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Change in gravitational potential energy for a slender

  1. Apr 2, 2014 #1
    1. The problem statement, all variables and given/known data

    I'll provide a picture for a clearer view: http://i.imgur.com/wkXPcJn.jpg

    Suppose that the slender rod starts at rest at theta = 0. For convenience we chose the datum at theta = 0.
    Now I want to calculate the gravitational potential energy at a later instant when theta = theta_0. But it's tricky since some points of the rod have moved a distance (0.6+0.2)sin(theta_0) and some points have not moved at all. So how does one deal with this case? I have a solution but how should I do in the general case?

    Just to be clear: I am looking for an analytical approach to it that does not involve some intuition because that can
    be dangerous...



    3. The attempt at a solution

    Think of the slender rod as a huge amounts of points uniformly spread. For each point at one side of the mass center there is a point on the other side of the mass center so that the distance between these are the distance from O to the mass center. Hence it should be mg(0.6+0.2)sin(theta_0)/2
     
    Last edited: Apr 2, 2014
  2. jcsd
  3. Apr 2, 2014 #2

    SammyS

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    A slender what ?

    The word slender is not a noun.
     
  4. Apr 2, 2014 #3
    I am sorry. I thought slender and rod is the same thing. I mean a slender rod
     
  5. Apr 2, 2014 #4

    SammyS

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    Yes.

    mg((0.6+0.2)/2)sin(θ0) is a valid expression for the gravitational potential energy of the rod.
     
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