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Tension in a moving pendulum

  1. Oct 19, 2006 #1
    hey guys
    i'm writing a computer prog in visual basic that models a gantry crane.
    (basically modeling a pendulum that has a moving point of suspension)

    the point of suspension, the cart, has a mass
    the bob of the pendulum, the load, has a mass also

    in order to calculate the net forces (horizontal) on the cart and load, to determine their accelerations, velocities and displacements, it is nescessary to know the tension in the cable that connects them.

    what i need is a formula for calculating the tension in the cable given the two masses , the length of cable and the driving force F on the cart!

    so far i have gotten the programme to work but am worried that my formula for tension is not complete

    i have taken the tension= loadmass*g*cos(angle) + loadmass*cablelength*angularvelocity
    , where the angle is the angle incurred by the cable to the verticle
    which i think is correct for a pendulum with a fixed point of suspension
    the second term is the centripedal force due to angular velocity

    the net horizontal force on the load = tension*sin(angle)
    and net horizontal force on cart = F- tension*sin(angle)

    has anyone got any suggestions
    i can "picture" it in my head;
    the faster i accelerate the cart (very large F)
    the greater the tension in the cable
    is this greater tension accounted for in the fact that if the cart accelerates very quicly, the anglular velocity will be much greater and as a result tension will be much greater?
    OR is it nescessary (as i suspect) to add another term containing F, the driving force on the cart, to the formula for tension?

    any suggestions or insights appreciated
  2. jcsd
  3. Oct 28, 2006 #2
    tension on cable = mg*(cos(angle of cable with normal)) + m*(v^2)/(cable length)

    Force on mass= mg*(sin(angle of cable with normal)
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