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):

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    – Mark
    Apr 6, 2017 at 17:43
  • $\begingroup$ are the counterweights just attached directly to the door, (I don't understand the leftward arrows on the diagram) $\endgroup$
    – agentp
    Apr 7, 2017 at 22:00

1 Answer 1


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

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


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