2 forces of 5N&7N respectively act on an object. (a) When will the resultant of 2 vectors be at a maximum? (b) When will the resultant of the 2 vectors be at a minimum?
a. When they are acting in the same
direction. F = 5+7 = 12 N.
b. When they are acting in opposite directions. F = 7-5 = 2 N.
To determine when the resultant of two vectors will be at a maximum or minimum, we can use vector addition. The resultant is maximized when the two vectors are in the same direction and minimized when they are in opposite directions.
(a) To find when the resultant is at a maximum, we need to determine when the two forces are acting in the same direction. In this case, the forces are 5N and 7N, implying they are acting in opposite directions.
To find the maximum resultant, we can add the magnitudes of the forces together:
Resultant = 5N + 7N = 12N
Therefore, the resultant will be at a maximum of 12N when the forces are acting in the same direction.
(b) To find when the resultant is at a minimum, we need to determine when the two forces are acting in opposite directions. In this case, the forces are already acting in opposite directions.
To find the minimum resultant, we can subtract the smaller force from the larger force:
Resultant = |7N - 5N| = |2N| = 2N
Therefore, the resultant will be at a minimum of 2N when the forces are acting in opposite directions.