Vertical forces on door hinges

[issisoccer10]

Homework Statement

A door with weight Mg has a horizontal width W and a vertical length L. There are two hinges that hold up the door along the right side of the door. The top hinge is a distance d from the top of the door and the bottom hinge is a distance d from the bottom of the door. What are the vertical and horizontal forces on each of the hinges?

Homework Equations

∑F = 0
∑τ = 0

The Attempt at a Solution

As for the horizontal forces, I believe that using torques, based on the the force on the upper hinge, F * (L-2d) = Mg(W/2). Then the horizontal force on the lower hinge would just be equal to that but in the opposite directon.
However, as for the vertical components, I'm a little stuck. Some similar questions have been asked in these forums, but they all seem to say something along the lines of "each hinge supports the weight of the hinge equally" or "only the top hinge supports the weight of the door." Yet my question does nothing of the sort. How should I go about finding the vertical components of the doors? I have the same question as for which direction each of the horizontal compontent of the hinges point. Is there a right or wrong answer for their direction, as long as they are opposite, since there is no indication in the question?

 

[BishopUser]

the direction of the horizontal forces is easy to visualize. the bottom hinge tries to push the door away and the top one tries to pull it back. as for the vertical forces i think you assume that each one is mg/2

 

[ogb p]

I would approach this problem by looking at the forces acting on the door and the hinges. The weight of the door, Mg, exerts a downward force on the hinges. This force can be broken down into horizontal and vertical components. The horizontal component will be equal on both hinges and can be calculated using torques as mentioned in the attempt at a solution.

However, the vertical component of the weight will be different for each hinge. The top hinge will experience a greater force since it is closer to the center of mass of the door. The bottom hinge will experience a smaller force since it is farther away from the center of mass.

To find the exact values of the vertical forces on each hinge, we can use the equations ∑F = 0 and ∑τ = 0. By setting the sum of the forces and torques equal to 0, we can solve for the unknown vertical forces on each hinge.

As for the direction of the horizontal forces, as long as they are opposite, it does not matter which direction they are pointing. However, in real-life scenarios, the hinges are usually designed to withstand forces in a specific direction, so it would be important to consider this when analyzing the problem.