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Conical Pendulum

  1. Aug 25, 2013 #1
    A mass of 80g is moving in a horizontal circle supported by a string 1.2m long suspended from a fixed point in the centre of the circle. The mass completes each revolution in 0.85s. Calculate the tension in the string.



    Relevant equations: I'm not entirely sure, but these were the ones I was considering:
    T = 2∏R/v
    F = mg
    ω = 2∏ / T




    3. The attempt at a solution
    I think that I need to find the angle between the string and the horizontal, but I don't know how to do that. I've got the hypotenuse of the triangle which is 1.2m..
    I also calculated ω using the above equation and got 7.39rad/s. But now I'm lost. Help?
     
  2. jcsd
  3. Aug 25, 2013 #2
    Because the mass is moving in a circle, it must have some acceleration. What is it?

    Given the acceleration, can you find the tension?
     
  4. Aug 25, 2013 #3
    The acceleration is given by v^2 / r...
    I don't know where to get those values..
     
  5. Aug 26, 2013 #4
    ## a = v^2 / r ## is the acceleration of circular motion. Now, you should also be able to express the acceleration from the forces. That should give you a system of equations.
     
  6. Aug 26, 2013 #5

    ehild

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    Draw a sketch of the problem. The mass moves along a horizontal circle of radius R - unknown yet. Draw also the force vectors, acting on it. Their resultant must give the horizontal centripetal force of the circular motion. What forces act on the mass? What is their direction?

    ehild
     
  7. Aug 26, 2013 #6
    Okay so I have a force diagram..
    gravity is the downwards force - F = mg
    acceleration is the horizontal force which is given by v^2/r
    Now what?
     
  8. Aug 26, 2013 #7
    No, you do not have a force diagram. You have one force acting vertically, and a horizontal acceleration. That is impossible.
     
  9. Aug 26, 2013 #8

    ehild

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    What about the string? Does it exert no force ?
    I thought of some picture like the attached one. The string exerts force of tension T along its length. The sum of gravity and the tension provides the centripetal force. It is horizontal and the magnitude is mv2/R. You see two similar triangles, one with sides proportional with the forces and the other for the geometric parameters. They share an angle (the shaded one). Can you proceed?

    ehild
     

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