Juggling balls on a scale?

Discussion in 'Physics & Math' started by Dinosaur, Mar 4, 2006.

  1. Dinosaur Rational Skeptic Valued Senior Member

    Messages:
    4,885
    What weights would be recorded if a person juggled balls while standing on a very precise digital scale? Assume the standard 3-ball juggle, not the circular method often used when juggling more than 3 objects. Also assume a very regular motion of the balls. If the man moves on the scales and/or tosses balls to different heights, the analysis becomes almost impossible.

    Assume a 100Kg man juggling three 1Kg balls, and consider determinig an equation showing X (the indicated weight) as a function of time.

    If he steps on the scale carrying the three balls and stands there for a few seconds, the scale will obviously indicate 103Kg just before he starts to juggle the balls.

    If the juggling is started by throwing one ball up without an initial downward movement of a hand, I suppose the scale will momentarily indicate more than 103Kg. Is this correct? I also suppose that the scale will momentarily indicate less than 103Kg and then momentarily indicate more than 103Kg if a toss is initiated with a downward movement of the hand.

    I suppose that the indicated weight will increase when a ball is tossed or caught. It seems that the scale will indicate less than 103Kg (and more than 102Kg) duriing some intervals while one ball is in the air and the other two are being held. There are time intervals when two balls are in the air. Will the scale ever indicate less that 102Kg? I think so, but this might depend on how high the balls are tossed and other details of the juggling process. Will the scale always indicate weights varying above and below 103Kg? Will the weights indicated average to 103Kg?

    Suppose the man starts juggling before he steps on the scale or he steps on the scale carrying two balls and somebody starts the juggling process by tossing the third ball from off the scale. I guess the scale will always indicate values below 103Kg. Is this a correct guess?

    After thinking about the above, consider a circular juggling process. For this process, I think there can be intervals during which all three balls are in the air. Might the scale ever indicate 100Kg during some interval for this process?I suppose a man could stand on the scale carrying no balls. The three balls could be tossed to him one at a time to start the juggling process. If the juggle started this way, would thescale ever indicate 100Kg?
     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. Physics Monkey Snow Monkey and Physicist Registered Senior Member

    Messages:
    869
    Hi Dinosaur,

    Here is a brief sketch of the situation. First, there will be tiny changes in force that occur when the juggler moves his hands up and down. This is easy to see since the center of mass of the juggler moves when he moves his hands

    Second, the juggler exerts a force on a ball when he reverses the direction of motion of the ball. If you integrate this force over time you must obtain the total change in the balls momentum (assuming the time of interaction is sufficiently short so that gravity may be neglected compared to the contact force). An estimate for the force the juggler must exert can be obtained by dividing this change in momentum by the time of interaction. The juggler feels the reaction force and to the extent that the juggler is stationary (held in place by a very massive Earth), an equal force will be exerted on the juggler at his feet.

    Third, on average the center of mass of the juggler plus his three balls doesn't move. Since the gravitational force on the whole system is (M+3m)g down, the average force exerted by the scale must be (M+3m)g up.

    I'm sure you can easily fill in the details.
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.

Share This Page