[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:01.44,Default,,0000,0000,0000,,Welcome back.
Dialogue: 0,0:00:01.44,0:00:03.95,Default,,0000,0000,0000,,I'll now do a couple of more\Nmomentum problems.
Dialogue: 0,0:00:03.95,0:00:07.06,Default,,0000,0000,0000,,So this first problem, I have\Nthis ice skater and she's on
Dialogue: 0,0:00:07.06,0:00:08.63,Default,,0000,0000,0000,,an ice skating rink.
Dialogue: 0,0:00:08.63,0:00:10.36,Default,,0000,0000,0000,,And what she's doing is\Nshe's holding a ball.
Dialogue: 0,0:00:10.36,0:00:14.74,Default,,0000,0000,0000,,And this ball-- let me draw\Nthe ball-- this is a 0.15
Dialogue: 0,0:00:14.74,0:00:15.99,Default,,0000,0000,0000,,kilogram ball.
Dialogue: 0,0:00:18.61,0:00:20.58,Default,,0000,0000,0000,,And she throws it.
Dialogue: 0,0:00:20.58,0:00:23.64,Default,,0000,0000,0000,,Let's just say she throws it\Ndirectly straight forward in
Dialogue: 0,0:00:23.64,0:00:25.20,Default,,0000,0000,0000,,front of her, although\Nshe's staring at us.
Dialogue: 0,0:00:25.20,0:00:27.23,Default,,0000,0000,0000,,She's actually forward\Nfor her body.
Dialogue: 0,0:00:27.23,0:00:32.79,Default,,0000,0000,0000,,So she throws it exactly\Nstraight forward.
Dialogue: 0,0:00:32.79,0:00:35.08,Default,,0000,0000,0000,,And I understand it is hard to\Nthrow something straight
Dialogue: 0,0:00:35.08,0:00:38.49,Default,,0000,0000,0000,,forward, but let's assume\Nthat she can.
Dialogue: 0,0:00:38.49,0:00:41.51,Default,,0000,0000,0000,,So she throws it exactly\Nstraight forward with a
Dialogue: 0,0:00:41.51,0:00:44.28,Default,,0000,0000,0000,,speed-- or since we're going to\Ngive the direction as well,
Dialogue: 0,0:00:44.28,0:00:48.00,Default,,0000,0000,0000,,it's a velocity, right, cause\Nspeed is just a magnitude
Dialogue: 0,0:00:48.00,0:00:51.20,Default,,0000,0000,0000,,while a velocity is a magnitude\Nand a direction-- so
Dialogue: 0,0:00:51.20,0:00:58.16,Default,,0000,0000,0000,,she throws the ball at 35 meters\Nper second, and this
Dialogue: 0,0:00:58.16,0:01:03.16,Default,,0000,0000,0000,,ball is 0.15 kilograms.
Dialogue: 0,0:01:03.16,0:01:08.56,Default,,0000,0000,0000,,Now, what the problem says is\Nthat their combined mass, her
Dialogue: 0,0:01:08.56,0:01:17.52,Default,,0000,0000,0000,,plus the ball, is 50 kilograms.\NSo they're both
Dialogue: 0,0:01:17.52,0:01:20.13,Default,,0000,0000,0000,,stationary before she does\Nanything, and then she throws
Dialogue: 0,0:01:20.13,0:01:22.99,Default,,0000,0000,0000,,this ball, and the question is,\Nafter throwing this ball,
Dialogue: 0,0:01:22.99,0:01:25.00,Default,,0000,0000,0000,,what is her recoil velocity?
Dialogue: 0,0:01:25.00,0:01:28.93,Default,,0000,0000,0000,,Or essentially, well how much,\Nby throwing the ball, does she
Dialogue: 0,0:01:28.93,0:01:30.23,Default,,0000,0000,0000,,push herself backwards?
Dialogue: 0,0:01:30.23,0:01:33.06,Default,,0000,0000,0000,,So what is her velocity in\Nthe backward direction?
Dialogue: 0,0:01:33.06,0:01:36.34,Default,,0000,0000,0000,,And if you're not familiar with\Nthe term recoil, it's
Dialogue: 0,0:01:36.34,0:01:39.60,Default,,0000,0000,0000,,often applied to when someone,\NI guess, not that we want to
Dialogue: 0,0:01:39.60,0:01:42.25,Default,,0000,0000,0000,,think about violent things, but\Nif you shoot a gun, your
Dialogue: 0,0:01:42.25,0:01:44.83,Default,,0000,0000,0000,,shoulder recoils back,\Nbecause once
Dialogue: 0,0:01:44.83,0:01:45.90,Default,,0000,0000,0000,,again momentum is conserved.
Dialogue: 0,0:01:45.90,0:01:48.27,Default,,0000,0000,0000,,So there's a certain amount of\Nmomentum going into that
Dialogue: 0,0:01:48.27,0:01:51.02,Default,,0000,0000,0000,,bullet, which is very light\Nand fast going forward.
