# What forces act on the supports of a rectangle?

1. Jan 5, 2013

### hyperddude

To anyone who saw my previous thread, yes, this is quite similar to it :tongue2:.

1. The problem statement, all variables and given/known data

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?

2. Relevant 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

3. 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.

2. Jan 5, 2013

### Dick

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.

Last edited: Jan 5, 2013
3. Jan 5, 2013

### hyperddude

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

4. Jan 5, 2013

### Dick

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.

Last edited: Jan 5, 2013