An almirah door is 6 ft high and 1.5 ft wide, weighing 8 kg . It is held up by two hinges placed 1 ft from its ends. Assuming the magnitudes of the forces exerted by the hinges on the door are identical, determine this magnitude.

Step-by-step solution

Let the acceleration due to gravity be g = 10 m/s ^2 . Weight of the door, W = mg = 8 10 = 80 N . Let the horizontal and vertical components of the reaction force at the upper hinge be H₁ and V₁ , and at the lower hinge be H₂ and V₂ . For translational equilibrium in the horizontal and vertical directions: F_x = 0 H₁ + H₂ = 0 H₁ = -H₂ F_y = 0 V₁ + V₂ = W = 80 N It is given that the magnitudes of the forces exerted by both hinges are identical: H₁^2 + V₁^2 = H₂^2 + V₂^2 Since H₁^2 = H₂^2 , we get V₁^2 = V₂^2 . As V₁