Engineering Statics

A-8


Determine the x and y coordinates of each of the forces shown.
Determine the magnitude and direction of the resultant.

whereWhen a force is defined by geometry rather than a trigonometric angle, we know that the x and y components of the force are proportional to the distances in the x and y direction.
The resultant of the two forces can be divided into components in the i and j directions.<BR>The x components are added together to get the resultant's x component in the i direction.
Similarly, the y components are added together to get the resultant's y component in the j direction.
This gives us the resultant in vector form.
The magnitude of resultant can be determined by taking the square root of the sum of the components squared.
Performing the arithmetic gives us the magnitude of the resultant.
The angle that the resultant makes with the positive x axis can be found by taking the inverse tangent of the y component divided by the x component of the resultant.
The negative angle indicates that the angles has been measured clockwise from the positive x direction.