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Merry Go Round (Centripetal Force)

  1. Oct 29, 2009 #1
    1. The problem statement, all variables and given/known data

    Two identical twins, Jena and Jackie, are playing one December on a large merry-go-round (a disk mounted parallel to the ground on a vertical axle through its center) in their school playground in northern Minnesota. Each twin has a mass of 29.0 kg. The icy coating on the merry-go-round surface makes it frictionless. The merry-go-round revolves at a constant rate as the twins ride on it. Jena, sitting a distance 1.80 m from the center of the merry-go-round, must hold on to one of the metal posts attached to the merry-go-round with a horizontal force of 58.0 N to keep from sliding off. Jackie is sitting at the edge, a distance 3.67 m from the center.

    With what horizontal force must Jackie hold on to keep from falling off?

    If Jackie falls off, what will be her horizontal velocity when she becomes airborne?


    I attempted this problem but got the wrong answer. What I did first was

    58N = 29kg*V^2
    =========
    1.80

    V = 1.89 m/s

    Fnet = m*v^2
    ---------
    R

    Fnet = (29kg)(1.89m/s)^2
    --------------------
    3.67

    Fnet = 28.4N


    What did I do wrong?
     
  2. jcsd
  3. Oct 29, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    1.89 m/s is not the velocity of Jack. Their angular velocities is the same.
    And angular velocity ω = v/R.
    So v1/R1 = v2/R2. So find v2.
     
  4. Oct 30, 2009 #3
    So

    1.89m/s
    -------- = V2/3.67m
    1.80 m

    V2 = 3.8585 m/s ?

    Then

    Fnet = (29kg)(3.8585m/s)^2/3.67m = 117.6N ?
     
  5. Oct 30, 2009 #4

    rl.bhat

    User Avatar
    Homework Helper

    Yes. That is right.
     
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