What forces act on the supports of a rectangle?

[hyperddude]

To anyone who saw my previous thread, yes, this is quite similar to it .

Homework Statement

Given a rectangle, say a painting, with with mass m, height h, and width w with two point supports to a wall at its two upper corners, what force does each support exert?

Homework Equations

Moment of inertia of a rectangle about its center: \frac{m(h^2+w^2)}{12}
Moment of inertia of a rectangle about a corner: \frac{m(h^2+w^2)}{3}
^Not sure if those equations will be relevant

The Attempt at a Solution

Common sense and intuition tells us that the vertical component from each support will be mg/2. But is there a horizontal component? That's what I'm trying to find out. One solution I had in mind was to break the mg downward force into components and try setting them as the forces by the pivots, but I ended up just going in circles.

 

[Dick]

To anyone who saw my previous thread, yes, this is quite similar to it .

Homework Statement

Given a rectangle, say a painting, with with mass m, height h, and width w with two point supports to a wall at its two upper corners, what force does each support exert?

Homework Equations

Moment of inertia of a rectangle about its center: \frac{m(h^2+w^2)}{12}
Moment of inertia of a rectangle about a corner: \frac{m(h^2+w^2)}{3}
^Not sure if those equations will be relevant

The Attempt at a Solution

Common sense and intuition tells us that the vertical component from each support will be mg/2. But is there a horizontal component? That's what I'm trying to find out. One solution I had in mind was to break the mg downward force into components and try setting them as the forces by the pivots, but I ended up just going in circles.

Sure there could be horizontal forces. But you know the horizontal forces must sum to zero. Otherwise the picture will accelerate in the horizontal direction.

 

[hyperddude]

You know the horizontal forces must sum to zero. Otherwise the picture will accelerate in the horizontal direction.

Yes, but I'm interested in finding what the horizontal force for one of the supports is.

 

[Dick]

Yes, but I'm interested in finding what the horizontal force for one of the supports is.

You can't find it. The horizontal forces can be anything as long as they cancel. How could you find it? If you know what direction the total force acts in, like if it's the tension supported by a string nailed to the wall, you might.