Answer:
A force of 12.857 newtons must be applied to open the door.
Explanation:
In this case, a force is exerted on the door, a moment is performed and the door is opened. If moment remains constant, the force is inversely proportional to distance respect to axis of rotation passing through hinges. That is:
[tex]F \propto \frac{1}{r}[/tex]
[tex]F = \frac{k}{r}[/tex] (Eq. 1)
Where:
[tex]F[/tex] - Force, measured in newtons.
[tex]k[/tex] - Proportionality ratio, measured in newton-meters.
[tex]r[/tex] - Distance respect to axis of rotation passing through hinges, measured in meters.
From (Eq. 1) we get the following relationship and clear the final force within:
[tex]F_{A}\cdot r_{A} = F_{B}\cdot r_{B}[/tex]
[tex]F_{B}=\left(\frac{r_{A}}{r_{B}} \right)\cdot F_{A}[/tex](Eq. 2)
Where:
[tex]F_{A}[/tex], [tex]F_{B}[/tex] - Initial and final forces, measured in newtons.
[tex]r_{A}[/tex], [tex]r_{B}[/tex] - Initial and final distances, measured in meters.
If we know that [tex]F_{A} = 5\,N[/tex], [tex]r_{A} = 0.9\,m[/tex] and [tex]r_{B} = 0.35\,m[/tex], then final force is:
[tex]F_{B}= \left(\frac{0.9\,m}{0.35\,m} \right)\cdot (5\,N)[/tex]
[tex]F_{B} = 12.857\,N[/tex]
A force of 12.857 newtons must be applied to open the door.
