3.2. COMPONENTS OF SPATIAL FORCES

RESULTANT OF SPATIAL FORCES

Finding the resultant of forces in the two-dimensional plane is easy. The following procedure is followed:

1. Determine the reference axes
2. Convert forces into their components
3. Add or subtract parallel forces according to the sign convention preferred (usually +x going to the right and +y upwards
4. Take the magnitude of the resultant by using the principle of Pythagorean theorem
                                
5. Solve for the inclination by taking the tangent function of  and .

Solving the resultant of spatial forces follows the same fundamental procedures although there are more steps in converting forces into their components.

1. Determine the reference axes, this time i, j, k references (similar with x, y, z axes)
2. Convert forces into i,j,k components. Be mindful of how the forces are drawn in order to properly break them down. This procedure might take several steps, depending on how the forces are given.
3. Add or subtract parallel forces still following same sign convention: +i going to the right, +j directed upwards, and +k coming out perpendicularly from plane ij (at times, the axes directed outwards from the plane of the paper)
4. The magnitude of the resultant is taken still using the principle of Pythagorean, only adding the k axis
                             
5. The inclination will be determine using the cosine function of the specific axis and the resultant

                                       

                                      
                                     


EXAMPLE 3.2.1: RESULTANT OF SPATIAL FORCES
EXAMPLE 3.2.2: RESULTANT OF SPATIAL FORCES