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 5 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

(a)

Given that,

F2 = 5*F1

For case 1,

Balance torque,

F1*b = F2*a

F1*b = 5*F1*a

b = 5a ....eq1

For case 2,

F2*b = F1*(1 - a)

5*F1*b = F1*(1 - a)

5b = (1 - a) .....eq2

From equation 1 and 2,

a = 0.0385 m

b = 0.1925 m

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