Dialogue: 0,0:01:51.02,0:01:54.94,Default,,0000,0000,0000,,But since momentum is conserved,\Nyour shoulder has
Dialogue: 0,0:01:54.94,0:01:55.78,Default,,0000,0000,0000,,velocity backwards.
Dialogue: 0,0:01:55.78,0:01:57.25,Default,,0000,0000,0000,,But we'll do another\Nproblem with that.
Dialogue: 0,0:01:57.25,0:01:58.96,Default,,0000,0000,0000,,So let's get back\Nto this problem.
Dialogue: 0,0:01:58.96,0:02:02.41,Default,,0000,0000,0000,,So like I just said, momentum\Nis conserved.
Dialogue: 0,0:02:02.41,0:02:05.76,Default,,0000,0000,0000,,So what's the momentum at the\Nstart of the problem, the
Dialogue: 0,0:02:05.76,0:02:08.29,Default,,0000,0000,0000,,initial momentum?
Dialogue: 0,0:02:08.29,0:02:09.69,Default,,0000,0000,0000,,Let me do a different color.
Dialogue: 0,0:02:09.69,0:02:11.73,Default,,0000,0000,0000,,So this is the initial\Nmomentum.
Dialogue: 0,0:02:11.73,0:02:18.06,Default,,0000,0000,0000,,Initially, the mass is 50\Nkilograms, right, cause her
Dialogue: 0,0:02:18.06,0:02:22.11,Default,,0000,0000,0000,,and the ball combined are 50\Nkilograms, times the velocity.
Dialogue: 0,0:02:22.11,0:02:23.81,Default,,0000,0000,0000,,Well the velocity is 0.
Dialogue: 0,0:02:23.81,0:02:29.80,Default,,0000,0000,0000,,So initially, there is 0\Nvelocity in the system.
Dialogue: 0,0:02:29.80,0:02:34.06,Default,,0000,0000,0000,,So the momentum is 0.
Dialogue: 0,0:02:34.06,0:02:37.43,Default,,0000,0000,0000,,The P initial is equal to 0.
Dialogue: 0,0:02:37.43,0:02:41.56,Default,,0000,0000,0000,,And since we start with a net 0\Nmomentum, we have to finish
Dialogue: 0,0:02:41.56,0:02:42.88,Default,,0000,0000,0000,,with a net 0 momentum.
Dialogue: 0,0:02:42.88,0:02:44.03,Default,,0000,0000,0000,,So what's momentum later?
Dialogue: 0,0:02:44.03,0:02:47.73,Default,,0000,0000,0000,,Well we have a ball moving at\N35 meters per second and the
Dialogue: 0,0:02:47.73,0:02:58.04,Default,,0000,0000,0000,,ball has a mass of 0.15\Nkilograms. I'll ignore the
Dialogue: 0,0:02:58.04,0:02:59.71,Default,,0000,0000,0000,,units for now just\Nto save space.
Dialogue: 0,0:02:59.71,0:03:01.93,Default,,0000,0000,0000,,Times the velocity\Nof the ball.
Dialogue: 0,0:03:01.93,0:03:05.06,Default,,0000,0000,0000,,Times 35 meters per second.
Dialogue: 0,0:03:05.06,0:03:08.93,Default,,0000,0000,0000,,So this is the momentum of the\Nball plus the new momentum of
Dialogue: 0,0:03:08.93,0:03:10.02,Default,,0000,0000,0000,,the figure skater.
Dialogue: 0,0:03:10.02,0:03:12.06,Default,,0000,0000,0000,,So what's her mass?
Dialogue: 0,0:03:12.06,0:03:14.44,Default,,0000,0000,0000,,Well her mass is going\Nto be 50 minus this.
Dialogue: 0,0:03:14.44,0:03:21.55,Default,,0000,0000,0000,,It actually won't matter a ton,\Nbut let's say it's 49--
Dialogue: 0,0:03:21.55,0:03:25.33,Default,,0000,0000,0000,,what is that-- 49.85 kilograms,
Dialogue: 0,0:03:25.33,0:03:28.18,Default,,0000,0000,0000,,times her new velocity.
Dialogue: 0,0:03:28.18,0:03:29.04,Default,,0000,0000,0000,,Times velocity.
Dialogue: 0,0:03:29.04,0:03:31.41,Default,,0000,0000,0000,,Let's call that the velocity\Nof the skater.
Dialogue: 0,0:03:31.41,0:03:34.89,Default,,0000,0000,0000,,So let me get my trusty\Ncalculator out.
Dialogue: 0,0:03:37.91,0:03:40.64,Default,,0000,0000,0000,,OK, so let's see.
Dialogue: 0,0:03:40.64,0:03:50.78,Default,,0000,0000,0000,,0.15 times 35 is\Nequal to 5.25.
Dialogue: 0,0:03:50.78,0:03:56.26,Default,,0000,0000,0000,,So that equals 5.25.
