Adding parallel forces
The observation from activity 3 is the third rule.
Two parallel forces in the same direction
To find the resultant of two forces acting in parallel in the same direction, those two forces must be added.
resultant = force 1 + force 2
Notice that this is the same as the first rule in section 9.2. Whether the two forces lie on one line or on two parallel lines makes no difference to the sum — only the direction does.
Worked example 1
The problem
Two strong threads tied to a trolley are held parallel to each other and pulled, one with a force of 8 N and the other with a force of 16 N. Find the resultant of these two forces.
Solution
The threads are parallel and both forces act the same way, so add them.
resultant = 8 N + 16 N
resultant = 24 N, in that direction.
Worked example 2 — finding the unknown force
The problem
Two threads tied to a trolley on a table are held parallel and pulled, and the resultant produced is 20 N. The force applied to thread A is 12 N. Find the force applied through thread B.
Solution
resultant = A + B
20 N = 12 N + B
B = 20 N − 12 N = 8 N
A subtraction happens here, but that does not mean the two forces oppose each other. When the sum is known, one part of it is found by subtracting — the rule is still "add".
Three rules now
Collinear, same direction — the sum. Collinear, opposite directions — the difference. Parallel, same direction — the sum. So there is only one case where you subtract: when the forces are set against each other.