# How to calculate force required to open a door on a horizontal hinge

I have a door that will hang on a vertical hinge. The door will be 20 feet wide and 10 feet tall, there will be one hinge at each end of the door and the hinges will be 11.75 inches from the top of the door, and will have an amount of counterweight above the hinge. The counterweight will be a series of weights along the 20' width of the door. The goal will be to open the door by creating torque at the hinge in the counterclockwise direction at either end, so I am trying to create an equation to determine the torque necessary so that I can play with the weight of the door (this is my first post, please let me know if there is any more information that you need): • Welcome to Engineering.SE. Fortunately, we're in one of the few scenarios where t̶h̶e̶o̶r̶e̶t̶i̶c̶a̶l̶ ̶e̶n̶g̶i̶n̶e̶e̶r̶i̶n̶g̶ physics can answer the question completely. Thanks for the well structured question and again, welcome to Engineering.SE! – Mark Apr 6 '17 at 17:43
• are the counterweights just attached directly to the door, (I don't understand the leftward arrows on the diagram) – agentp Apr 7 '17 at 22:00

## 1 Answer

This is a simple matter of balancing moments.

You have a force $F$ applied at a distance $x_F$ from the hinge. This generates a moment of $M=Fx_F$.

You also have a distributed load $q$ applied along the door (of height $h$ and width $w$). The total resultant force of this load is $Q=qhw$, applied at an average position equal to $\frac{h}{2}$, for a moment of $M=qwh\frac{h}{2}$.

Equalizing both moments, you get

$$\begin{gather} Fx_F = \frac{qwh^2}{2} \\ \therefore F = \frac{qwh^2}{2x_F} \end{gather}$$