MHB Finding Inclination of Rod on Cylinder to Wall

AI Thread Summary
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.
Suvadip
Messages
68
Reaction score
0
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
 
Mathematics news on Phys.org
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?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Back
Top