Unraveling Spaceman #1's Atomic Pop Gun Mystery

[rczmiller]

I have been playing around with an idea for a few years and I am interested in receiving any feedback. I am an amateur, so if there are any issues with my logic, please feel free to straighten out my thoughts.

First, imagine 2 astronauts floating in space. The first astronaut has an atomic popgun that shoots a cork with the mass of 1/10 of the total mass of spaceman/gun/cork at the speed of 99% the speed of light. This cork is attached to the atomic pop gun with a 16 foot string. Please forget the mechanics of how a sting could stop a mass traveling at this speed.

When spaceman #1 shoots the popgun, Newton’s physics says that there will be an equal and opposite reaction. Since the cork is 1/10 the mass of the spaceman, for every 10 feet the cork travels, spaceman #1 will travel 1 foot in the opposite direction. Spaceman #1 can use the other spaceman as a reference point to measure the distance traveled.

However, Special Relativity tells us that as objects reach relativenistic speeds, they appear to become more massive. Using this information, when an object travels at 99% the speed of light, it appears to become 7 times more massive. Due to the conservation of energy, I believe the cork would travel approximately 9 feet and the spaceman would travel approximately 7 feet at which point the string would stop the travel of the cork away from the spaceman. After firing the atomic pop gun, the cork and spaceman #1 have stopped moving, they are 16 feet apart and spaceman #1 has moved 7 feet relative to spaceman #2. Am I OK so far?

Intrigued by this event, spaceman #1 slowly pulls in the cork on the string to reload the atomic pop gun. Since the cork is pulled back at a non-relativenistic speed, its mass will not change (1/10 of total mass). For every 10 feet the cork moves, spaceman #1 will only move 1 foot back. Once the cork is reloaded, spaceman #1 would have moved a total of approximately 5.5 feet relative to spaceman #2. With my current understanding, if spaceman #1 repeated this process over and over, each repetition would result in him moving 5.5 feet further away from the second spaceman. What am I missing?

Now comes 2 questions that have been bothering me. First, what if instead of a cork, the object being propelled from the atomic pop gun was vibrating (like a quartz crystal with an electrical charge being applied)? As the atoms vibrate side-to-side and back-and forth, could these speeds influence the perceived mass of the moving object? In other words, after summing up all of the velocities, the objects mass would appear to be larger than a non-vibrating object traveling at the same speed?

Second, I know that space/time is relative, but would there be any changes to this scenario if the astronauts were moving? What if the two spacemen were launched from Earth so that they were traveling at 1% the speed of light? This speed is well below the relativenistic speed needed to perceive a major warping of space/time, but would these velocities affect the experiment mentioned above?

Any thoughts would be greatly appreciated. Thank you for your time!

 

[pete worthington]

My thought is you have posted an interesting multi layered question which has 5 or so question marks. When I first started posting in this forum 2 months ago I attempted to keep the question straight forward and singular in focus. If you get some good hits on the initial thought question then attempt to expand it. This is a great forum so don't be frustrated by your lack of response on this post.

 

[Crosson]

You are really into this idea that "going fast increases mass".

I can tell you what the quartz crystal does have more of then the cork: energy.

If you want to associate this energy with a mass E = mc^2, then be my guest. But don't confuse yourself.

In other words, after summing up all of the velocities, the objects mass would appear to be larger than a non-vibrating object traveling at the same speed?

What does "...appear to be larger..." actually mean? It means that if I push on the object, it doesn't accelerate as much as I expected. In terms of direct observation, that's all it means.

Thats why I prefer to talk about energy and momentum, rather then velocity and mass.

 

[Alligator]

You're missing the mass of the string, the increased mass of the cork, and the time needed to accelerate to 99% the speed of light. Also, how did you get the 7x mass number at 99% the speed of light?

 

[NateTG]

Either calculate everything in relativistic terms, or do not. Either way, you should discover that the center of mass does not move - i.e. that linear momentum is preserved and there is no net motion. The problem is that you're mixing relativistic, and classic notions of momentum.

Specifically you're calculating the launch of the cork using non-relativistic mechanics so the kick is too small - while the cork is being accelerated, its mass-energy increases. For the example of vibrating objects, the corresponding momentum per velocity i.e. mass-energy, would be increased in a relativistic setting - so that momentum is preserved.

Note that there is a problem with nomenclature in physics where relativistic mass (i.e. mass-energy) and invariant mass (i.e. rest mass) are both referred to as mass. This ambiguity is part of your calculation.

P.S. The mass gain associated with energy can be physically detected. For example in some chemical compounds where the mass of the compound can be slightly larger or smaller than the mass of the constituents in an amount that is consisten with the changed bonding energies.