A rope connects boat A to boat B. Boat A starts from rest and accelerates to a speed of 9.5 m/s in a time t = 47 s. The mass of boat B is 54

Question

A rope connects boat A to boat B. Boat A starts from rest and accelerates to a speed of 9.5 m/s in a time t = 47 s. The mass of boat B is 540 kg. Assuming a constant frictional force of 230 N acts on boat B, what is the magnitude of the tension in the rope that connects the boats during the time that boat A is accelerating?

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Thái Dương 5 months 2021-08-09T06:53:24+00:00 1 Answers 0 views 0

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    2021-08-09T06:54:56+00:00

    Answer: 339.148N

    Explanation:

    Data

    Time (t) = 47s

    U = 0m/s

    V = 9.5m/s

    Mass of B = 540kg

    Frictional force on B = 230N

    Both boats are connected so if A moves, B moves too.

    Acceleration of boat A =?

    Using equation of motion,

    V = u + at

    9.5 = 0 + a*47

    a = 9.5 / 47

    a = 0.2021 m/s²

    The force required to accelerate boat B since it’s the same force moving both boats =?

    F = Mass * acceleration

    F = 540 * 0.2021 = 109.14N

    A frictional force of 230N exists on boat B

    Total force (Tension) = frictional force + normal force = (109.15 + 230)N = 339.148N

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