Equilibrium - Questions 3 Help

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When all the individual forces acting upon an object are balanced, then the object is at equilibrium. When a force is at an angle to the traditional x-y axes, it is customary to consider the components of the force in the analysis. The components of a force vector are the projections of that vector onto the x- and the y-axis. By thinking in terms of components, it is considerably easier to determine what forces would be required to bring an object to equilibrium.

Every question in the Wizard Difficulty Level is very similar. Three forces are given - two angled and one horizontal. You must add two forces that would balance the three given forces. One of the two added forces must be an east-west force and the other must be a north-south force. Here is an example of such a question.

Version 1:
Consider the three angled forces below. Add one E-W force and one N-S force so that the object is at equilibrium.

"Reading" the Diagram
In this problem, you want to balance the three given force by adding two forces to the object. Two of the three given forces are angled forces. Like all angled forces, they have x- and a y-components. Since the forces are drawn on a background grid of squares that represent 10 N along each edge, it is easy to determine the x- and the y-components. For instance, an angled force vector that stretches horizontally for 7 squares has an x-component of 70 N. If the same angled vector stretches vertically across 4 squares, then the y-component is 40 N. Begin this problem by determining the x- and the y-component of the three given forces.

"Vector Summing" the Forces
The next step is to add the components of the three given forces. Components are vectors too so when you add components you must consider their direction. Add the x-component of the three vctors - A, B, and C - to get the total amount of x-Force provided by Vectors A, B, and C. Repeat the process for the y-components; add the y-components of the three given vectors to determine the total amount of y-Force provided by Vectors A, B, and C. (And by the way, it doesn't hurt to have a scratch pad by your side to write some numbers down.)

Balance the Forces
If the three given forces have a combined (sum) x-component of 70 N to the west, then you need to add an equal strength force in the opposite direction. That is the only way that you can balance the given forces. So add a force of 70 N to the east. By the same reasoning, you will have to add a vertical force to balance the combined (sum) y-component of Forces A, B, and C. So if the combined y-component is 40 N to the north, then add a 40 N force directed southward.

Try this link to The Physics Classroom Tutorial for more help:

Equilibrium