Taking one force from the other
The three cases of activity 2 give the second rule.
Two collinear forces in opposite directions
When forces are applied collinearly in opposite directions on an object, the resultant force is given by the difference between those two forces, and its direction is the direction of the greater force.
resultant = larger force − smaller force
Direction: the direction of the larger force.
Worked example 1
The problem
An object on a table is pulled with a force of 5 N in one direction and 2 N in the opposite direction. What are the magnitude and the direction of the resultant of the pulling forces?
Solution
Take the direction of the 5 N as positive; the 2 N against it is then negative.
resultant force = (5 N) + (−2 N)
resultant force = 3 N
So it is pulled along in the direction of the 5 N force with a resultant force of 3 N.
Do not make both signs positive
If one direction is taken as positive the other has to be negative. Writing "(5 N) + (2 N) = 7 N" is the commonest error in this section — it treats the two forces as though they acted the same way. And if your answer comes out negative, all that means is that you chose the wrong direction as positive; keep the magnitude and write the direction as the other way.