## College Physics (4th Edition)

(a) The buoyant force is $8.82~N$ (b) The buoyant force is $9.62~N$
(a) If the ice is floating freely in the water, then the buoyant force is equal in magnitude to the weight of the ice. We can find the buoyant force: $F_b = mg = (0.90~kg)(9.80~m/s^2) = 8.82~N$ The buoyant force is $8.82~N$ (b) According to Archimedes' principle, the buoyant force is equal to the weight of the water that is displaced. Let $m_i$ be the mass of the ice. Let $m_w$ be the mass of the water that is displaced by the ice. Let $V$ be the volume of the ice. The buoyant force is equal to the weight of the water with a volume $V$: $F_b = m_w~g$ $F_b = \rho_w~V~g$ $F_b = \rho_w~(\frac{m_i}{\rho_i})~g$ $F_b = \frac{(1000~kg/m^3)(0.90~kg)(9.80~m/s^2)}{917~kg/m^3}$ $F_b = 9.62~N$ The buoyant force is $9.62~N$.