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24 October, 20:53

An open train car, with a mass of 2130 kg, coasts along a horizontal track at the speed 2.93 m/s. The car passes under a loading chute and, as it does so, gravel falls vertically into it for 3.03 s at the rate of 465 kg/s. What is the car's speed v f after the loading is completed

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  1. 24 October, 21:03
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    The final speed after the loading is completed is 1.764 m/s

    Explanation:

    Given;

    mass of open train car, m₁ = 2130 kg

    initial speed of the car, u₁ = 2.93 m/s

    loading rate of gravel = 465 kg/s

    time of loading = 3.03 s

    mass of the gravel, m₂ = 465 kg/s x 3.03 s = 1408.95 kg

    From the principle of conservation of linear momentum

    m₁u₁ + m₂u₂ = v (m₁+m₂)

    where;

    v is the final speed after the loading is completed

    2130 x 2.93 + 0 = v (2130 + 1408.95)

    6240.9 = v (3538.95)

    v = 6240.9/3538.95

    v = 1.764 m/s

    Therefore, the final speed after the loading is completed is 1.764 m/s
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