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Rotating rod with an object connected by a cable on the end, a trebuchet simulator

  1. Mar 1, 2012 #1
    1. The problem statement, all variables and given/known data
    A mass-less rod of length, Ls, is rotating clockwise about a point, P1 in the horizontal plane. Attached by a cable of length, Ls, to the end of the rod and at angle θ is an object of mass, M. Starting at rest and then with the rod having and angular acceleration α, describe the motion of the object.

    I am attempting to make a trebuchet simulator and I am stuck of this part. If I could figure out the motion in this simplified example I feel I can add gravity and all of the variables that will effect α.

    A picture can be seen here:

    2. Relevant equations
    It seems to me that the conservation of angular momentum, r*MV, and relating Linear Kinetic energy KE = 1/2MV^2 with rotational Kinetic energy KEr = 1/2Iω^2 would be the way to go. The problem for me appears to be in figuring out what the tension in the sling will be. F=ma=T(tension) but how do I relate the translation of the rod tip to the translation of the object?

    3. The attempt at a solution
    I had attempted to take the acceleration tangential of the rod tip and set it equal to the acceleration of the object in the same direction, similar to how if this was a static problem and we knew the force perpendicular to the arm we could then find the tension in the sling by using similar triangles, but that seemed to give me some pretty strange numbers, plus it would mean that if the arm was experiencing a negative α, the projectile would also decelerate, which is not correct.
  2. jcsd
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