Physics problem - mass of a container plus its contents

Factual Questions
1

I’m sure if I’d taken physics classes more recently than when Reagan was in his office and Sting was still with the Police, I might have a better grasp of this.

(But only might. I was always pretty sucky in area.)

Anyway, let’s say you have a flimsy plastic container. It weighs, I dunno, 6oz.

You fill it half-way–meaning there’s a good amount of room left–with cast-iron toy soldiers. Now the container and the toy soldiers combined weigh 22oz.

(This may be too small or too large an estimate… What can I say, I never had toy soldiers to play with as a girl! Doesn’t really matter for the purposes of the exercise.)

The issue is, you need to carry this container a few blocks, and you can tell this not-very-high quality container can barely hold together because it’s a bit wobbly and the toy soldiers are of really good quality cast iron. (Made in Bavaria!)

Okay. Now, in an attempt to solve this conundrum, through some miracle of science, you take all the gravity out of the very-tightly-sealed container. The toy soldiers float.

At last, the question, which I think I just figured out* in my head while typing this, but I’ll ask it anyway:

Do the airborne soldiers this make the container weigh less, thus allowing the box to be carried without much problem, OR does the weight remain the same, thus still compromising the container’s structural integrity?

I feel like this is a really rudimentary problem and I should’ve been able to find it on my own. But I’m not coming up with the right keywords, probably because of my physics suckage. So, what do you think?

Note: this is NOT HOMEWORK. I am thirty-mumble years from having homework. It’s a thought problem and also a problem I need to solve in a geeky RPG I’m playing in. Shut up.

  • My guess:

At first I couldn’t figure out why this wouldn’t save the container, but now I’m thinking that despite the floating soldiers, they’re still displacing the air volume at the same mass as they weigh in a non-gravity environment, and so this wouldn’t work. Is that anywhere roughly right?

2

If the toy soldiers are floating they will not affect the ‘weight’ of the container, but… They still retain their mass. This means that if you exert any force on the container, the soldiers will resist. Start walking and they will want to stay still; if you get them moving (very slow start maybe) then any time yo try to turn a corner, they will want to carry on in a straight line. When you stop, they will carry on.

The problem you have is that the soldiers are free floating and there is spare room in the container. This means that whenever you start, stop or alter direction, they will keep going until they hit the side; it would be better if they were constrained (think seatbelts in a car). Imagine floating in a car as it travels along the road; you would be bouncing all over the place.

So long as you accelerate, turn corners and decelerate very gently, your flimsy container should hold up. My WAG is that floating or not will make little difference.

I did think that this might be the same as the “canaries in a van” riddle. but canaries fly by displacing air and not using anti-gravity.

3

Wouldn’t it depend on the means to remove the gravity? Maybe it’s removed by somehow neutralizing the mass. On the last episode of ST:Discovery, Tilly places a 5 ton piece of rock with an approximate 5 cm diameter into a gravity-neutralizing container, and she was able to manipulate the container as if it were empty.

4

Yeah, we need to know the details of the magic spell you’re using. You want to talk to a wizard, not a physicist.

5

But unless he is riding a rocket ship those few blocks, the rate of acceleration (and therefor force) on the box due to motion is going to be a lot smaller than the acceleration due to gravity, and so unless the box is made of a soap bubble it should be able to survive the trip even it it can’t hold up the soldiers under normal gravity.

Another concern about turning gravity off in side the box, is that the box and its contents would suddenly be much lighter than the surrounding air, causing it to be pushed up. So the force required to keep the box from floating away might be enough to destroy it depending on how fragile it is. Still this is going to be much less that the force exerted by the soldiers with gravity on.

6

Consider this, A box of photons, which are massless particles, will itself have mass due to the energy of those photons.

It is the total energy content of an ensemble that results in what we call mass. The way the particles are arranged, how they move and how much energy they contain changes the mass.

A compressed spring has more mass than a relaxed spring and a cup of hot coffee has more mass than it does when it is cold. In fact molecule has less mass than the atoms that make it up would if you measured them independently.

This is one implication of E = MC[sup]2[/sup]

7

Rather than magically removing gravity from inside the container, does your question remain the same if the container/toy soldiers are assumed to be aboard the International Space Station? The soldiers will float inside the flimsy container, which one can then attempt to move from place to place.

