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Mr. Andersen explains the concept of momentum. He also shows you how to solve simple momentum problems. He finally shows you how momentum is both conserved and relative.
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Transcript Provided by YouTube:
00:04
Hi. It’s Mr. Andersen and today I’m going to be talking about momentum. The
00:09
equation for momentum is this. P = mv. Or if we were to write that out, momentum, which
00:21
is P is equal to mass. And we always measure mass in kilograms. So it’s mass times velocity.
00:35
And we have to measure velocity in meters per second. So momentum is simply the product
00:43
of mass times velocity. So let’s say an object has no mass. What is its momentum? The right
00:50
answer would be 0. Let’s say an object has no velocity. What would its momentum be? Right
00:55
answer would be 0. And so that’s a pretty easy one. We’ll do a question in just a second.
01:00
And so this is a famous application of that. This is a train that was coming into a train
01:03
station in Paris. And the brakeman was trying to save a little bit of time. And so he didn’t
01:07
pull on the brake soon enough. And that train had so much momentum, it had so much mass
01:12
that it just kept going and going. It went through a giant wall and then crashed off
01:16
this terrace. Surprisingly nobody was killed in this accident except a woman who happened
01:21
to be sitting right below. But that’s momentum. So what are some typical problems that you
01:27
might get as far as momentum goes? This would be a typical one. This is the first car that
01:31
I ever had. This is a 1981 Honda Civic. And so let’s say Mr. Andersen’s 1981 Honda Civic
01:37
has a mass of 1200 kg and a top speed of 38.6 m/s. Calculate the maximum momentum of this
01:44
car. Well, first thing we have to do is right out the equation. So remember P = mv. In this
01:53
case momentum then equals the mass. And so the mass in this case is 1200 kg. And we’re
02:02
going to multiply that times the velocity. And the velocity is 38.6 m/s. Now we want
02:12
to make sure that the mass is in kilograms. And that the velocity is in meters per second.
02:17
If it isn’t you’re going to have to convert it to that. And then we simply multiply those
02:21
two values. And if I multiply those two values together on my calculator I get 46320 kg m/s.
02:36
That’s the units for momentum. Now the next thing you want to do is look back and check
02:39
your significant digits. If we look at 1200 kilograms, that’s going to have two significant
02:44
digits. If we look at 38.6, that’s going to have three significant digits. And so my answer
02:49
can only have two. And so the way I would write this is momentum equals 4.6 times 10
02:58
to the 4th kilogram meters per second. So that would be the right answer and the correct
03:08
number of significant digits. Remember though if that Civic isn’t moving then it would have
03:14
momentum of zero. And so you could have an object that’s much smaller than that. In other
03:18
words if that car was going at that speed, and I were to throw and object that has a
03:22
mass much smaller than that, straight at it with an incredible velocity I could actually
03:27
stop it if those momentums were to match. So that’s what momentum is. Next thing you
03:32
should understand is that momentum is conserved. Now one of my favorite toys as a physics teacher
03:37
was this. It’s called Newton’s cradle. And I don’t have mine right here. But what you
03:41
can do is you can lift up one ball and that will hit the balls. And the other ones will
03:44
go flying up on the other side. I don’t have an actual one today. But I do have a virtual
03:49
Newton’s cradle right here. And so what I can do is I can lift up on this ball on this
03:54
side. There’s a slight pause there. But what happens is the balls on the other side are
03:59
going to move up. And so what’s happening to the momentum? The momentum is just moving
04:03
back and forth and back and forth. Now to get one of these to work, it’s actually pretty
04:07
hard. You have to make sure that all of the balls have the exact same mass. And you have
04:11
to make sure that they’re all the same height. Let me try to grab that for a second. So next
04:17
thing I could do is lift up two. And so if I have two balls now, I’ve doubled my mass.
04:21
It’s going to have the same velocity. So when I let it down that momentum is going to be
04:25
transferred back and forth again. So that’s cool. The one thing you want to play with
04:31
as you do this is then what happens with three? So if I lift three up like this. Let me get
04:36
those stopped for a second. There we go. Okay. If I lift three up on this side what’s going
04:43
to happen there? Well the momentum is going to be the same. And so how am I going to get
04:47
three balls to go up on the other side? Well let’s just try it. So what happens is two
04:53
will maintain their position. And then that momentum is transferred back and forth. And
04:58
so momentum remember is conserved in any kind of a collision. So solving problems with one
05:04
object is really easy. And so is solving problems with two objects. And so let’s say we have
05:09
object one now and object two. And object one is an eight ball. And so let’s say this
05:14
is before the collision. And so we can figure out its momentum. We’ll call that mass one
05:19
times velocity one. Plus mass 2, this is the cue ball now, times the velocity 2. And so
05:27
the momentum of this ball plus this ball before the collision is going to equal the same after
05:33
the collision. And so this would be mass one. Its mass isn’t going to change. Times its
05:37
velocity after the collision. Plus mass two times it’s velocity after the collision. And
05:46
so if we say that this is a collision where object two strikes object one, and object
05:52
two remains stationary, in other words if it doesn’t move. So how would we solve this?
