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Roller Coaster Loop Loop

  1. Mar 23, 2015 #1
    1. The problem statement, all variables and given/known data
    At one point in a roller-coaster, a single 300 kg car goes around a vertical, circular loop with a diameter of 24 m. It enters the loop at the bottom with a speed of 20 m/s. What will its speed be at the top?

    2. Relevant equations
    Kinetic Energy = 1/2mv^2
    Gravitational Energy = mgh

    3. The attempt at a solution
    Initial Energy = Final Energy => Kinetic Energy of the Bottom = Kinetic Energy of the Top + Gravitational Energy at the Top

    I set up the equation for this problem and plugged in numbers to solve this, but I have a negative answer under the square root. Am I missing something else here?
     
  2. jcsd
  3. Mar 23, 2015 #2

    ehild

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    You are right, that car will not reach the top.
     
  4. Mar 23, 2015 #3

    Simon Bridge

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    To check - and help you understand your result - ask instead: "does the car have enough initial kinetic energy to get to the top?"
    Or, another way, what is the highest the car can reach?
     
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