Question

The door of an almirah is 6 ft high, 1⋅5 ft wide and weighs 8 kg. The door is supported by two hinges situated at a distance of 1 ft from the ends. If the magnitudes of the forces exerted by the hinges on the door are equal, find this magnitude.

Answer 1

It is given that the magnitudes of the forces exerted by the hinges on the door are equal.

Therefore, we have

Resultant of N₁ and F₁ at point A = Resultant of N₂ and F₂ at point B

\[\Rightarrow \sqrt{\left( N_1 \right)^2 + \left( F_1 \right)^2} = \sqrt{\left( N_2 \right)^2 + \left( F_2 \right)^2}...........(1)\]

System is in translation equilibrium. Therefore, we have

N₁ = N₂;

\[8g = F_1 + F_2\]

Putting the value in eq. (1), we get

F₁ = F₂

\[\Rightarrow 2 F_1 = 8g\]

\[ \Rightarrow F_1 = 40\]

Let us take the torque about point B. We get

\[N_1 \times 4 = 8g \times 0 . 75\]

\[ \Rightarrow N_1 = \frac{\left( 80 \times 3 \right)}{4 \times 4} = 15 N\]

Now, the forces exerted by the hinges A on the door,

\[\sqrt{\left( F_1^2 + N_1^2 \right)} = \sqrt{\left( {40}^2 + {15}^2 \right)} = 42 . 72 = 43 N\]