Angle between two equal forces with resultant magnitude

When two equal forces act on a body, the resultant force is the vector sum of the two forces. If the magnitude of the resultant force is equal to the magnitude of either of the forces, it indicates a specific relationship between the two forces and the angle between them.

Explanation:

Let's consider two equal forces, F1 and F2, acting on a body at different angles with respect to a reference axis. The resultant force, R, is given by the vector sum of F1 and F2:

R = F1 + F2

Since the magnitudes of F1 and F2 are equal, we can express them as F:

R = F + F
R = 2F

If the magnitude of the resultant force, R, is equal to the magnitude of either of the forces (F), then we have:

2F = F
F = F

This implies that the forces are acting in the same direction, and the angle between them is 0 degrees. In other words, the two forces are collinear, or they are acting along the same line of action.

Conclusion:

Therefore, if the resultant of two equal forces has the same magnitude as either of the forces, the angle between the two forces is 0 degrees. This indicates that the forces are acting in the same direction and are collinear.

It is important to note that this conclusion holds true only when the forces have the same magnitude. If the magnitudes of the forces are different, the angle between them will not be 0 degrees.

120 degree just apply parallelogram law mechanic