Most objects feel several forces at once. What decides how an object moves is their combined effect, the net force. Along a line, you find it the way you add signed numbers.
Key idea
Pick a positive direction. Forces that way are positive; forces the other way are negative. Add them up: the result is the net force, $\Sigma F$. If it is zero, the forces are balanced.
Why it works
Two forces in the same direction team up, so their sizes add. Two forces in opposite directions fight, so one cancels part of the other: in a tug of war, 300 N to the right against 250 N to the left leaves $300 - 250 = 50$ N to the right. Only the leftover, unbalanced part can change the motion.
Worked example: Same direction
Two friends push a stalled car forward, one with 400 N and one with 350 N. Find the net force (ignore friction).
- Both forces point forward, so add: $400 + 350 = 750$ N.
Answer: $750$ N forward
Worked example: Opposite directions
In a tug of war, team A pulls left with 620 N and team B pulls right with 580 N. Taking right as positive, find the net force.
- Right is positive: $+580$ N. Left is negative: $-620$ N.
- $\Sigma F = 580 + (-620) = -40$ N.
- The minus sign means the net force points left. Team A slowly wins.
Answer: $-40$ N, that is, 40 N to the left
Common mistake
Adding the sizes of two opposing forces: $620 + 580 = 1{,}200$ N. Opposite forces subtract. Check: the net force can never be bigger than the sum of the sizes, and when forces oppose, it is smaller than the bigger force.