So far I have that the Total Weight of the board is 343N, given that the force a

Question

So far I have that the Total Weight of the board is 343N, given that the force acts directly on scale B, its contribution is equal to 107*sin(60)N, which makes the boards contribution of force at scale B =  (294 - 107*sin(60)) = 201 N, the force on Scale A = (343-201)= 142N.

But I'm not sure how to translate this information to find the length of the board. Any help? This assignment is largely on torque, would I use that to find the length?

A uniform board has a mass of 35 kg and sits horizontally at rest, supported as shown, by two scales that measure vertical force only (but the scales can exert both vertical and horizontal forces). The force shown is 107 N and is applied directly over scale B. The reading on scale B is 294 N. How long is the entire board?

Explanation / Answer

let the last portion of the board after scale B be x..

so.. total lenght = 1.35 + 4.26 + x = 5.61 + x

so.. the mid-point is at distance = (5.61 + x ) / 2 - from the ends
= 2.805 + 0.5*x from the ends..

so the distance from A = 2.805 + 0.5*x - 1.35 = 1.455 + 0.5*x


so.. now.. componet of force perpendicular to scale = 107*sin 60 = 92.6647182 N

so.. taking moment of all the forces abount point A
(1.455 + 0.5*x )*35*9.81 + 92.6647182*4.26 = 294*4.26

so.. x = 2.0860000026 m

so.. total length = 5.61 + x = 5.61 + 2.0860000026 = 7.6960000026 m

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