Problem Set

NBPhO 2025

6. Birds Jaan Kalda 4 pts

Mechanics · Statics, Buoyancy, Torque equilibrium

Find the maximum number of identical birds a floating square-cross-section beam can hold above water, given a specific one-bird tipping condition.

Problem by Jaan Kalda.

A long and thin homogenous beam with uniform thickness and square cross-section floats horizontally in water with its top surface parallel to the water surface. A bird lands on one end of the beam, and as a result, the beam sinks so that the edge of the upper face on the bird’s side is exactly at the same height as the water surface, while at the other end of the beam the lower face does not rise above the water. What is the maximum number of such birds that this beam can hold above water?