How To Find The Magnitude When Force & Angle Is Given?

When a force works in the same direction as a body moves, the entire force acts on the body. In many cases, however, the force points in a different direction. When an object slides down a slope, for instance, gravity acts straight downward, but the object moves at an angle. The effective force on the object is a vector quantity related to but separate from the original force. The two vectors are related through trigonometry.

Step 1

Subtract the angle between the force and the resultant vector you want to calculate from 90. If, for instance, the force acts at a 30-degree angle from the object's direction of motion then 90 – 30 = 60.

Step 2

Find the sine of this angle. With the example for Step 1, sin (60) = 0.866.

Step 3

Multiply this answer by the original force. If the force equals, for instance, 100 Newtons then 0.866 × 100 = 86.6 Newtons. This is the magnitude of the resultant force vector on the object.