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A square frame of side 10cm rests on a table. Confined within the frame are 500 ants, each of mass 0.001g. The ants rush about randomly with constant speed 0.02m/s, colliding with each other and with the walls. Assuming the collisions are perfectly elastic, calculate for force on each side of the square due to the ants' movement.

Attempt:

Assuming a random motion factor ( I don't really know what's the proper name for it) of 1/2 instead of 1/3 as we are dealing with a 2-dimensional motion, and applying the usual kinetic theory formula, answer is 10

^{-6}N.

Thoughts:

What I don't entirely understand is this:

Are we trying to postulate that the net vector force acting in the region is zero? If that's the case then why the need to have the ants moving "parallel to the sides of the frame"? The resultant force will still be zero if they move at 45° to the planes AND perpendicular to each other.Assume that the word "random" implies that the motion is equivalent to two groups of 250 antsrunning at right angles to each other and parallel to the sides of the frame.

Can anyone please provide a more elaborate explanation on the bold statement? Thank you!