Consider two forces, one having a magnitude of 20 N. The other having a magnitude of 12 N. What is the possible net force for these two forces? Maxim?

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caledon eNotes educator| Certified Educator

Forces are vectors, which means they have a magnitude (in other words, a "strength") and a direction. We usually represent them as arrows to indicate their direction, and sometimes the arrows are sized in proportion to their strength. 

An important thing to take into consideration is that forces are additive. That means that if you add two force vectors together, it is the same as having a single force vector that blends the two together. For example, if you had a force of 10N pointing straight up, and a force of 10N pointing straight down, they would cancel each other out. You would have an overall force vector of 0. 

On the other hand, if one of those vectors was pointing 90 degrees relative to the other, you would get a force whose strength was equal to the hypotenuse of a 45-degree right triangle, with a direction of 45 degrees.

You can think about this in terms of whether it makes practical sense, as well. For example, you know that two people carrying a table will make the job feel easier, even if one is much stronger than the other. If only the largest vector mattered, then the weaker person's help would not be felt at all. You also know that if you counteracted the strong person's force, perhaps by pushing down on the table, that would make the job harder.

From your example, it sounds like the strength of these force vectors is fixed, but they can change direction. This means that the greatest total force would result from both force vectors going in the same direction. In this case, we would just add the vectors together and get 20 + 12 = 32N. 

The lowest force we could get is if the vectors were pointing in opposite directions; this would result in 20 - 12 = 8N. 

Any combination other than these two would result in a force vector with a diagonal angle and a strength somewhere between 8N and 32N.