Adding Forces As Vectors
If two forces act at a point and the forces act at right angles to each other, as shown below, the two forces can be considered to act as a single force.
The magnitude of the force is the length of the diagonal on the scale diagram below, but can also be found using Pythagoras theorem, and the angle the force makes to one of the forces is the anglewhich can be measured or found using simple trigonometry:
If the forces are not at right angles, we can still find the magnitude of the resultant using a scale or vector diagram. The diagram below shows two forces acting at a point. A force of 7 N acts at 30° above the horizontal and a force of 9 N acts at 10° right of vertical.
The resultant is found by constructing a parallelogram with sides scaled to the magnitudes of the forces. The diagonal will then be scaled to the magnitude of the resultant. If we do this for the forces above we obtain the diagram below. The resultant and the angle the resultant makes with the verical (or the horizontal if desired) can be measured.