# balancing a plank on springs ( Torques )

There is a complicated piece of machinery sitting on a plank of metal which

is 2 m long. The metal and machinery have a combined mass of 430 kg. The center

of mass is approximately 1.2 m from the left side of the plank. We need to attach 2

springs to the plank to lift it off the ground, but it needs to be level. One spring has

a spring constant of 2200 N/m and is attached to the right edge of the plank. If the

other spring has a spring constant of 1500 N/m, where should we put it to make sure

everything is level?

So what I did is that I wanted to balance torques and forces.

Forces:

mg= Fs1 + Fs2

mg= 2200Δx + 1500 Δx ( Since it is level, then I assumed that delta x is the same)

mg = 3700 Δx

430*9.8= 3700 Δx

Δx = 1.4

Then, I started balancing torques.

I have set the left end to be my pivot.

mg(1.2)= Fs2y ( Where y is the distance of the second spring from the left end)

mg(1.2) = KΔx y

430*9.8*1.2 = 1500*1.4 y

y = 2.4 , which is obviously impossible since the length of the plank is just 2 metres.

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