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 4 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 =F
Then, magnitude of F2 = 4F
Side of Square = 1m

As we know Net Torque = 0
For Diagram a -
F1 * b = F2 * a

Substituting Values -
F * b = 4 F * a
b = 4a ------------1

For diagram b -
F2 * b = F1 (1 -a)
Substituting Values -
4F b = F (1-a)
4b = 1- a
a = 1-4b ------2

Using Equation 1 and 2 -
b = 4 (1-4b)
b = 4 -16b
b = 4/17 m = 0.235 m

a = 1 -4 (4/17)
a = 1 -16/17
a = 1/17 = 0.0588 m

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