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19 October, 15:22

A box of mass m is pushed horizontally on a rough floor with an initial speed of 2 m/s. The coefficient of kinetic friction between the surface and the box is µ_k = 0.1. Calculate the distance the box will move before stopping.

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  1. 19 October, 18:06
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    The box is pushed initially.

    F = ma;

    m - mass of box

    a - acceleration.

    ma = - mu_k mg

    a = - mu_k g

    Equation of motion: v^2 = u^2 + 2as

    The box comes to a rest, v = 0 m/s

    Here, u = 2 m/s and a = - 'mu_k g = - 0.1 xx 9.81 = - 0.981 m/s^2

    Thus, u^2 = - 2as

    s = u^2 / (-2a) = (2^2) / (-2 x - 0.981) = 2.04 m.

    So the box will move a distance of 2.04 m over the rough surface.
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