Question

Two forces, one of magnitude 2 N and the other of magnitude 3 N, are applied to the ring of a force table. The directions of both forces are unknown. Which best describes the limitations on R, the resultant? Explain carefully the basis for your answer. (a) R≤5 N (b) 2 N≤R≤3 N (c) R≥3 N (d) 1 N≤R≤5 N (e) R≤2 N.

Answer 1

the highest magnitude occurs when the two forces are in the same direction (in which case, add the two forces)

the lowest magnitude occurs when the two forces are in the opposite direction, in which case they'll partially cancel out each other (subtract the two forces. magnitude is always positive, so take the positive version of the result).

from there, it's lowest value ≤ R ≤ highest value