Solve Statics Problems

Solve Statics Problems-8
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.

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.

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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.

Therefore, the force of gravity (also known as weight) is 50 N, down. If the any two of these three are known, then the third quantity can be determined using trigonometric functions.

As another example that illustrates this idea, consider the symmetrical hanging of a sign as shown at the right.

A sketch of this situation (see diagram below) reveals that the tension in the cable can be found using the sine function.

The triangle below illustrates these relationships. There is an important principle that emanates from some of the trigonometric calculations performed above.

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.

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.

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