What is the weight of my table using only one scale?

[eddyq]

I have a table and I want to get the weight of the table. I only have one scale. I weighed the left side then the right side. I believe this is a simple statics problem but I can't figure it out. I have broken this down into this:

A beam with points A, CG, and B. A is the left side, B is the right side and CG is the center of gravity. L is the length of the beam. Assume the angle of the beam is negligible while pivoting. While B is a pivot, the force on A (weight on the scale) is Fa and the moment would be L*Fa. While A is a pivot, the force on B is Fb (weight on the scale) and the moment would be L*Fb. And while A and B are not pivots then the force at CG would be the weight of the beam and the sum of those moments would be 0.

Am I on the right track?

 

[mfb]

If the height of the scale is negligible, you can just add the readings - that's the total force needed to keep in on the ground. With a relevant height of the scale it is more work.

If there is nothing problematic on the table, what about turning it upside down for a direct measurement?

 

[eddyq]

Thanks, I thought the presence of the pivot point would skew the end weights. I would turn it upside down but it is my wife's antique writing desk and she would kill me if I scratched it.

 

[AlephZero]

If you want to just add the two weights, you need to keep the table level for both weighings. If you used something like bathroom scales, just use some books etc to raise the other end of the table, then swap over the books and the scale for the second weighing.

Or you want to live dangerously, lift up the other end of the table till it is just on the point of toppling over. In that position, the center of mass will be directly above the scale, and the scale will read the full weight of the table. But if it is a fragile antique, doing this might snap the table legs!

 

[eddyq]

Thanks for all your help. I was trying to make an easy thing hard.