A quantity of flour of volume 72 cm³ forms a conical pile on a board. The coefficient of static friction between flour grains is μₛ = √π. Find the maximum height of the pile in cm.
Physics · Newtons law of motion and Friction · friction and single block problem
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Question

A quantity of flour of volume 72 cm³ forms a conical pile on a board. The coefficient of static friction between flour grains is μₛ = √π. Find the maximum height of the pile in cm.

G1 Physics · Accepted Answer

At the angle of repose, tanθ = μₛ = √π. For the cone, h/r = √π, so r = h/√π. Volume V = (1/3)πr²h = h³/3. Given V = 72 cm³, h³ = 216 and h = 6 cm.