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Math Help - mass

  1. #1
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    mass

    A body of mass 10kg is initially at rest on a rough horizontal surface. it is pulled along the surface by a constant force of 60N inclined 60degrees above the horizontal. if the resistance to motion totals 10N, find the acceleration of the body and the distance travelled in the first 3seconds.

    any help would be great
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  2. #2
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    Consider the body as a point mass, and position the origin at the point mass. The sum of forces acting on the object is:
    F_{net} = F + F_n + F_k + F_g = ma

    Note that the external forces here are vectors. The forces acting on the object horizontally are resistance force and [applied] constant force. The sum of forces acting in the x-direction:

    F_x = F\cos{30} + F_k\cos{180} = ma_x

    Note also that the sum of forces acting in the y direction is zero, so acceleration has only the x-component. Solving for a_x, we get:

    a_x = \frac{F\cos{30} + F_k\cos{180}}{m}

    Simply plug in F, F_k, and m to get the acceleration. To find the distance travelled, you use the kinematic equation:
    \Delta x = v_i~t + \frac{1}{2}at^2

    Where \Delta x is the horizontal displacement and v_i is the initial speed (0).
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