Solving Static Equilibrium Problems

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The leftward pull of cable A must balance the rightward pull of cable B and the sum of the upward pull of cable A and cable B must balance the weight of the sign.

Suppose the tension in both of the cables is measured to be 50 N and that the angle that each cable makes with the horizontal is known to be 30 degrees. This question can be answered by conducting a force analysis using trigonometric functions.

(Recall that the net force is "the vector sum of all the forces" or the resultant of adding all the individual forces head-to-tail.) Thus, an accurately drawn vector addition diagram can be constructed to determine the resultant. For most students, the resultant was 0 Newton (or at least very close to 0 N).

This is what we expected - since the object was at equilibrium, the net force (vector sum of all the forces) should be 0 N.

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Another way of determining the net force (vector sum of all the forces) involves using the trigonometric functions to resolve each force into its horizontal and vertical components.

Once the components are known, they can be compared to see if the vertical forces are balanced and if the horizontal forces are balanced.

The sign isn't going anywhere (it's not accelerating), therefore the three forces are in equilibrium. We used component analysis since it's the default approach.

As always, make a nice drawing to show what's going on. We use this brainless, brute force approach to problems all the time.

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