PHYSICS

An 800.0 kg roller coaster car is at rest at the top of a 95 m hill. It rolls down the first drop to a height of 31 m. When it travels to the top of the second hill, it is moving at 28 m/s. It then rolls down the second hill until it is at ground level.
What is the kinetic and potential energy at the top and bottom of each hill?

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  1. They presumably want to to assume total mechanical energy (kinetic + potential) is constant, even though that is not the case.

    At the top of the 95 m hill, all of the energy is potential, and equals
    M g H = 744,800 J. Use the height or velocity at the other location, and the total energy (748,800 J) , to determine kinetic and potential energies

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  2. 1.
    PE1 = mgh1 = 800•9.8•95 =744800 J.
    KE1=0.
    Total E1 = PE1+ KE1=744800 J.
    2.
    PE2 = 800•9.8•31=243040
    PE1= PE2+KE2
    KE2 = PE1- PE2 =
    =744800 - 243040=501760 J.
    Total E2 = PE2+ KE2=744800 J.
    3.
    KE3 =mv²/2= 800•(28)²/2 =313600 J.
    PE3 =744800-313600 = 431200 J.
    Total E3 = PE3+ KE3=744800 J.
    4.
    PE4=0.
    KE4 = 744800 J.
    Total E4 = PE4+ KE4=744800 J.

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