# Principle of virtual work

• Mar 18th 2013, 10:04 AM
Principle of virtual work
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 θ to the horizontal is given by

acos3θ+bsin3θ=c

• Mar 18th 2013, 12:18 PM
ebaines
Re: Principle of virtual work
Sorry, but I'm having a hard time following your description. It sounds like the arrangement of cylinder, wall, and bar is like the attached, but then the bar would be stable only if theta = 0 (otherwise it would slide off). What am I missing?

Attachment 27587
• Mar 19th 2013, 06:36 AM
ebaines
Re: Principle of virtual work
On thinking about this further, I wonder if the question is about using geometry to find the length of a line from a vertical wall to a tangent point on a circle, as per the figure below. If so, it's pretty easy to show that the length of that line is equal to the $\displaystyle c/\cos \theta + b \tan \theta$. Upon rearranging, and using 2a for the length of the rod, you get:

$\displaystyle c = 2a \cos \theta - b \sin \theta$

But this does not equal the formula provided in the question. For example, if theta = 0 then this formula yields c = 2a whereas the formula provided in the original question yields a=c.
Attachment 27595