A rotational axis is directed perpendicular to the plane of a square and is loca

Question

A rotational axis is directed perpendicular to the plane of a square and is located as shown in the drawing. Two forces, vector F 1 and vector F 2, are applied to diagonally opposite corners, and act along the sides of the square, first as shown in part a and then as shown in part b of the drawing. In each case the net torque produced by the forces is zero. The square is one meter on a side, and the magnitude of vector F 2 is 6 times that of vector F 1. Find the distances a and b that locate the axis. Note that a and b are not drawn to scale. a = m, b = m?

Explanation / Answer

Let
     Magnitude of F1 = x
   Magnitude of F2 = 6 x
     Side of the square = 1 m
    Case (a):
                  Clockwise torque = Anticlockwisetorque
                                F2 * a = F1 * b
                               6 x * a = x * b
                                     6a = b ................(1)
    Case (b):
                  Clockwise torque = Anticlockwisetorque
                            F2 * b = F1 * ( 1 - a )
                              6x * b =x * ( 1- a )
                                    6 b = 1 - a .................(2)
                by sub. ( 1 ) in ( 2 )
                                  6 * 6 a = 1 - a
                                         36 a = 1 - a
                                         37 a = 1
                                                 a = 1 / 37
                                                    = 0.027 m
                              Then, b = 6 a = 6 * 0.027
                                                      = 0.1621 m

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