A steel cable lying flat on the floor drags a 20 kg block across a horizontal, frictionless floor. A 110 N force applied to the cable causes

Question

A steel cable lying flat on the floor drags a 20 kg block across a horizontal, frictionless floor. A 110 N force applied to the cable causes the block to reach a speed of 3.9 m/s at a distance of 1.9 m. What is the mass of the cable?

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Latifah 4 years 2021-08-26T05:23:37+00:00 1 Answers 100 views 0

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  1. Ben
    0
    2021-08-26T05:24:51+00:00
    Reply

    Answer:

    The answer is;

    The mass of the cable is 7.428 kg

    Explanation:

    Force = 110 N

    Mass of block = 20 kg

    velocity = 3.9 m/s

    We apply the law of motion which is

    v² = u² + 2·a·s

    Where a = acceleration

    s = distance = 1.9 m and

    u = initial velocity = 0 m/s

    v = velocity = 3.9 m/s

    ∴ v² = 2·a·s

    3.9² = 2×1.9×a which gives

    a = 4.003 m/s²

    F= m×a

    Where F= Force = 110 N

    m = mass

    a = acceleration = 4.003 m/s²

    ∴ m = F/a = 110/4.003 = 27.482 kg

    Since the mass of the block = 20 kg

    Mass of cable + block = 27.482 kg

    Mass of cable = 27.428 kg – mass of block = 27.428 kg – 20 kg = 7.428 kg

    Mass of cable = 7.428 kg

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