The resultant force acting on an object is the vector sum of the set of forces acting on that one object. It is very important to remember that we consider all the forces that act on the object under consideration - not the forces that the object might, in turn, apply on other objects.
The easiest way to determine this resultant force is to construct what we call a force diagram. In a force diagram we represent the object by a point and draw all the force vectors connected to that point as arrows. Remember from the Vectors chapter that we use the length of the arrow to indicate the vector's magnitude and the direction of the arrow to show which direction it acts in.
The second step is to rearrange the force vectors so that it is easy to add them together and find the resultant force.
Let us consider an example to get started:
Two people push on a box from opposite sides with a force of 5 N.
When we draw the force diagram we represent the box by a dot. The two forces are represented by arrows, with their tails on the dot.
See how the arrows point in opposite directions and have the same magnitude (length). This means that they cancel out and there is no net force acting on the object.
This result can be obtained algebraically too, since the two forces act along the same line. Firstly we choose a positive direction and then add the two vectors taking their directions into account.
Considering direction towards right as the positive direction
As you work with more complex force diagrams, in which the forces do not exactly balance, you may notice that sometimes you get a negative answer (e.g. -2 N). What does this mean? Does it mean that we have something which is opposite of the force? No, all it means is that the force acts in the opposite direction to the one that you chose to be positive. You can choose the positive direction to be any way you want, but once you have chosen it you must stick with it.
Once a force diagram has been drawn the techniques of vector addition introduced in the previous chapter can be implemented. Depending on the situation you might choose to use a graphical technique such as the tail-to-head method or the parallelogram method, or else an algebraic approach to determine the resultant. Since force is a vector, all of these methods apply!
Always remember to check your signs
Worked Example 13 Single Force on a block
Question: A block on a frictionless flat surface weighs 100 N. A 75 N force is applied to the block towards the right. What is the net force (or resultant force) on the block?
Step 1 : Firstly let us draw a force diagram for the block:
RIAAN Note image on page 68 is missing
Be careful not to forget the two forces perpendicular to the surface. Every object with mass is attracted to the centre of the earth with a force (the object's weight). However, if this were the only force acting on the block in the vertical direction then the block would fall through the table to the ground. This does not happen because the table exerts an upward force (the normal force) which exactly balances the object's weight.
Step 2 :
Thus, the only unbalanced force is the applied force. This applied force is then the resultant force acting on the block.