MHB Finding Inclination of Rod on Cylinder to Wall

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The discussion centers on determining the inclination angle, θ, of a uniform heavy rod resting on a smooth circular cylinder, positioned parallel to a vertical wall. The relationship between the rod's inclination and the distances involved is expressed by the equation a cos³(θ) + b sin³(θ) = c. Participants request a visual representation of the setup to better understand the geometry involved. Additionally, they ask for clarification on the work and ideas already explored in solving the problem. The conversation emphasizes the need for clear illustrations and foundational concepts in statics to facilitate problem-solving.
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A smooth circular cylinder of radius $$b$$ is fixed parallel to a smooth vertical wall with its axis horizontal at distance $$c$$ from the wall. A smooth uniform heavy rod of length $$2a$$ rests on the cylinder with one end on the wall in a vertical plane perpendicular to the wall. Show that its inclination $$\theta$$ to the horizontal is given by

$$a\cos^3\theta+b\sin^3\theta=c$$

Please help
 
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Re: statics

Two things:

1. Could you please post a picture of the situation?

2. Could you please show what work and ideas you've had?
 

Thread 'Area of Overlapping Squares'

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