A solid block is attached to a spring scale. The reading on the scale when the b

Question

A solid block is attached to a spring scale. The reading on the scale when the block is completely immersed in water is 24.8 , and the reading when it is completely immersed in alcohol of density 806 is 25.9 . What's the volume of the block?

Explanation / Answer

There are three forces acting on the block. gravity (downwards): Fg = m_block ·g = ? _block·V_block·g buoyancy (upwards) Fb = ? _fluid·V_block·g and the upward force of the suspension Fs All forces together are at equilibrium hence Fg + Fb + Fs = 0 => Fs = - Fg - Fb = (? _block - ? _fluid)·V_block·g Here we have measurement in two different fluids (i) Fsw = (? _block - ? _water)·V_block·g (ii) Fsa = (? _block - ? _alcohol)·V_block·g To find the volume of the block solve the equations for the unknown block density, equate them and then solve for the volume:: (i) => Fsw/(V_block·g) + ? _water = ? _block (ii) => Fsa/(V_block·g) + ? _alcohol = ? _block => Fsw/(V_block·g) + ? _water = Fsa/(V_block·g) + ? _alcohol ? _water - ?_alcohol = (Fsa - Fsw) / (V_block·g) => V_block = (Fsa - Fsw) / [ g · (? _water - ?_alcohol) ] = (Fsa - Fsw) / [ g · (? _water - ?_alcohol) ] = (25.9N - 24.8N ) / [ 9.81m/s² · (1000kg/m³ - 806kg/m³ ] = 5.780×10^-4m³ = 0.5780 L = 578.0 cm³

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