A rollercoaster is not moving and has 50,000 J of GPE at the top of a hill. How much kinetic energy will it have halfway down the hill, assu

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A rollercoaster is not moving and has 50,000 J of GPE at the top of a hill. How much kinetic energy will it have halfway down the hill, assuming there is no friction

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Lệ Thu 1 month 2021-08-07T20:06:56+00:00 1 Answers 0 views 0

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    2021-08-07T20:08:15+00:00

    Answer:

    The kinetic energy is 25000 J

    Explanation:

    At the top of the hill, the potential energy = 50000 J

    the potential energy = mgh

    where m is the mass

    g is the acceleration due to gravity

    h is the vertical height at the top of the hill

    Note the mass of the roller coaster and acceleration due to gravity will always remain constant, so that halfway down the hill, only the height changes by half its initial value.

    This means that at halfway down the hill, the potential energy of the roller coaster is

    PE = mg\frac{h}{2} = 50000/2 = 25,000 J

    We also know that the total mechanical energy of a system is given as

    ME = KE + PE = constant

    where

    ME is the mechanical energy of the system

    PE is the potential energy of the system

    KE is the kinetic energy of the system

    Let us now analyse.

    At the top of the hill, all the mechanical energy of the roller coaster is equal to its potential energy due to the height on the hill above ground, since the roller coaster is not moving (kinetic energy is energy due to motion). Halfway down, the mechanical energy of the roller coaster is due to both the kinetic energy and the potential energy, since the roller coaster is moving down, and is still at a given height above the ground. Having all these in mind, we can proceed and say that at halfway down the hill, ignoring friction,

    ME = KE + PE = constant

    50000 = KE + 25000

    therefore

    KE = 25000 J

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