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Finding velocity of car in Carnival ride

  1. Mar 12, 2013 #1
    1. The problem statement, all variables and given/known data
    You've taken your neighbor's young child to the carnival to ride the rides. She wants to ride The Rocket. Eight rocket-shaped cars hang by chains from the outside edge of a large steel disk. A vertical axle through the center of the ride turns the disk, causing the cars to revolve in a circle. You've just finished taking physics, so you decide to figure out the speed of the cars while you wait. You estimate that the disk is 6m in diameter and the chains are 6m long. The ride takes 10s to reach full speed, then the cars swing out until the chains are 30degrees from vertical.


    2. Relevant equations
    Fc=m(v^2)/r
    w=mg

    3. The attempt at a solution
    I summed the Forces in the Y direction, so 0=Ft*cos30 -mg
    Ft being the tension force on the cable of the car
    Ft=mg/cos30
    2nd equation: Ft*sin30 -Fc
    Fc=Ft*sin30
    sub in mv^2/r for Fc
    solved for v and i got v=sqrt(r*g*tan30)
    i plugged in the radius of the disk which is 3m and gravity which is 9.81m/s^2
    v=4.122m/s^2, but that was wrong
    What am I doing wrong?
     
  2. jcsd
  3. Mar 12, 2013 #2

    PhanthomJay

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    The radius of the cars circle is not the same as the disc radius.
     
  4. Mar 12, 2013 #3

    TSny

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    Careful. Are you sure r is the radius of the disk?
     
  5. Mar 12, 2013 #4
    if I do radius as 9m then I get 7.14m/s as the velocity, which is wrong also
     
  6. Mar 12, 2013 #5

    PhanthomJay

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    You are not calculating the radius correctly. Recheck your geometry and trig for the swing angle
     
  7. Mar 12, 2013 #6
    ok how would I go about calculating it properly, I have no idea
     
  8. Mar 12, 2013 #7

    TSny

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    Draw a side view of the disk. Draw the car hanging vertically (before the ride starts). On the same figure draw the car hanging from the same point at 30 degrees from the vertical (after the ride starts). Draw a line representing the radius of the circle that the car is traveling in. Can you see how to determine the value of the radius?
     
  9. Mar 12, 2013 #8
    well doesnt it make a 30 60 90 triangle?
    so the radius would be 3+(2*9/root3)?
     
  10. Mar 12, 2013 #9

    TSny

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    Yes.
    The expression in the parentheses is incorrect. Which side of the 30 60 90 triangle represents the additional amount you need to add to the 3 m radius of the disk? What is the length of the hypotenuse of the triangle?
     
  11. Mar 12, 2013 #10
    the hypotenuse would be the length i need to add by 3. so it should be 3+(2*6/root3)
    because the side opposite of the 60 degree angle is a*root3 and the hypotenuse is 2a.
     
  12. Mar 12, 2013 #11

    TSny

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    Is your diagram similar to the attached figure? If so, what is the length of the hypotenuse of the triangle a b c?
     

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