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Old Feb 16th 2017, 06:40 AM   #1
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Energy and momentum in a closed system

A thought experiment: You have a box (spacecraft) stationary, in free fall. Inside box, against one wall is a precompressed spring with a small mass against the end of the spring opposite the wall.

Release spring. Its elastic potential energy turns to kinetic energy (and momentum), as it accelerates the box and the small mass in opposite directions.

IF the small mass reached the opposite wall of the box and was captured by a similar spring-and latch assembly so force curve equal and opposite to the original spring-release event was applied to that opposite wall, and all the kinetic energy and momentum of the small mass was reconverted to elastic potential energy (and captured by the latch) , then of course the small mass and box would be decelerated together (though in opposite directions) and all parts would return to their original resting state.

BUT if instead of being caught by a lossless perfectly elastic spring-and-latch, the small mass comes to rest in a sandbag which converts some of the small mass's kinetic energy to heat, then energy is not lost, but it seems that momentum is, and the box-and-small-mass would continue moving in the direction in which the box alone was originally accelerated by the energy released by the spring.

This does not FEEL right to me, I am eager to be told I am wrong but need to know why/where. The heat energy in the sand has to come out of the kinetic energy of the small mass, and will ( it seems) be unavailable to decelerate the box.
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Old Feb 16th 2017, 06:49 AM   #2
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Originally Posted by Leyzorek View Post
A thought experiment: You have a box (spacecraft) stationary, in free fall. Inside box, against one wall is a precompressed spring with a small mass against the end of the spring opposite the wall.

Release spring. Its elastic potential energy turns to kinetic energy (and momentum), as it accelerates the box and the small mass in opposite directions.

IF the small mass reached the opposite wall of the box and was captured by a similar spring-and latch assembly so force curve equal and opposite to the original spring-release event was applied to that opposite wall, and all the kinetic energy and momentum of the small mass was reconverted to elastic potential energy (and captured by the latch) , then of course the small mass and box would be decelerated together (though in opposite directions) and all parts would return to their original resting state.

BUT if instead of being caught by a lossless perfectly elastic spring-and-latch, the small mass comes to rest in a sandbag which converts some of the small mass's kinetic energy to heat, then energy is not lost, but it seems that momentum is, and the box-and-small-mass would continue moving in the direction in which the box alone was originally accelerated by the energy released by the spring.

This does not FEEL right to me, I am eager to be told I am wrong but need to know why/where. The heat energy in the sand has to come out of the kinetic energy of the small mass, and will ( it seems) be unavailable to decelerate the box.
I must be psychic. I was actually mulling over this problem in the shower.

You are correct on all counts.

Assuming a perfect system the spacecraft will actually move. The spring releases the small mass the spacecraft will indeed move. etc, etc. Note that the spacecraft does actually move while the small mass is in flight. But it can't move the center of mass of the system.

Where this goes all wrong is, as you say, if the small mass runs into the sand. I prefer to think of the loss of kinetic energy in the system as the deformation of the shape of the sand.

-Dan
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Old Feb 16th 2017, 07:45 AM   #3
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thanks!
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Old Feb 16th 2017, 08:13 AM   #4
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Thank you, Dan! So do I correctly understand that you agree that the CG of spacecraft-with-small-internal-mass system will remain in motion after small mass comes to rest in the sandbag, its net KE being equal to that part of the KE of the small spring-propelled mass that was turned into heat or permanent deformation in the sand?
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Old Feb 16th 2017, 10:16 AM   #5
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I disagree. Momentum of the system is not lost - it's zero throughout the entire experiment. When the small mass hits sand and does not rebound, its KE is converted to heat. The source of that KE was originally the PE of the compressed spring - hence what has happened is the PE of the spring is ultimately converted to heat. The KE of the ship plus small mass is initially zero, and is also zero at the end. The CG of the system does not move. And the momentum of the system is zero throughout the experiment.
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Old Feb 16th 2017, 01:24 PM   #6
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I find the phrase "stationary, in free fall" confusing! If it is "in free fall", it can't be "stationary".
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