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The 235-kg cart in the figure starts from rest and rolls with negligible friction. It is pulled by three ropes as shown. It moves 600. m horizontally. Find the final velocity of the cart.

F1 = 500N at 0 degree
F2 = 500N at 40.1 degree
F3 = 400N at 30 degree

  • physics -

    X = hor. = 500 + 500cos40.1 + 400cos30,
    X = 500 + 382.5 + 346.4 = 1229N.

    Y = ver. = 500sin40.1 + 400sin30,
    Y = 322.1 + 200 = 522.1N.

    F^2 = X^2 + Y^2,
    F^2 = (1229)^2 + (522)^2,
    F^2 = 1,783,029.
    F = 1335N. = Resultant force.

    a = F / m = 1335 / 235 = 5.69m/s^2.

    (Vf)^2 = Vo^2 + 2ad,
    (Vf)^2 = 0 + 2*5.69*600 = 6828,
    Vf = 82.6m/s.

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