LESSON 2: Sum of Forces


Now that we have covered the basics of vectors, let’s move on to the main idea of statics. One of the major concepts in statics is: the sum of the forces in the y-direction equals zero and the sum of the forces in the x-direction equals zero. The word “static” essentially means still, or motionless. So, this main concept of statics is essentially: all the forces going up must equal all the forces going down and all the forces going to the right must equal all the forces going to the left. This makes sense; if you take an object with a large force pushing it right, and a small force pushing it left, the block will move to the right and it will not be static, or motionless. Here is an example:


Seeing that there are two forces (represented as green vectors) pushing the block to the right, each with a magnitude of 15 N, what must be the magnitude of the red vector pushing the block to left? The red vector must have a magnitude of 30 N to cancel the two 15 N forces. Mathematically this looks like this:

Here is another example where a metal bar is held up by a pin joint and a wire. Let’s say the bar has a weight of 20 N and the wire has a tension of 7 N.

The pin joint helps to hold the bar up; therefore there is a vertical force that the pin joint exerts on the metal bar. What
is the magnitude of this force created by the pin joint? If the bar weighs 20 N (creating a downward force) and the tension in the wire is 7 N (an upward force) this means that the pin joint must create an upward force of 13 N (20-7) . Now the bar is static, the 7 N force and 13 N force (going up) combine to cancel out the 20 N force (going down).

In the next section we will expand on this concept by using vectors that act at an angle, rather than simply using vectors that are perfectly horizontal or vertical.