Question

A cube of an unknown mass is placed on a flat surface. The cube has a volume of 8 cm^3. If the pressure exerted by the cube on the surface is 5 Pa, what must be the mass of the cube?

Answer 1

First, take into account that the pressure exerted by a force on a certain area, is given by:

$P=\frac{F}{A}$

In this case, the force F is the weight of the box, that is:

F = W = m*g

where m is the mass of the box and g the acceleration gravitational constant 9.8m/s^2.

The area where the force due to the weight is applied is given by:

$A=a^2$

where a is the length of the side of the box. To find the value of a, you can use the information about the volume of the box, as follow:

$\begin{gathered} V=a^3 \\ a=\sqrt[3]{V} \\ a=\sqrt[3]{8cm^3} \\ a=2cm \end{gathered}$

Now, you can calculate the area A (but in this case we express a in meters by convenience):

$\begin{gathered} a=0.02m \\ A=(0.02m)^2=4\cdot10^{-4}m^2 \end{gathered}$

Next, in the expression for the pressure P=F/A, replace F by m*g and solve for m:

$\begin{gathered} P=\frac{m\cdot g}{A} \\ m=\frac{A\cdot P}{g} \end{gathered}$

All parameters A, P and g are known parameters, then, you obtain:

$m=\frac{(4\cdot10^{-4}m^2)(5Pa)}{9.8\frac{m}{s^2}}\approx2.0\cdot10^{-4}kg$