FYKOS Year 36 Series 2 Problem 3 — crane on the raft · FYKOS 36 #36.2.3

Physics · mechanics

Problem

There is a raft in the middle of the river. The mass of the raft is negligible, and it carries a crane on board. The crane moves boxes of building material of mass

m

from one river bank to another. In one cycle, the crane loads material at one side of the river, rotates to the other river bank, unloads the material there, and rotates back. Calculate the smallest value of angular displacement of the raft from its original position during one cycle. Approximate the crane by a homogenous cylinder of mass

M_{\mathrm{j}}

and radius

r

, and a rotating jib in the shape of a slim rod of length

kr

. Assume that the velocity of the river and the “friction” between the raft and the water are negligible.

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