Solving Static Equilibrium Problems

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Sometimes, however, there are clever solutions available. 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.The weight of the sign is equal to the sum of the upward components of the tension in the two cables.Thus, a trigonometric function can be used to determine this vertical component. Since each cable pulls upwards with a force of 25 N, the total upward pull of the sign is 50 N. The idea is that the tension, the angle, and the weight are related.This extends from Newton's first law of motion. A common physics lab is to hang an object by two or more strings and to measure the forces that are exerted at angles upon the object to support its weight.But having an acceleration of 0 m/s/s does not mean the object is at rest. The state of the object is analyzed in terms of the forces acting upon the object.We would have to conclude that this low margin of experimental error reflects an experiment with excellent results.We could say it's "close enough for government work." The above analysis of the forces acting upon an object in equilibrium is commonly used to analyze situations involving objects at static equilibrium.The diagram below shows vectors A, B, and C and their respective components.For vectors A and B, the vertical components can be determined using the sine of the angle and the horizontal components can be analyzed using the cosine of the angle.


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