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Math Help - Principle of virtual work

  1. #1
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    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

    Please help
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  2. #2
    MHF Contributor ebaines's Avatar
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    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?

    Principle of virtual work-wall.jpg
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  3. #3
    MHF Contributor ebaines's Avatar
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    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  c/\cos \theta + b \tan \theta. Upon rearranging, and using 2a for the length of the rod, you get:

    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.
    Principle of virtual work-wall2.jpg
    Last edited by ebaines; March 19th 2013 at 06:39 AM.
    Thanks from emakarov
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