b = m a = m b = m As shown in the figure below, we have a square one meter on a

Question

b= m

a= m

b= m

As shown in the figure below, we have a square one meter on a side that is free to rotate about an axis perpendicular to the plane of the square, a distance a from one side and a distance b from the other side. Two forces,F *1, find the distances a and b that locate the axis. It should be noted that a and b are not drawn to scale. a= m b= m 2 is 4 times that of F2, are applied to diagonally opposite corners, and act along the sides of the square, first as shown in case (i) and then as shown in case (ii) of the drawing. In each case the net torque produced by the forces is zero. If the magnitude of F1 and F

Explanation / Answer

For case 1

As the torque produced by these forces about the point is zero then

F1 * b - F2 * a = 0

So as F2 =4 F1

F1 * b - 4 F1 * a = 0

.   b= 4a       .............................................1

For case 2

F1 * (1-a) - F2 * b = 0

F1 * (1-a) - 4 F1 * b = 0

1-a -4 b =0 ....................................2

As b=4 a

1-a-16 a =0

17 a=1

So a=0.0588 m

.   b=0.235 m

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