M1, Mechanics

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A particle of mass 4kg is suspended from a point A on a vertical wall by means of a light inextensible string of length 130cm.A horizontal force P, is applied to the particle so that it is held in equilibrium a distance of 50cm from the wall. Find the value of P and the tension in the string.

  • M1, Mechanics -

    50/130 is the sine of the angle the string makes with the wall. That angle is therefore A = 22.6 degrees. (The string, wall and horizontal form a 5-12-13 right triangle)

    Now write horizontal and vertical force balance equations and solve for P and T. (T is the tension)

    The vertical equilibrium equation will be:
    T cos22.6 = M g
    so you can already solve for T.

    The horizontal equilbrium equation is
    T sin22.5 = P

    You finish it.

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