is just 15 Newtons.
Dialogue: 0,0:15:08.23,0:15:10.91,Default,,0000,0000,0000,,Whoo, I did it, 15 Newtons.
Dialogue: 0,0:15:10.91,0:15:12.55,Default,,0000,0000,0000,,T1 is 15 Newtons.
Dialogue: 0,0:15:12.55,0:15:14.44,Default,,0000,0000,0000,,We got T1. That's one of them.
Dialogue: 0,0:15:14.44,0:15:15.88,Default,,0000,0000,0000,,How do we get the other?
Dialogue: 0,0:15:15.88,0:15:19.20,Default,,0000,0000,0000,,You start back over at the very beginning.
Dialogue: 0,0:15:19.20,0:15:21.56,Default,,0000,0000,0000,,No, not really, that would be terrible.
Dialogue: 0,0:15:21.56,0:15:23.13,Default,,0000,0000,0000,,You actually just take this T1,
Dialogue: 0,0:15:23.13,0:15:25.95,Default,,0000,0000,0000,,and you plug it right into\Nhere, boop, there it goes.
Dialogue: 0,0:15:25.95,0:15:27.98,Default,,0000,0000,0000,,So T2, we already got it.
Dialogue: 0,0:15:27.98,0:15:29.43,Default,,0000,0000,0000,,T2 is just T1 root 3.
Dialogue: 0,0:15:29.43,0:15:32.35,Default,,0000,0000,0000,,So all I have to do is\Nmultiply root 3 by my T1,
Dialogue: 0,0:15:32.35,0:15:33.18,Default,,0000,0000,0000,,which I know now.
Dialogue: 0,0:15:33.18,0:15:37.52,Default,,0000,0000,0000,,And I get that T2 is just\N15 times root 3 Newton.
Dialogue: 0,0:15:37.52,0:15:39.91,Default,,0000,0000,0000,,So once you get one of the forces,
Dialogue: 0,0:15:39.91,0:15:41.39,Default,,0000,0000,0000,,the next one is really easy.
Dialogue: 0,0:15:41.39,0:15:42.88,Default,,0000,0000,0000,,This is just T2.
Dialogue: 0,0:15:42.88,0:15:46.05,Default,,0000,0000,0000,,So T2 is 15 root 3, and T1 is just 15.
Dialogue: 0,0:15:47.50,0:15:49.54,Default,,0000,0000,0000,,So in case you got lost in the details,
Dialogue: 0,0:15:49.54,0:15:52.02,Default,,0000,0000,0000,,the big picture recap is this.
Dialogue: 0,0:15:52.02,0:15:55.35,Default,,0000,0000,0000,,We drew a force diagram,\Nwe used Newton's Second Law
Dialogue: 0,0:15:55.35,0:15:57.64,Default,,0000,0000,0000,,in the vertical direction\Nwe couldn't solve,
Dialogue: 0,0:15:57.64,0:15:59.15,Default,,0000,0000,0000,,because there were too many unknowns.
Dialogue: 0,0:15:59.15,0:16:02.50,Default,,0000,0000,0000,,We used Newton's Second Law\Nin the horizontal direction,
Dialogue: 0,0:16:02.50,0:16:04.16,Default,,0000,0000,0000,,we couldn't solve because\Nthere were two unknowns.
Dialogue: 0,0:16:04.16,0:16:06.22,Default,,0000,0000,0000,,We put all four of these unknowns
Dialogue: 0,0:16:06.22,0:16:09.38,Default,,0000,0000,0000,,in terms of only two unknowns, T1 and T2,
Dialogue: 0,0:16:09.38,0:16:12.56,Default,,0000,0000,0000,,by writing how those components depended
Dialogue: 0,0:16:12.56,0:16:13.99,Default,,0000,0000,0000,,on those total vectors.
Dialogue: 0,0:16:13.99,0:16:17.32,Default,,0000,0000,0000,,We substituted these expressions\Nin for each component.
Dialogue: 0,0:16:17.32,0:16:19.26,Default,,0000,0000,0000,,Once we did that, we had two equations,
Dialogue: 0,0:16:19.26,0:16:23.19,Default,,0000,0000,0000,,with only T1, T2, and T1 and T2 in them.
Dialogue: 0,0:16:23.19,0:16:27.68,Default,,0000,0000,0000,,We solved one of these\Nequations for T2 in terms of T1,
Dialogue: 0,0:16:27.68,0:16:29.92,Default,,0000,0000,0000,,substituted that into the other equation.
Dialogue: 0,0:16:29.92,0:16:32.79,Default,,0000,0000,0000,,We got a single equation\Nwith only one unknown.
Dialogue: 0,0:16:32.79,0:16:34.93,Default,,0000,0000,0000,,We were able to solve for that unknown.
Dialogue: 0,0:16:34.93,0:16:37.51,Default,,0000,0000,0000,,Once we got that, which is our T1,
Dialogue: 0,0:16:37.51,0:16:39.14,Default,,0000,0000,0000,,once we have that variable,
Dialogue: 0,0:16:39.14,0:16:40.62,Default,,0000,0000,0000,,we plug it back into that first equation
Dialogue: 0,0:16:40.62,0:16:42.29,Default,,0000,0000,0000,,that we had solved for T2.
Dialogue: 0,0:16:42.29,0:16:45.56,Default,,0000,0000,0000,,We plug this 15 in, we get\Nwhat the second tension is.
Dialogue: 0,0:16:45.56,0:16:48.06,Default,,0000,0000,0000,,So even when it seems\Nlike Newton's Second Law
Dialogue: 0,0:16:48.06,0:16:49.90,Default,,0000,0000,0000,,won't get you there, if you have faith,
Dialogue: 0,0:16:49.90,0:16:52.72,Default,,0000,0000,0000,,and you persevere, you will make it.
Dialogue: 0,0:16:52.72,0:16:53.56,Default,,0000,0000,0000,,Good job.