Dialogue: 0,0:03:56.26,0:04:02.35,Default,,0000,0000,0000,,plus 49.85 times the skater's\Nvelocity, the final velocity.
Dialogue: 0,0:04:02.35,0:04:04.55,Default,,0000,0000,0000,,And of course, this equals\N0 because the initial
Dialogue: 0,0:04:04.55,0:04:05.93,Default,,0000,0000,0000,,velocity was 0.
Dialogue: 0,0:04:05.93,0:04:10.00,Default,,0000,0000,0000,,So let's, I don't know, subtract\N5.25 from both sides
Dialogue: 0,0:04:10.00,0:04:18.20,Default,,0000,0000,0000,,and then the equation becomes\Nminus 5.25 is equal to 49.85
Dialogue: 0,0:04:18.20,0:04:20.28,Default,,0000,0000,0000,,times the velocity\Nof the skater.
Dialogue: 0,0:04:20.28,0:04:23.48,Default,,0000,0000,0000,,So we're essentially saying that\Nthe momentum of just the
Dialogue: 0,0:04:23.48,0:04:25.38,Default,,0000,0000,0000,,ball is 5.25.
Dialogue: 0,0:04:25.38,0:04:29.48,Default,,0000,0000,0000,,And since the combined system\Nhas to have 0 net momentum,
Dialogue: 0,0:04:29.48,0:04:32.66,Default,,0000,0000,0000,,we're saying that the momentum\Nof the skater has to be 5.25
Dialogue: 0,0:04:32.66,0:04:35.96,Default,,0000,0000,0000,,in the other direction, going\Nbackwards, or has a momentum
Dialogue: 0,0:04:35.96,0:04:39.23,Default,,0000,0000,0000,,of minus 5.25.
Dialogue: 0,0:04:39.23,0:04:41.48,Default,,0000,0000,0000,,And to figure out the velocity,\Nwe just divide her
Dialogue: 0,0:04:41.48,0:04:43.78,Default,,0000,0000,0000,,momentum by her mass.
Dialogue: 0,0:04:43.78,0:04:48.38,Default,,0000,0000,0000,,And so divide both sides by\N49.85 and you get the velocity
Dialogue: 0,0:04:48.38,0:04:49.70,Default,,0000,0000,0000,,of the skater.
Dialogue: 0,0:04:49.70,0:04:50.72,Default,,0000,0000,0000,,So let's see.
Dialogue: 0,0:04:50.72,0:05:01.52,Default,,0000,0000,0000,,Let's make this a negative\Nnumber divided by 49.85 equals
Dialogue: 0,0:05:01.52,0:05:05.37,Default,,0000,0000,0000,,minus 0.105.
Dialogue: 0,0:05:05.37,0:05:15.52,Default,,0000,0000,0000,,So minus 0.105 meters\Nper second.
Dialogue: 0,0:05:15.52,0:05:16.27,Default,,0000,0000,0000,,So that's interesting.
Dialogue: 0,0:05:16.27,0:05:20.37,Default,,0000,0000,0000,,When she throws this ball out at\N35 meters per second, which
Dialogue: 0,0:05:20.37,0:05:24.67,Default,,0000,0000,0000,,is pretty fast, she will\Nrecoil back at about 10
Dialogue: 0,0:05:24.67,0:05:28.44,Default,,0000,0000,0000,,centimeters, yeah, roughly 10\Ncentimeters per second.
Dialogue: 0,0:05:28.44,0:05:30.53,Default,,0000,0000,0000,,So she will recoil a lot\Nslower, although
Dialogue: 0,0:05:30.53,0:05:31.74,Default,,0000,0000,0000,,she will move back.
Dialogue: 0,0:05:31.74,0:05:34.35,Default,,0000,0000,0000,,And if you think about it, this\Nis a form of propulsion.
Dialogue: 0,0:05:34.35,0:05:35.79,Default,,0000,0000,0000,,This is how rockets work.
Dialogue: 0,0:05:35.79,0:05:40.12,Default,,0000,0000,0000,,They eject something that maybe\Nhas less mass, but super
Dialogue: 0,0:05:40.12,0:05:44.50,Default,,0000,0000,0000,,fast. And that, since we have a\Nconservation of momentum, it
Dialogue: 0,0:05:44.50,0:05:47.74,Default,,0000,0000,0000,,makes the rocket move in\Nthe other direction.
Dialogue: 0,0:05:47.74,0:05:51.55,Default,,0000,0000,0000,,Well anyway, let's see if we\Ncould fit another problem in.
Dialogue: 0,0:05:51.55,0:05:54.60,Default,,0000,0000,0000,,Actually, it's probably better\Nto leave this problem done and
Dialogue: 0,0:05:54.60,0:05:56.76,Default,,0000,0000,0000,,then I'll have more time for the\Nnext problem, which will
Dialogue: 0,0:05:56.76,0:05:58.52,Default,,0000,0000,0000,,be slightly more difficult.
Dialogue: 0,0:05:58.52,0:05:59.76,Default,,0000,0000,0000,,See you soon.