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Lets say a door is entirely supported by two hinges, one at the bottom corner and one at the top corner.

I know that the two vertical forces of the hinges are produced by newton third law, however where does the horizantal forces came from,why are they produced??

I see that since the body is at rest the horizontal forces and torques must be in opposite direction so the horizontal forces must be on opposite direction

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  • $\begingroup$ the context for this question is that is related to statics $\endgroup$
    – VOZ ESTOICA
    Mar 27 at 18:28
  • $\begingroup$ It looks like you also might be confused about newton's third law. It isn't that the force of gravity on an object "always has an equal and opposite force on that same object cancelling it out" (otherwise gravity would never do anything). It's that if object A exerts a force on object B, object B also exerts an equal and opposite force on object A. So the "opposite force" of the gravity affecting the door is the door also pulling on the earth. $\endgroup$
    – AXensen
    Mar 27 at 18:37
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    $\begingroup$ "I know that the two vertical forces of the hinges are produced by newton third law," How do you know that? $\endgroup$
    – Bob D
    Mar 27 at 18:41
  • $\begingroup$ because of newton third law the weight of the door must have a reaction on the point of contant opposite to the weight or can the reaction be horizontal? $\endgroup$
    – VOZ ESTOICA
    Mar 27 at 18:43
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    $\begingroup$ "because of newton third law the weight of the door must have a reaction on the point of contant opposite to the weight or can the reaction be horizontal?" - no, the weight of the door is caused by the Earth, so the reaction force is from the door on the planet. These two forces are equal and opposite, but they don't cancel out, as they act on different objects. The two vertical forces act on the door and are produced by the material of the hinges resisting; it must be the case that they add up to the weight because the door is static, not because of N3rdL. $\endgroup$
    – Filip Milovanović
    Mar 27 at 19:15

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The one-word answer is torque.

The door is not moving. That means that all forces must balance. So far so good. That is where the vertical forces on the hinges come from. The door has weight, which is in your diagram. (Don't let anybody be snide about your diagram. It's better than I would have done free-hand.) You have to assume something about the stiffness of the door and hinges to get the fraction of the door's weight each hinge holds, but never mind that for now.

But the door is of finite size. And therefore, when you apply the weight of the door as net being at it's center of mass (COM) it winds up applying a torque relative to the hinges.

This is the thing about torque. It requires a center around which to calculate it. When you apply the definition $\overrightarrow{\tau} = \overrightarrow{r} \times \overrightarrow{F}$ you need an origin for the $\overrightarrow{r}$.

And here's the thing about picking an origin for torque. The door is not rotating around any possible origin. It's not moving at all. So the torque has to be zero around any possible origin.

So you can pick a helpful one. For example, you could pick the top left corner of the door. Or the middle-left edge. And then you sum up all the torque values around each of those points, and set it to zero.

Now notice, the door is not moving left or right. So the horizontal force on one hinge has to be the negative of that on the other hinge, because those are the only horizontal forces, and they have to cancel.

And pretty quickly you see where the forces come from. And, hopefully, you will see why if you tried to support yourself off a door, the hinge that most probably fails first is the top one.

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