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Roller coaster rider weight problem

  1. Dec 17, 2011 #1
    1. The problem statement, all variables and given/known data
    Suppose the vertical loop has a radius of 6.81 m. What is the apparent weight (Wap) of a rider on the roller coaster at the bottom of the loop? (Assume that friction between roller coaster and rails can be neglected. Give your answer in terms of m and g.)

    R = 6.81 m
    2. Relevant equations
    F=m(a_c)

    3. The attempt at a solution
    Since the roller coaster is at the bottom the centripetal acceleration should be smaller than the weight of the rider on the roller coaster... I think...
     
  2. jcsd
  3. Dec 17, 2011 #2

    PeterO

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    Homework Helper

    For a start "centripetal acceleration" is an acceleration - units ms-2 and "weight of the rider" is a force - units N so I am not sure what you mean that one will be less than the other. Like saying I a taller than you weigh!

    Secondly - ever been in a car that drives through a dip? Did you feel lighter or heavier at the time?
     
  4. Dec 17, 2011 #3
    Sorry I meant centripetal force vs. the force of gravity. I don't really pay much attention while I'm in a car driving through loops. I reckon you are heavier.
     
  5. Dec 17, 2011 #4

    PeterO

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    That is correct, so from your own experience you already know that the answer to this question will be that your apparent weight is greater at the bottom.
    The next difficulty is - how much bigger?

    As far as the centripetal force is concerned, the size of that depends on how fast you are going. You do know that Fc = mv2/R

    Now if you knew from what height the cart had come from you could use the transformation of PE to KE to work that out.

    PEtop → KEbottom

    so mgh → 0.5mv2

    so mv2 = 2mgh → mv2/R = 2mgh/R
     
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