A bus contains a 1500 kg flywheel (a disk that has a 0.600 m radius) and has a total mass of 10,000 kg. (a) Calculate the angular velo

Question

A bus contains a 1500 kg flywheel (a disk that has a 0.600 m radius) and has a total mass of 10,000 kg.
(a) Calculate the angular velocity the flywheel must have to contain enough energy to take the bus from rest to a speed of 20.0 m/s, assuming 90.0% of the rotational kinetic energy can be transformed into translational energy.
(b) How high a hill can the bus climb with this stored energy and still have a speed of 3.00 m/s at the top of the hill? Explicitly show how you follow the steps in the Problem-Solving Strategy for Rotational Energy.

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Nem 3 years 2021-08-16T21:43:53+00:00 1 Answers 8 views 0

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  1. Acacia
    0
    2021-08-16T21:45:45+00:00
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    Answer:

    Explanation:

    moment of inertia of flywheel = 1/2 m R²

    = .5  x 1500 x .6²

    = 270 kg m²

    If required angular velocity be ω

    rotational kinetic energy = 1/2 I ω²

    = .5 x 270 x ω² = 135 ω²

    kinetic energy of bus when its velocity is 20 m/s

    = 1/2 x 10000 x 20²

    = 2000000 J

    Given 90 % of rotational kinetic energy is converted into bus’s kinetic energy

    135 ω² x 0.9 = 2000000 J

    ω²=16461

    ω = 128.3 radian /s

    b )

    Let the height required be h .

    Total energy of bus at the top of hill = mgh + 1/2 m v²

    m ( gh + .5 v²)

    = 10000 ( 9.8h + .5 x 3²)

    From conservation of mechanical energy theorem

    10000 ( 9.8h + .5 x 3²) = 2000000

    9.8h + .5 x 3² = 200

    9.8h  = 195.5

    h = 19.95 m .

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