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:
![F \propto \frac{1}{r}](https://tex.z-dn.net/?f=F%20%5Cpropto%20%5Cfrac%7B1%7D%7Br%7D)
(Eq. 1)
Where:
- Force, measured in newtons.
- Proportionality ratio, measured in newton-meters.
- 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:
(Eq. 2)
Where:
,
- Initial and final forces, measured in newtons.
,
- Initial and final distances, measured in meters.
If we know that
,
and
, then final force is:
![F_{B}= \left(\frac{0.9\,m}{0.35\,m} \right)\cdot (5\,N)](https://tex.z-dn.net/?f=F_%7BB%7D%3D%20%5Cleft%28%5Cfrac%7B0.9%5C%2Cm%7D%7B0.35%5C%2Cm%7D%20%5Cright%29%5Ccdot%20%285%5C%2CN%29)
![F_{B} = 12.857\,N](https://tex.z-dn.net/?f=F_%7BB%7D%20%3D%2012.857%5C%2CN)
A force of 12.857 newtons must be applied to open the door.