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Sign problem

  1. Sep 10, 2007 #1
    1. The problem statement, all variables and given/known data

    A smooth ring of mass m can slide on a fixed horizontal rod.A string tied to the ring passes over a fixed pulley and carries a mass M(<m).At an instant the angle between the rod and the string is θ.Show that if the ring slides with a speed v,the block descends with a speed v cosθ.With what acceleration will the ring start to move if the system is released from rest at θ=30*?

    I have attached the figure in a pdf file so that you may see it

    2. Relevant equations
    3. The attempt at a solution

    I take z axis downwards,x axis rightwards.

    The force equations:T cosθ=m D²x
    Mg-T=M D²z

    Now,we are to find the constraint equation.

    I got this:(using the length conservation)

    √[x²+c²]+z=L...............c is a const
    Differentiating twice w.r.t. t we get: Dz=-Dx (cosθ)


    What is annoying me is the (-)ve sign before the ansswer.

    Somehow this is not correct.Because,in the next part we require this result:

    D²z=-D²x cosθ+0(initially Dx=0)

    This gives an error in the final answer.

    Can anyone please help?
     

    Attached Files:

  2. jcsd
  3. Sep 10, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    In your constraint equation, it looks like you use "x" to represent the horizontal distance between sliding mass and pulley. x decreases as the mass slides. So the acceleration of the sliding mass should be -D²x.
     
  4. Sep 10, 2007 #3
    Exactly!!! was not careful to write the force equations...it should be consistent with the constraint equation's sign convention.
    I got the correct answer!

    Thank you very much.
     
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