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3 October, 16:55

Two boxes on a horizontal plane with coefficient of friction µ are connected by a massless string. The left-hand box has mass m and the right-hand box has mass 2m. A force F is applied to the right-hand mass at an angle θ with respect to the horizontal so that they move to the right at constant acceleration. What is the magnitude of the tensi

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  1. 3 October, 17:09
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    T = (3μmg - Fcosθ) / 2

    Explanation:

    Since the boxes move to the right, the net force on box of mass 2m is

    Fcosθ - 2μmg + T = ma (1) where Fcosθ = horizontal component of applied force, 2μmg = frictional force and T = tension in string and a = acceleration of box

    The net force on the box with mass m is

    μmg - T = ma (2) where μmg = frictional force, T = tension and a = acceleration of boxes.

    Equating (1) and (2) we have

    Fcosθ - 2μmg + T = μmg - T

    collecting like terms

    Fcosθ - 2μmg - μmg = - T - T

    Fcosθ - 3μmg = - 2T

    (3μmg - Fcosθ) / 2 = T

    T = (3μmg - Fcosθ) / 2
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