two equal forces have their resultant equal to either.what is the inclination between them?
120 degrees
To determine the inclination between two equal forces with their resultant equal to either, we need to use some basic trigonometry.
Let's denote the magnitude of each force as F. Since the forces are equal, the magnitude of each force will be F.
Now, let's consider the forces as vectors. Since their resultant is equal to either, the vectors must be equal in magnitude and opposite in direction.
If we represent the first force vector as F1 and the second force vector as F2, we can say:
F1 = F and F2 = -F
To find the inclination between the two forces, we need to calculate the angle between the force vectors. We can do this by using the dot product of the force vectors.
The dot product of two vectors A and B is given by the equation: A · B = |A| |B| cosθ
In this case, since the vectors have the same magnitude (F), the equation simplifies to:
F1 · F2 = F^2 · cosθ
Substituting the values of F1 and F2:
(F) · (-F) = F^2 · cosθ
- F^2 = F^2 · cosθ
Now, let's solve for cosθ:
cosθ = -1
The inclination between the two forces can be found by taking the inverse cosine (cos⁻¹) of -1. Since -1 corresponds to an angle of 180 degrees (or π radians), we can conclude that the inclination between the two equal forces is 180 degrees (or π radians).
Therefore, the inclination between the two equal forces is a straight line, with one force acting in the opposite direction to the other.