05:58
Well if you think about it, let’s do this. Let’s call this case one where the cue ball
06:02
just stops. And so in case one, what’s its velocity before the collision? Let’s call
06:09
that zero. And what’s the mass of the cue ball before the collision. Well let’s add
06:13
some numbers to it. Let’s say that a typical cue ball has a mass of 0.2 kilograms. And
06:20
to make this easy let’s say it’s going 6 meters per second. And so we could take it’s mass
06:28
and velocity before the collision. So that would be mass of 0.2 times 6 meters per second.
06:33
And so it’s momentum before the collision would be 1.2 kilograms meters per second.
06:43
And so after the collision, let’s say that this cue ball starts moving now. And this
06:47
one stays stationary. So we’d say well its momentum is going to be zero now. And so all
06:53
of that momentum is going to be transferred to the other object. And so as long as this
06:59
eight ball, and I think they all have the same mass, has a mass of 0.2 kilograms then
07:03
it’s going to move with the same velocity. And so it’s going to be a velocity of 6 meters
07:09
per second. In other words the momentum would be conserved. Let’s call that case one. And
07:13
now if we make it a little trickier. Let’s do case two now. So in case two let’s say
07:20
those two objects become linked. in other words let’s say this ball hits this ball and
07:26
they both move forward. In other words they don’t move. Well how would we do that? We’ve
07:31
got mass. The first one has a momentum of 0. This one we said has a momentum of 1.2
07:38
kilograms meters per second. Now after the collision the mass of this one is going to
07:44
be 0.2 times the velocity. And I’m just going to call this v. Because the velocity is going
07:51
to be the same. Plus the mass of the other one, 0.2 times v, because we’re saying the
07:56
mass or the velocities are going to be the same. So 1.2 kilogram meters per second now
08:04
equals 0.4v. And so the velocity at this point would equal 3 meters per second. In other
08:14
words if this ball comes in and it has a velocity of 6 meter per second, since their velocity
08:21
of 6.0 meters per second. Since their masses are exactly the same it’s going to leave with
08:25
a velocity roughly half that. Or of about 3 meters per second. And so that’s how you
08:30
do momentum problems if you have two objects. Now another thing that I failed to mention
08:35
before that’s really important is that momentum is a vector. And so to solve momentum problems
08:42
the other thing that you want to have is a direction as well. And so most of the problems
08:47
I’ve done before are just linear. But if we’re breaking, so this is a pool ball. Let’s say
08:52
we have the cue ball here and we break the balls, there’s going to be a lot of different
08:56
vectors of velocities that are created by that. And so the sum of all of those velocities
09:02
is going to equal the sum of that first momentum of that first cue ball. And so momentum is
09:08
conserved. Momentum is also relative. And now we get a little bit deep. But it’s not
09:13
that deep. And so let’s say you’re this person right here. Let’s say you’re person A and
09:18
you’re watching an object come by. Let’s say this is an elevator. And it has an apple in
09:22
it. And the elevator and the apple are both moving at a constant velocity. Well when you
09:28
look at that object, it’s going to have a certain momentum that we could calculate.
09:32
So let’s say the apple has a mass of 0.2 kilograms. And it’s going at a speed or a velocity of
09:38
20 meters per second. Then we can figure out exactly what the momentum of that object is.
09:45
But let’s say we put you inside. And we sometimes refer to this as Einstein’s elevator. Let’s
09:49
say we put you inside. And now that elevator is still moving at a constant velocity, but
09:55
your reference has changed. And so when you look at this object, it’s not moving. It’s
10:01
moving with you. And so we would say that its momentum now is 0. And the reason why
10:06
is that we’ve shifted your time or your reference point. Where you’re observing it from. And
10:12
so does it have a momentum here when you’re watching it? Yeah. Does it have no momentum
10:16
here when you’re watching it when you’re in the elevator? Yeah. And so that’s relativity.
10:21
Or that’s a little bit of relativity. And so I hope that’s helpful.
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This post was previously published on YouTube.
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Photo credit: Screenshot from video.