Two forces of 4N and 10N act on a body. Which of the following could not be the resultant magnitude? (14N, 7N, 6N, 3N)

My first thought when dealing with resultant forces is to try out the most common combinations: combined and opposite. In this case 10N + 4N = 14N and 10N - 4N = 6N. This tactic does rule out two of the answers, but we are still left wondering what is the difference between the remaining answers: 7N and 3N. Why those two options were given? If, say, 7N is obtainable, then how?The trick to "which one is not" questions is to think in terms of boundaries, not values. By their nature, such questions imply that a whole range of values exists and your job is to figure out the boundaries of that range. There is an infinite number of angles that those two forces can be acting at, but the edge cases we have looked at before provide us with the maximum and minimum values of that range. Therefore, 3N is not obtainable, since, no matter the configuration, 10N - 4N = 6N is the absolute minimum resultant force.

AJ
Answered by Aleksandr J. Physics tutor

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