Determine the volume contraction of a solid c | vedclass

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(D) The bulk modulus of copper is $B = 140 	imes 10^{9} \; Pa$.The formula for bulk modulus is $B = \frac{p}{\Delta V / V}$,where $p$ is the pressure

Vedclass · Accepted Answer

$5 	imes 10^{-2} \; cm^{3}$

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(D) The bulk modulus of copper is $B = 140 	imes 10^{9} \; Pa$.The formula for bulk modulus is $B = \frac{p}{\Delta V / V}$,where $p$ is the pressure,$V$ is the original volume,and $\Delta V$ is the change in volume.Rearranging for volume contraction $\Delta V$,we get $\Delta V = \frac{p V}{B}$.The original volume of the cube is $V = l^{3} = (10 \; cm)^{3} = (0.1 \; m)^{3} = 10^{-3} \; m^{3}$.Substituting the values: $\Delta V = \frac{7.0 	imes 10^{6} \; Pa 	imes 10^{-3} \; m^{3}}{140 	imes 10^{9} \; Pa}$.$\Delta V = \frac{7.0 	imes 10^{3}}{140 	imes 10^{9}} = 0.05 	imes 10^{-6} \; m^{3} = 5 	imes 10^{-8} \; m^{3}$.Since $1 \; m^{3} = 10^{6} \; cm^{3}$,we have $\Delta V = 5 	imes 10^{-8} 	imes 10^{6} \; cm^{3} = 5 	imes 10^{-2} \; cm^{3}$.Thus,the volume contraction is $5 	imes 10^{-2} \; cm^{3}$.

Determine the volume contraction of a solid copper cube,$10 \; cm$ on an edge,when subjected to a hydraulic pressure of $7.0 \times 10^{6} \; Pa$.

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