Question

A cube 200mm side is subjected to a compressive force of 3.6MN on each face.Calculate E & K if change in volume is 5000mm3. Take μ = 0.28.

Answer 1

ohhhhhhhhhhhbbbbbbbbuuhbb

Answer 2

Answer:

Value of $E$ is $6.25*10^{-4}$. Value of $K$ is $144000$ $Pa$.

Step-by-step explanation:

• Bulk modulus can be defined as the measure of the ability of a material to stand against a change in volume when compressed on all of its sides.
• Stress is equal to the force applied divided by the area of the face on which force is applied.

The formula for bulk modulus is:

$K=\frac{dP}{\frac{dV}{V} }$

where $dP$ is the small change in pressure

           $dV$ is the change in volume.

           $V$ is the original volume.

Step 1:

Force applied is given as $3.6 *10^{6}$ $N$.

Area of a face $=(200^{2} )$ $mm^{2}$

                        $= 40000$ $mm^{2}$

$dP=\frac{3.6 *10^{6}}{40000}$ $N/mm^{2}$

     $=90$ $N/mm^{2}$

Step 2:

We will calculate $E$ now:

$E=\frac{dV}{V}$

$E=\frac{5000mm^{3} }{(200^{3})mm^{3} }$

$E=6.25*10^{-4}$

The bulk modulus of the cube, $K=\frac{90}{6.25*10^{-4}}$ $Pa$

                                                        $=144000$ $Pa$

So, the bulk modulus of the cube is $144000$ $Pa$.