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Would a Brick or Feather Fall Faster : What would fall faster on the moon?
相關課程
- Let's say we were to take a little excursion
- into the moon. And so here we are sitting on the surface of the moon. That's the surface of the moon
- and with us to our excursion to the moon, we brought two things. We brought ourself a concrete brick. That's my brick right over there. My concrete brick.
- Although it's orange... It's an orange concrete brick.
- I also brought a bird feather with us... So this is the bird feather.
- My question to you is if I were both the brick and the bird feather at the same time, and I were to let go at both of them at the same time,
- and ask you which one would hit the surface of the moon first, and what would you say?
- Well, if you were to base it on your experience on Earth -- On, Earth, if you were to take a brick and a bird feather,
- brick would just go straight down. Brick would immediately just fall to the Earth, it would do it quite quickly...
- It would accelerate quite quickly, and while a feather would kind of float around.
- If you had a feather on Earth, it would just float around. It would go that way, and then it would go that way,
- And it would slowly make its way down to the ground. So on Earth, at least in the presence of air, it looks like the brick will hit the ground first.
- But what will happen on the moon? And what's interesting about the moon is that we have no atmosphere.
- We have no air to kind of provide resistance for either the brick or the feather.
- So what do you think is going to happen? So your first temptation is to just say 'Let's use the universal law of gravity.'
- What is the force of gravity on the brick? So the force on the brick is -- Well, you could calculate that out
- The force of gravity on the brick is going to be equal to big G time the mass of the moon --
- I'll say it's m for mass and the subscript is lowercase m for moon
- The mass of the moon times the mass of the brick, divided by the distance between
- the brick and the center of the moon squared.
- So this is the difference between the brick and the center of the moon and you square it. Fair enough.
- That's the force on the brick. What's going to be the force on the feather?
- The force due to gravity on the force -- Or, another way to think about it, the weight of the feather on the moonz
- so what is the force on the feather? Well, we'll the do the same calculation. The force
- on the feather is going to be equal to big G times the mass of the moon times the mass of the feather,
- divided by the distance between the distance between the center of this feather and the center of this moon, squared.
- That's the distance, and then we square it. So if you look at both of these expressions,
- they both have this quantity right over here, G times the mass of the moon
- divided by the distance between this height and the center of the moon squared.
- So they both have this exact expression on it. Let's just replace that expression--
- Let's that call that the gravitational field on the moon. If you multiply this number by any
- mass, it will tell the weight of that object on the moon.
- Or the gravitational force acting downwards on that object on the moon
- So this is the gravitational field of the moon. So I'll just call it G sub m.
- All it is, is all these quantities combined. So if we simplify it that way, the force on the brick
- due to the moon is going to be equal to that lowercase g on the moon--
- Normally we use this lowercase g for the gravitational constant on Earth, or the force of the gravitational
- field on Earth, or sometimes acceleration of gravity on Earth, but now we're referring to the moon.
- That's what this lowercase subscript m is doing for us.
- So it's equal to that, times the mass of the brick. For the case of the feather,
- the force on the feather is equal to all of this business, so that's the g sub m times the mass of the feather.
- So now, assuming that the mass of the brick is much greater than the mass of the feather.
- So we're going to assume, which is a reasonable thing to assume, that the mass of
- the brick is greater than the mass of the feather.
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