Physics- Elena please help!

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Part of a roller-coaster ride involves coasting down an incline and entering a loop 30.0 m in diameter. For safety considerations, the roller coasters speed at the top of the loop must be such that the force of the seat on a rider is equal in magnitude to the rider’s weight. From what height above the bottom of the loop must the roller coaster descend to satisfy this requirement?

  • Physics- Elena please help! -

    R = 15 meters

    Ac = w^2 R = v^2/R

    Ac = 2 g to balance weight plus to give additional mg force

    9.8 * 2 = v^2/15
    v^2 = 294 m^2/s^2
    v at top of loop = 17.1 m/s

    potential energy at top of loop = m g h
    = m (9.8)(30) = 294 m
    kinetic energy at top of loop = (1/2) m (294) = 147 m
    total energy at top of loop = 441 m

    we need 441 m Joules of potential energy at start to make it
    m g h = 441 m
    9.8 h = 441
    h = 45 meters high

  • Physics- Elena please help! -

    Thank you!

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