Suppose we have a cylindrical container which contains water filled up to the brim. We now consider gravity free conditions. Then we shine some light on the water container from all the directions (isotropically). Now the water will evaporate due to absorption of heat, and consequently the center of mass of the container-water system changes. However since we're shining the light from all the directions the net force on the cylinder-water system is 0, but regardless of this the center of mass of the system is changing. Is this a violation of Newton's 2nd law for a system of particles $F_\text{ext}=Ma_\text{COM} $ or am I missing something?
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1$\begingroup$ That's a beautiful question!!! $\endgroup$– Apoorva ShuklaCommented Jun 4 at 18:46
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2$\begingroup$ Why do you think the CoM is changing? $\endgroup$– JEBCommented Jun 5 at 1:59
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2$\begingroup$ I don't get the setup. Is the container open to one or more sides, and if so which?As I'm reading it you are just pumping heat into a closed, completely filled container, so I would not only question whether the CoM changes but even whether water evaporates to begin with. $\endgroup$– MisterMiyagiCommented Jun 5 at 10:27
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$\begingroup$ What do you define as the system? Some answers seem to think a tube that is open at one end. As the water vapor escapes from one end only, the cylinder will move. However the 'system' includes that water vapor. $\endgroup$– Jason GoemaatCommented Jun 5 at 14:18
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$\begingroup$ System=initial water+container $\endgroup$– tensorman666Commented Jun 5 at 17:45
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2 Answers
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According to Newton's 3rd law action has equal and opposite reaction. Which means as the water evaporates outwards the expanding gas will push container in opposite direction. The center of mass for whole system (cylinder + vapor) will remain the same while cylinder and vapor are moving away from each other. The cylinder isn't stationary object and it can also move.
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5$\begingroup$ In effect, what you have created is a rocket. A very weak and very inefficient rocket, but a rocket none the less. Indeed this sort of propulsion is used on satellites today. Here is a link to a company that produces some that have been demonstrated on orbit. (I have no affiliation, they just appeared on my google search) $\endgroup$ Commented Jun 5 at 5:42
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Since you are shining the light from all directions, with the same energy, the water will evaporate isotropically, such that the net momentum is zero, and hence, the centre of mass won't be moving anywhere.
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$\begingroup$ From how I read the question, "a cylindrical container filled to the brim" would mean that the container has a brim - one opening, on one side. So as the volume of the water expands (because some of it becomes gaseous), some of it would have to escape out of that one opening, on only one side, no? Though with the escaping water moving in one direction and the cylinder in the other, we'd still have net zero momentum and stationary CoM $\endgroup$– SyndicCommented Jun 5 at 6:22