Worked examples
Both rules are now in hand. All that is left is one decision — are the two forces the same way, or against each other?
Example 1 — a push and a pull
The problem
One child pushes an object on a table in one direction with a force of 5 N while another child pulls that object in the same direction with a force of 7 N. What is the resultant of the two forces applied to the object?
Solution
One is a push and one is a pull — but both are in the same direction.
resultant = 5 N + 7 N
resultant = 12 N, in that direction.
Do not let the words "push" and "pull" convince you the forces oppose each other. It is the direction that decides, not the word.
Example 2 — set against each other
The problem
Two children push a box resting on a horizontal surface. One applies 15 N from the left towards the right, the other 11 N from the right towards the left. Find the resultant of these two forces.
Solution
The forces are in opposite directions, so take the difference.
resultant = 15 N − 11 N
resultant = 4 N, towards the right (the direction of the 15 N force).
Example 3 — finding the unknown force
The problem
A force of 10 N towards the west is applied to an object resting on a table. A force X towards the east is applied to it as well. If the object is pulled along towards the west with a force of 5 N, what is the magnitude of X?
Solution
The object goes west, so the larger force is the western one — the 10 N.
resultant = 10 N − X
5 N = 10 N − X
X = 10 N − 5 N = 5 N
Check it: 10 N west against 5 N east leaves 5 N west. That is exactly what the problem stated.
Direction first, arithmetic second
Every collinear problem has one of two answers: if the forces are the same way, add; if they oppose, subtract. Settle that first; the calculation comes afterwards.