FYKOS Year 31 Series 2 Problem 5 — raining glass · FYKOS 31 #31.2.5
Physics · mechanics
Problem
A worker brought a bag of marbles to a skyscraper construction, to show off in front of his colleagues. But, what an unlucky accident -- the marbles pour out and start falling through the scaffolding towards the ground. The scaffolding consists of different levels separated by height h. The floor of each level is made out of identical metal grid in which the holes constitute k % out of the whole grid area. Consider a simplified model of marbles falling through the scaffolding, in which if marble lands in the hole of the grid it goes through unobstructed and if it lands on the solid part of the grid its velocity drops to 0 and starts to fall down again immediately (i.e. the size of the marbles is insignificant with respect to the size of the holes in the scaffolding and the marbles don't bounce upon landing, instead they stop and immediately roll down into a hole and continue with their fall). Ignore any potential collisions between marbles themselves. If we assume the marbles pour out of the bag with a constant mass flow of Q, what is the force on each level of the scaffolding, when the situation comes to a steady state?