## College Physics (4th Edition)

(a) The density of the object is $140~kg/m^3$ (b) 17% of the object's volume will be submerged in the ethanol.
(a) If the object is floating in the water, then the buoyant force is equal in magnitude to the weight of the object. According to Archimedes' principle, the buoyant force is equal to the weight of the water that is displaced. Let $V$ be the volume of the object. Let $m_o$ be the mass of the object. Let $m_w$ be the mass of the water that is displaced by the ice. We can find the density of the object $\rho_o$: $m_o~g = m_w~g$ $m_o = m_w$ $\rho_o~V = \rho_w~(0.14~V)$ $\rho_o = 0.14~\rho_w$ $\rho_o = (0.14)~(999.87~kg/m^3)$ $\rho_o = 140~kg/m^3$ The density of the object is $140~kg/m^3$ (b) Let $V_e$ be the volume of ethanol that is displaced by the object. We can find the ratio $\frac{V_e}{V}$: $m_e~g = m_o~g$ $m_e = m_o$ $\rho_e~V_e = \rho_o~V$ $\frac{V_e}{V} = \frac{\rho_o}{\rho_e}$ $\frac{V_e}{V} = \frac{140~kg/m^3}{807~kg/m^3}$ $\frac{V_e}{V} = 0.17$ 17% of the object's volume will be submerged in the ethanol.