Find the greatest and least resultant of two forces whose magnitude are 12 N and 8 N respectively
Bas
To find the greatest and least resultant of two forces, we need to consider their magnitudes and directions. Let's denote the 12 N force as force A and the 8 N force as force B.
To find the greatest resultant, we need to consider the forces acting in the same direction. In this case, we can simply add the magnitudes of the forces:
Greatest Resultant = 12 N + 8 N = 20 N
So, the greatest resultant of the two forces is 20 N, when they are acting in the same direction.
To find the least resultant, we need to consider the forces acting in opposite directions. In this case, we can subtract the magnitudes of the forces since they are acting in opposite directions:
Least Resultant = 12 N - 8 N = 4 N
So, the least resultant of the two forces is 4 N, when they are acting in opposite directions.
Therefore, the greatest resultant is 20 N and the least resultant is 4 N.
To find the greatest and least resultant of two forces, we can use the concept of vectors.
Forces are represented as vectors, which have both magnitude (the length of the vector) and direction. In this case, we are given two forces: 12 N and 8 N.
To find the resultant force, we need to add these two forces. However, since forces are vectors, we need to consider their directions as well.
The resultant force will be greatest when the two forces are in the same direction, and least when they are in opposite directions.
Let's consider the greatest resultant force first. Since the forces have the same direction, we simply add their magnitudes together:
12 N + 8 N = 20 N
Therefore, the greatest resultant force is 20 N.
Now let's consider the least resultant force. Since the forces are in opposite directions, we need to subtract their magnitudes:
|12 N - 8 N| = |4 N| = 4 N
Therefore, the least resultant force is 4 N.
To summarize:
- The greatest resultant force is 20 N when the two forces are in the same direction.
- The least resultant force is 4 N when the two forces are in opposite directions.
Greatest resultant occurs when the forces act in the same direction:
Resultant = 12 N + 8 N = 20 N, in the direction of the forces.
Least resultant occurs when the forces act in opposite directions:
Resultant = 12 N - 8 N = 4 N, in the direction of the 12 N force.