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, 1 and 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 2 is 6 times that of 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


Section 9.1 The Action of Forces and Torques on Rigid Objects

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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