Solving Static Equilibrium Problems

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Thus, the net force is zero and the acceleration is 0 m/s/s.

Objects at equilibrium must have an acceleration of 0 m/s/s.

The most common application involves the analysis of the forces acting upon a sign that is at rest.

For example, consider the picture at the right that hangs on a wall.

Understand the rules, describe them using commands a computer understands, put numbers in, get answers out.

Sometimes, however, there are clever solutions available. Consider the two objects pictured in the force diagram shown below.Note that the two objects are at equilibrium because the forces that act upon them are balanced; however, the individual forces are not equal to each other. is the key word that is used to describe equilibrium situations. 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 magnitude and direction of each component for the sample data are shown in the table below the diagram. The sample data used in this analysis are the result of measured data from an actual experimental setup.The difference between the actual results and the expected results is due to the error incurred when measuring force A and force B.(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.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.

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