Four forces are acting at a point P in equilibrium as shown in figure. The ratio of force F 1 to F 2 is 1 : x where x = _____ .

Step-by-step solution

Here, θ = 45 ° Applying equilibrium conditions, Taking components along x & y Considering right side positive, ∑ F x = 0 F 1 + 1 sin 45 ° - 2 sin 45 ° = 0 F 1 = 2 sin 45 ° - 1 sin 45 ° F 1 = 2 - 1 2 = 2 - 1 2 = 1 2 Taking upward positive, ∑ F y = 0 1 cos 45 ° + 2 cos 45 ° - F 2 = 0 F 2 = 1 cos 45 ° + 2 cos 45 ° F 2 = 2 + 1 2 = 2 + 1 2 = 3 2 F 1 : F 2 = 1 : 3 x = 3