Question

A $2.0cm\times 2.0cm\times 6.0cm$block floats in water with its long axis vertical. The length of the block above water is $2.0cm$. What is the block’s mass density?

Short answer

The block's mass density is${\rho }_b=667kg/m^3$

Step-by-step solution

Mass density.

The mass density of a substance, material, or item could be a measure of what quantity mass (or what number particles) it's in regard to the number of space it takes up.

Derive the mass formula.

Because the block is afloat That's, the burden performing on it's capable to the buoyant force, and it's not moving, neither up nor down. That is,

$$\begin{gathered} m_{b}g={\rho }_{w}g{V}_w \\ \Rightarrow m_b={\rho }_w{V}_w \end{gathered}$$

where $b$stands for block and $w$for water.

Find the mass density.

We can calculate the mass of a body by multiplying its density by its mass, $m_b={\rho }_b{V}_b$.

$$\begin{gathered} {\rho }_b{V}_b={\rho }_w{V}_w \\ \Rightarrow {\rho }_b=\frac{{\rho }_w{V}_w}{V_b} \\ ={\rho }_w\frac{a\times b\times (2/3)c}{a\times b\times c} \\ =\frac{2}{3}{\rho }_w \end{gathered}$$

We can calculate the density of a block using the density of water.

$$\begin{gathered} {\rho }_b=\frac{2}{3}1000 \\ =667\mathrm{kg}/{\mathrm{m}}^3 \end{gathered}$$