Finding the Resultants of Forces

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Suppose we have 3 forces acting at a point.

The Resultant of these three forces

The Magnitude of the Resultant is

The angle

In general we have forces in N acting at a point and have resolve vertically and horizontally to find the components.

Example: Find the Resultant of the 3 forces shown:

Resolving Vertically: The 7 and 10N forces are up, in a positive direction but the 9N force is down, in a negative direction:

Resolving Horizontally: The 10 N force is right, in a postive direction, and the 7 N force is left, in a negative direction:

The Resultant Force is illustrated:

The Magnitude of the Resultant is the length of the diagonal:

The bearing of the resultant force is given by

Example: Find the Resultant of this System.


Resolving Vertically: 40+60cos 70 -50sin30 = 35.52N

Resolving Horizontally: 80-60sin 70-50cos 30 = -19.68N

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