Answer to Question #241437 in Classical Mechanics for obi

Question

How much water (density = 1.00 X 10³ kg/m3 ) must be displaced to float a cubic block of wood (density 655 kg/m3) that is 15.0 cm on a side?

Answer 1

$a = 15cm = 0.15m$

$\rho_w = 1*10^3\frac{kg}{m^3}$

$\rho _c= 655\frac{kg}{m^3}$

$g = 9.8 \frac{kg}{m^3}$

$\text{Forces acting on a wooden cube:}$

$F_A = \rho_wgV_1$

$V_1 - \text{The volume of a part of the cube immersed in}$

$\text{water and also the volume of displaced water}$

$F_g = m_cg$

$m_c- \text{mass of a wooden cube}$

$m_c = V_c\rho_c = a^3\rho_c$

$F_g = F_A$

$a^3\rho_c g = \rho_wgV_1$

$V_1 = \frac{a^3\rho_c} {\rho_wg}= \frac{0.15^3*665}{10^3}=2.24*10^{-3}m^3$

$m_1 -\text{mass of displaced water}$

$m_1 = \rho_wV_1= 2.24kg$

$\text{Answer:}$

$2.24kg-\text{mass of displaced water}$

$2.24*10^{-3}m^3 \text{-volume of displaced water}$