# The Naked Scientists Forum

### Author Topic: momentum question  (Read 5774 times)

#### cuso4

• Angel Delight
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##### momentum question
« on: 29/04/2003 13:24:12 »
My physics teacher was telling us about the conservation of momentum in the lesson and he gave us a rather silly example:

"If I was to jump out the window...and'splat!'[xx(], the momentum is still conserved because as I falling down, the earth is moving up to meet me with the same momentum."

I sort of get it, but is he right about the earth moving up?

AG

#### NakedScientist

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##### Re: momentum question
« Reply #1 on: 29/04/2003 23:08:28 »
The best example of conservation of momentum is the experiment involving firing a pellet from a gun into a block of plasticine on a model railway carriage.

If you weigh the pellet and you know how fast the gun fires it, you can calculate the momentum (mv) of the pellet.

If you weigh the train carriage (M) and measure its velocity after it is hit by the pellet you can show that (mv)PELLET=(MV)TRAIN, hence proving that momentum is conserved.

TNS

#### Dickie

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##### Re: momentum question
« Reply #2 on: 30/04/2003 11:22:57 »
Your teacher is indeed right about the earth moving up. You fall because of the force of gravity. By Newton's 3rd, an equal and opposite force is exerted on the earth, so it accelerates up to meet you.

Now, acceleration=force/mass = (your weight)/(mass of earth) = very small, but not zero.

#### cuso4

• Angel Delight
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##### Re: momentum question
« Reply #3 on: 30/04/2003 20:38:00 »
Cheers for clearing that up. We did a experiment using gliders on air track but the result wasn't very good.

AG

#### NakedScientist

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##### Re: momentum question
« Reply #4 on: 30/04/2003 21:49:35 »
I'm surprised that the result was poor as this normally works really well - maybe you've got a crappy airtrack ?!

TNS

#### syhprum

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##### momentum question
« Reply #5 on: 05/08/2007 05:51:45 »
This shows that Galileo's famous experiment was wrong the 100Kg cannon ball will reach the ground in a slightly shorter time than the 1Kg one if they are taken up the tower together and dropped separately.
« Last Edit: 05/08/2007 08:13:48 by syhprum »

#### chris

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##### momentum question
« Reply #6 on: 05/08/2007 12:05:45 »
Because the Earth will move up to meet the 100kg mass more quickly?

#### another_someone

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##### momentum question
« Reply #7 on: 05/08/2007 12:53:38 »
This shows that Galileo's famous experiment was wrong the 100Kg cannon ball will reach the ground in a slightly shorter time than the 1Kg one if they are taken up the tower together and dropped separately.

Galileo's experiment was in any case flawed because it was not done in a vacuum, and so would have had aerodynamic drag to contend with.

#### Bored chemist

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##### momentum question
« Reply #8 on: 05/08/2007 14:14:54 »

Err, if the earth comes up to meet the 100 KG cannonball early , won't it also meet the 1KG ball early?

The thing that Galileo should be famous for is having worked out using logic that the usual given answer for his day, based on the ideas of Aristotle was wrong. He didn't need to do the experiment except to show people who couldn't understand logic.
The prevailing belief was that heavy things fell faster than light things.
Galileo wondewred what would happen if you tied a light ball to a heavy one with a bit of string and dropped the combined object. This compound object is clearly heavier than either of the 2 things it's made from so, according to Aristotle, it should fall faster.
But the light ball will fall slower than the heavy one and get left behind.
That means the the light one must pull on the string and therefore on the heavy one, pulling it upwards. That would obviously make the heavy one fall slower. But for Aristotle to be right it would have to fall faster. This doesn't make sense.
The only way round this is for them all to fall at the same speed.

OK, hands up all those people who thought Einstein invented the "thought experiment"?

The effect of drag on these things was small enough to make it clear that Galileo had a point.

#### lightarrow

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##### momentum question
« Reply #9 on: 06/08/2007 08:28:35 »

Err, if the earth comes up to meet the 100 KG cannonball early , won't it also meet the 1KG ball early?
Earlier with the 100 kg ball than with the 1 kg one.

#### chris

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##### momentum question
« Reply #10 on: 06/08/2007 09:33:41 »
So what you're saying is that the acceleration of the earth towards to 100kg ball is larger than the 1kg ball and therefore the large ball should strike Earth a tiny amount sooner because the Earth has moved up more to meet the falling ball?

#### lightarrow

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##### momentum question
« Reply #11 on: 06/08/2007 13:11:54 »
So what you're saying is that the acceleration of the earth towards to 100kg ball is larger than the 1kg ball and therefore the large ball should strike Earth a tiny amount sooner because the Earth has moved up more to meet the falling ball?

It seems so:

F = -GMm/r2   is the gravitational force between two bodies with masses M and m and distance r.

Let's say M is earth's mass and m the ball's mass. The ball's acceleration is:

aball = F/m = -GM/r2

and so it doesn't depend on the ball's mass m (as we know).

The earth's acceleration is:

aearth = F/M = -Gm/r2

and so it does depend on the ball's mass m.

#### ramphysix

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##### momentum question
« Reply #12 on: 11/08/2007 12:01:26 »
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