Two forces act at a point such that their greatest resultant is 12 N and their smallest resultant is 8 N. Find the magnitudes of the two forces.

12 N and 8 N
4 N and 8 N
3 N and 9 N
10 N and 2 N

Correct answer: 10 N and 2 N

Solution

F1+F2 = 12 (max resultant when forces are in the same direction). |F1-F2| = 8 (min resultant when forces are in opposite directions). Adding: 2*max(F1,F2) = 20 => F1 = 10 N. Subtracting: 2*min = 4 => F2 = 2 N. The two forces are 10 N and 2 N.

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