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
$\Rightarrow \sqrt{{\left(N_1\right)}^2+{\left(F_1\right)}^2}=\sqrt{{\left(N_2\right)}^2+{\left(F_2\right)}^2}$ ...(i)
System is in translation equilibrium. Therefore, we have:
N₁ = N₂;
$8g=F_1+F_2$
Putting the value in eq. (i), we get:
F₁ = F₂
$$\begin{gathered} \Rightarrow 2F_1=8g \\ \Rightarrow F_1=40 \end{gathered}$$
Let us take the torque about point B. We get:
$$\begin{gathered} N_1\times 4=8g\times 0.75 \\ \Rightarrow N_1=\frac{\left(80\times 3\right)}{4\times 4}=15\mathrm{N} \end{gathered}$$
Now, the forces exerted by the hinges A on the door,
$\sqrt{\left(F_1^2+N_1^2\right)}=\sqrt{\left({40}^2+{15}^2\right)}=42.72=43\mathrm{N}$