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15 September, 05:01

An open train car, with a mass of 2150 kg, coasts along a horizontal track at the speed 2.83 m/s. The car passes under a loading chute and, as it does so, gravel falls vertically into it for 2.95 s at the rate of 481 kg/s. What is the car's speed v f after the loading is completed? Ignore rolling friction.

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  1. 15 September, 05:31
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    The car's final speed after the loading is completed is 1.71 m/s

    Explanation:

    Given;

    mass of the open car, m₁ = 2150 kg

    initial speed of the car, u = 2.83 m/s

    loading rate of the gravel, m' = 481 kg/s.

    loading time of the gravel, t = 2.95 s

    Then, mass of the gravel, m₂ = m' x t = 481 x 2.95 = 1418.95 kg

    To determine the car's speed after the loading is completed, we apply the principle of conservation of linear momentum;

    Initial momentum = Final momentum

    m₁u = v (m₁ + m₂)

    where;

    v is the car's final speed after the loading is completed

    2150 x 2.83 = v (2150 + 1418.95)

    6084.5 = 3568.95v

    v = 6084.5 / 3568.95

    v = 1.71 m/s

    Thus, the car's final speed after the loading is completed is 1.71 m/s
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