Short Question about Torque on a Ladder Hinge

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SUMMARY

The discussion focuses on calculating the torque exerted by the mass of a ladder about its hinge when propped at an angle α. The torque formula τ = r x F is applied, where the force is the weight of the ladder (M_ladder * g) and the distance r is determined by the ladder's geometry. The correct expression for torque is τ = (M_ladder / 2) * g * (L/2) * sin(α), with r defined as L * sin(α) / 2. This analysis clarifies the relationship between the ladder's angle, mass, and the resulting torque.

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  • Basic understanding of static equilibrium in mechanics.
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Homework Statement


So this is a small part of a much larger problem that I'm working on that I don't want to post here. Basically, I want to find the contribution to the torque about the hinge of a ladder BY the mass of the ladder itself. A ladder is propped open at an angle α. What is the torque about the hinge of the top of the ladder of length L by the ladder itself?

Homework Equations


τ = r x F

The Attempt at a Solution


Will the torque from one side of the ladder I'm ignoring the other side of the ladder for now). be M_ladder / 2 * g * L/2 sinα ? I'm basically wondering what to put for r, the perpindicular distance from the force applied to the point of torque. Should it just be the center of that side of the ladder? In that case, should it be Lsinα /2?
 
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Are alpha the angle one leg encloses with the vertical, and M the total mass of the ladder? In that case, the expression for the torque due to the weight is correct.
 

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