Momentum
Momentum: Ice skater throws a ball A simple conservation of momentum problem involving an ice skater and a ball
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- Welcome back.
- I'll now do a couple of more momentum problems.
- So this first problem, I have this ice skater and she's on
- an ice skating rink.
- And what she's doing is she's holding a ball.
- And this ball-- let me draw the ball-- this is a 0.15
- kilogram ball.
- And she throws it.
- Let's just say she throws it directly straight forward in
- front of her, although she's staring at us.
- She's actually forward for her body.
- So she throws it exactly straight forward.
- And I understand it is hard to throw something straight
- forward, but let's assume that she can.
- So she throws it exactly straight forward with a
- speed-- or since we're going to give the direction as well,
- it's a velocity, right, cause speed is just a magnitude
- while a velocity is a magnitude and a direction-- so
- she throws the ball at 35 meters per second, and this
- ball is 0.15 kilograms.
- Now, what the problem says is that their combined mass, her
- plus the ball, is 50 kilograms. So they're both
- stationary before she does anything, and then she throws
- this ball, and the question is, after throwing this ball,
- what is her recoil velocity?
- Or essentially, well how much, by throwing the ball, does she
- push herself backwards?
- So what is her velocity in the backward direction?
- And if you're not familiar with the term recoil, it's
- often applied to when someone, I guess, not that we want to
- think about violent things, but if you shoot a gun, your
- shoulder recoils back, because once
- again momentum is conserved.
- So there's a certain amount of momentum going into that
- bullet, which is very light and fast going forward.
- But since momentum is conserved, your shoulder has
- velocity backwards.
- But we'll do another problem with that.
- So let's get back to this problem.
- So like I just said, momentum is conserved.
- So what's the momentum at the start of the problem, the
- initial momentum?
- Let me do a different color.
- So this is the initial momentum.
- Initially, the mass is 50 kilograms, right, cause her
- and the ball combined are 50 kilograms, times the velocity.
- Well the velocity is 0.
- So initially, there is 0 velocity in the system.
- So the momentum is 0.
- The P initial is equal to 0.
- And since we start with a net 0 momentum, we have to finish
- with a net 0 momentum.
- So what's momentum later?
- Well we have a ball moving at 35 meters per second and the
- ball has a mass of 0.15 kilograms. I'll ignore the
- units for now just to save space.
- Times the velocity of the ball.
- Times 35 meters per second.
- So this is the momentum of the ball plus the new momentum of
- the figure skater.
- So what's her mass?
- Well her mass is going to be 50 minus this.
- It actually won't matter a ton, but let's say it's 49--
- what is that-- 49.85 kilograms,
- times her new velocity.
- Times velocity.
- Let's call that the velocity of the skater.
- So let me get my trusty calculator out.
- OK, so let's see.
- 0.15 times 35 is equal to 5.25.
- So that equals 5.25.
- plus 49.85 times the skater's velocity, the final velocity.
- And of course, this equals 0 because the initial
- velocity was 0.
- So let's, I don't know, subtract 5.25 from both sides
- and then the equation becomes minus 5.25 is equal to 49.85
- times the velocity of the skater.
- So we're essentially saying that the momentum of just the
- ball is 5.25.
- And since the combined system has to have 0 net momentum,
- we're saying that the momentum of the skater has to be 5.25
- in the other direction, going backwards, or has a momentum
- of minus 5.25.
- And to figure out the velocity, we just divide her
- momentum by her mass.
- And so divide both sides by 49.85 and you get the velocity
- of the skater.
- So let's see.
- Let's make this a negative number divided by 49.85 equals
- minus 0.105.
- So minus 0.105 meters per second.
- So that's interesting.
- When she throws this ball out at 35 meters per second, which
- is pretty fast, she will recoil back at about 10
- centimeters, yeah, roughly 10 centimeters per second.
- So she will recoil a lot slower, although
- she will move back.
- And if you think about it, this is a form of propulsion.
- This is how rockets work.
- They eject something that maybe has less mass, but super
- fast. And that, since we have a conservation of momentum, it
- makes the rocket move in the other direction.
- Well anyway, let's see if we could fit another problem in.
- Actually, it's probably better to leave this problem done and
- then I'll have more time for the next problem, which will
- be slightly more difficult.
- See you soon.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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