Suppose we have 3 forces acting at a point.
The Resultant of these three forces
The Magnitude of the Resultant is
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