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- Homework Statement
- 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 Mc 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.

- Relevant Equations
- torque1+torque2=0

What is meant by "the smallest value of angular displacement of the raft from its original position during one cycle"? I understand that I am supposed to solve this problem using torques of the crane and and of the boxes, but I am totally confused by that "smallest angular displacement". If it was the biggest angular displacement, I would understand it, but this is just strange. What does it mean?

I suppose I should use an equation that torque1+torque2=0, then the crane is stable. Torque1= Mga (a = distance of the gravity force Mg from the rotation axis ). Torque2=-mgb (b= distance of the gravity force mg from the rotation axis). But what am I to calculate anyway? I only need to know what that weird angle is.

I suppose I should use an equation that torque1+torque2=0, then the crane is stable. Torque1= Mga (a = distance of the gravity force Mg from the rotation axis ). Torque2=-mgb (b= distance of the gravity force mg from the rotation axis). But what am I to calculate anyway? I only need to know what that weird angle is.