two force of 5n and 7n respectively act an object , when will the resultant of the two vectors be at a maximum
When they are acting in the same direction.
Fmax = 5 + 7 = 12 N.
12N
To find when the resultant of two vectors is at a maximum, we need to consider the concept of vector addition. The resultant is the vector sum of the two forces acting on the object.
To add vectors, we use the parallelogram law of vector addition. According to this law, if we draw the two vectors as sides of a parallelogram, the diagonal of the parallelogram represents the resultant vector.
The magnitude of the resultant vector is maximum when the two vectors are in the same direction. In this case, we want to maximize the magnitude of the resultant vector.
Given two forces of 5N and 7N, there are two possible scenarios:
Scenario 1: When the two forces are in the same direction
To maximize the resultant vector, both forces should be in the same direction. In this case, the resultant vector magnitude will be the sum of the magnitudes of the two forces:
Resultant = 5N + 7N = 12N
Scenario 2: When the two forces are in opposite directions
To minimize the resultant vector, the two forces should be in opposite directions. In this case, the resultant vector magnitude will be the difference between the magnitudes of the two forces:
Resultant = |5N - 7N| = 2N
Therefore, the resultant of the two forces will be at a maximum magnitude of 12N when the forces are in the same direction. In all other cases, the magnitude of the resultant will be less than 12N.