To find the ratio of force F1 to F2 when the forces are in equilibrium, we apply the equilibrium conditions. Since P is in equilibrium, the sum of horizontal and vertical components of forces must be zero.
Horizontal Components: Let F1 be the force on the horizontal axis.
The horizontal components of the forces are: F1 to the right, 1 N × cos(45°) to the right, and 2 N × cos(45°) to the left.
To satisfy equilibrium: F1 + 1cos(45°) = 2cos(45°)
Using cos(45°) = 1/√2:
F1 + 1/√2 = 2/√2 F1 = (2/√2) - (1/√2) = 1/√2
Vertical Components: The vertical components are:
F2 acting downward, 1 N × sin(45°) acting upward, and 2 N × sin(45°) acting up.
For equilibrium: F2 = 1sin(45°) + 2sin(45°)
Using sin(45°) = 1/√2:
F2 = (1/√2) + (2/√2) = 3/√2
Ratio of F1 to F2:
F1:F2 = (1/√2):(3/√2) = 1:3
The ratio of F1 to F2 is 1:3, which is within the given range of (3, 3).
