What is the minimum number of unequal forces whose vector sum can equal zero?

What is the minimum number of unequal forces whose vector sum can equal zero?

• A. Two
• B. One
• C. Three
• D. Four

Answer: (C)

At equilibrium, the forces must sum to zero, meaning their vectors form a closed figure when added tip-to-tail. Two forces can only cancel each other if they have equal magnitudes and opposite directions, so two unequal forces cannot sum to zero. A single nonzero force cannot sum to zero either. But with three forces, you can always arrange them so that one force is opposite to the resultant of the other two, giving a zero total. This third force can have a magnitude different from the first two, so all three can be unequal. For example, take two perpendicular forces of 4 N and 3 N; the resultant is a vector of magnitude 5 N in some direction, and a third force of 5 N opposite to that resultant completes the triangle, giving a zero sum. Therefore, the minimum number of unequal forces whose vector sum can be zero is three.

At equilibrium, the forces must sum to zero, meaning their vectors form a closed figure when added tip-to-tail. Two forces can only cancel each other if they have equal magnitudes and opposite directions, so two unequal forces cannot sum to zero. A single nonzero force cannot sum to zero either. But with three forces, you can always arrange them so that one force is opposite to the resultant of the other two, giving a zero total. This third force can have a magnitude different from the first two, so all three can be unequal. For example, take two perpendicular forces of 4 N and 3 N; the resultant is a vector of magnitude 5 N in some direction, and a third force of 5 N opposite to that resultant completes the triangle, giving a zero sum. Therefore, the minimum number of unequal forces whose vector sum can be zero is three.