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Forces B and C create a torque about D
Further examination of your graph will reveal that forces B and C both create a torque about D, and they both create a clockwise or negative torque. Sincethere are no more forces being exerted on the board, the sum of the torques cannot be zero.
Thus, we can tell by inspection that this body is not in equilibrium.
For completeness...
Just for completeness, let's compute the torque about the point at D. If you extend the line of action for force B down and to the left, you will see thatthe distance from point D to that line, along a path that is perpendicular to the line, is 2.12 units. (You can compute that distance using eithertrigonometry or the Pythagorean theory.)
The components of the torque about the point at D are:
The sum of the torques about point D is not zero. Instead, it is -8.936. Therefore, the system does not satisfy the second condition for equilibrium.
Can equilibrium be achieved through the addition or modification of forces?
Obviously, if you add four more forces that are equal in magnitude and opposite in direction to the four existing forces, the system will be inequilibrium.
Also, if you allow the board to turn clockwise by several degrees, there is a point at which it will stop turning and will be in equilibrium.
Beyond those possibilities, I am unable, simply by inspection, to identify any forces thatcould be modified or added to bring the system into equilibrium. If it is required to add or modify forces to achieve equilibrium, I would need toconstruct and solve some simultaneous equations involving trigonometry. I have decided to opt out of that and will leave that as an exercise for the student.
The examples that follow will be less complicated than that.
A fisherman's scale
What is a spring balance or spring scale? A spring scale is often called a fisherman's scale because a lot of fishermen carry one in their tackle box. Theyuse it weigh the fish that they catch.
An old-fashioned spring scale consists of a stiff coil spring with a hook connected to each end. The spring is enclosed in a case that has a vertical slotwith numbers along the side of the slot. There is a pointer attached to the spring that sticks out through the slot.
When you hold the top hook with one hand and hang something on the bottom hook, the spring extends causing the pointer to move downward. The distance thatthe pointer moves is an indication of the weight of the mass connected to the bottom hook.
A luggage scale
Because of the high fees that the airlines charge for overweight luggage, I carry a modern version of a spring scale when I travel so that I can weigh myluggage before check-in and make adjustments to the contents of each piece of luggage as appropriate. My spring scale isvery similar to a fisherman's scale except that it is designed to weigh much heavier items than fish and is more modern in appearance.
My spring scale is designed to make it easy to measure the weight of a piece of luggage. (It also has abuilt-in tape measure, calibrated in both inches and centimeters that can be used to measure the dimensions of a piece of luggage, but that is not germane tothis discussion.)
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