(Note: Drawing a visual presentation with labeling before solving the problem) A

Question

(Note: Drawing a visual presentation with labeling before solving the problem) A mad engineer builds a cube, 2.5 m on a side, in which 6.2-cm-diameter rubber balls are constantly sent flying in random directions by vibrating walls. He will award a prize to anyone who can figure out how many balls are in the cube without entering it or taking out any of the balls. You decide to shoot 6.2-cm-diameter plastic balls into the cube, through a small hole, to see how far they get before colliding with a rubber ball. After many shots, you find they travel an average distance of 2.4 m. How many rubber balls do you think are in the cube?

Explanation / Answer

given cube volume is V = 2.53 = 15.625 m3

mean free distance = 2.4 m

rubber balls = N = ?

using equation

mean free distance is = 1 / 1.41 X 3.14 X d2 X ( N/V )

2.4 = 15.625 / 1.41 X 3.14 X 0.0622 X N

N = 15.625 / 1.41 X 3.14 X 0.0622 X 2.4

N = 382.53 balls

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