What is the Mass of the Block Placed on a Stiff Board in Static Equilibrium?

[whoareyou]

Homework Statement

Two supports, made of the same material and initially of equal length, are 2.0m apart. A stiff
board with a length of 4.0m and a mass of 10 kg is placed on the supports, with one support
at the left end and the other at the midpoint. A block is placed on the board a distance of
0.50m from the left end. As a result the board is horizontal. The mass of the block is:

A. zero
B. 2.3kg
C. 6.6kg
D. 10 kg
E. 20 kg

Homework Equations

∑F = 0 = N₁ + N₂ - mg - Mg
∑τ = 0 = -1/2 N₁ + 1/2 N₂ - 1/2 Mg

The Attempt at a Solution

Those equations above are a result of a free body diagram I drew. However, if I begin to solve the equation for m, I end up with an expression in terms of N₁ (ie. 2N₁ = mg). Is there enough information in the question? By the way, I'm calculating torque from the position where the mass is placed.

 

[BvU]

Could you post the drawing ?

 

[voko]

I think the key to this problem is this: "supports made of the same material and initially of equal length". What that means is that they are not rigid, but elastic, so as they are loaded, they contract and exert Hookean force on the board; these forces and the weights due to the board and the block balance one another so that everything is horizontal.

 

[BvU]

Pretty bright, voko. I agree. So youhoo has his/het work cut out.
And yes, there is enough info in the question (provided you accept voko's deduction -- which I do)

 

[whoareyou]

So if the supports are made of the same material and initially of equal length, then that means that, since the board is horizontal, they compress by the same amount and as a result, apply equal forces?

 

[voko]

Spot on.