Ultimately, it becomes a question of how quickly you try to move the container, slowly and it will likely survive, quickly and it will likely break, just as it would in full Earth gravity.

8

The soldiers may act similar to an ideal gas, and one could consider that the soldiers can never “sit still” and try and calculate the pressure compared to the wall strength.

With that steady state “pressure” you could calculate the increase in pressure during acceleration by moving the box.

As Cheesesteak mentioned how fast you move the box will be important but you will probably also induce harmonic oscillations when moving the box. Accelerating at some speeds may result in constructive “waves” and break the box.

But as an ideal gas the exterior “weight” wouldn’t change, because like a box of photons the energy content doesn’t change. The inertial mass may seem smaller for a very brief period on horizontal accelerations until all of your “particles” are accelerated but that would be very short lived.

9

Wow this is a lot to absorb. Really interesting answers, guys!

Amazingly Cheesesteak has come very close to the specific situation I was trying to analogize with my hypothetical plastic box and toy soldiers. And in fact I realize that I was asking the question a bit backwards in my scenario. But you all helped me envision this and understand the problems that might arise.

Well, here’s the “actual” situation, which may have an effect on the answers (or maybe not; see “choie sucks at science” in my OP). Also, please feel free to grade me from 1 - 10, wherein “1” means “extremely cool and admirable” and “10” means “OMG what a geek loser who probably sleeps wearing Vulcan ears.”

Basically I’m attempting to crowdsource an answer to a sci-fi-related RPG. It might be cheating, and I’m probably foolhardy since the GM actually posts here, so I can only cross my fingers that he doesn’t venture into GQ! Anyway the trouble is that my character should know this stuff, but I don’t, and I don’t want her to look dumb by suggesting something that changes the laws of physics…

Situation: We need to evacuate a colony of thousands before their star explodes in only a few hours. Trouble is, there’s only our ship (TOS-era Enterprise-alike), and we can apparently only fit 1/4 of the doomed residents without taxing our life-support systems… Every solution that my fellow players and I have come up with, involving getting this huge number on the ship, has been ruled out.

I am quite certain this is a Kobayashi Maru, no-win situation, short of some last-minute cavalry arriving courtesy of the GM. But even accepting that as an eventuality, I want to make sure we’ve tried everything.

Now: the human colonists live under two massive domes, because this is a non-M-class planet. I keep looking at those domes (mentally speaking) and wondering if they could be detached and fused into a giant hollow shere. They obviously have some type of anti-gravity/life-support system already in place, if all the residents could hang out there and our ship just pull the dang thing behind us like a trailer.

But I don’t know if the ship is strong enough to pull this dome along with multiple thousands of people. I was wondering if turning the anti-gravity off would make this an easier task. Note: I’m not entirely sure what the gravity is on this planet, which would affect whether the dome can even be lifted out. I’m just trying to account for the weight of the people as well.

This is what I get for taking on a character who’s supposed to be way the hell more knowledgeable than I am. As someone with an engineering background, she would know how gravity and physics work. I just don’t want her to look dumb by suggesting something that will make her superiors think she’s an utter incompetent.

Like I said, I am pretty sure this is going to be knocked down too as an option, for plot reasons, but I still want to come up with a viable, if crazy, solution. Something that could work, if not for _____ (where “____” = the unique issues in this game’s parameters).

Thanks… and I’m sorry to ask such a bizarre question here.

(And if you’re reading this, Mr. Game Master person, please don’t smack me down for this breach of RPG etiquette!)

10

Okay so you don’t know both the mass and the diameter of the planet. And the mass of the primary, probably. Do you know the distance from the primary to the planet? And are the domes close enough together that they COULD be on the far side of the planet when the primary goes up?

Do you know how much more distance the colonists need to put between themselves and the explosion?

If it IS a Kobayashi Maru situation, you of course know that the only way to survive one is by cheating, right? So cheat.

Program the holodeck to recreate the most powerful wizard ever imagined by the minds of sentient creatures anywhere. Spill a cup of coffee into the control panel to make it fuck up and actually CREATE that wizard. Then have the wizard manipulate the laws of physics as they pertain to the star, so that it explodes with the force of a damp firecracker.

Then get the grateful colonists to assist you as you storm the bridge, physically overpower the Space Wizard (‘cos you KNOW he’s going to want to take over the universe), and repair the holodeck.