Determine the minimum area of a flat ice floe 1.0 meter thick if it is to support a 2000-kg car above seawater. (ρice = 920 kg/m³, ρsea = 1020 kg/m³.) A)20 m² B)40 m² C)60 m² D)80 m² E)100 m²

Question

Quizplus · Accepted Answer

The buoyant force on the ice floe must be equal to the weight of the car. The buoyant force is equal to the weight of the water displaced by the ice floe. The weight of the water displaced is equal to the volume of the water displaced times the density of the water. The volume of the water displaced is equal to the area of the ice floe times the thickness of the ice floe. Therefore, the area of the ice floe is equal to the weight of the car divided by the density of the water times the thickness of the ice floe.$$A = \frac{W}{ho_{water} t}$$$$A = \frac{2000 	ext{ kg}}{(1020 	ext{ kg/m}^3)(1.0 	ext{ m})}$$$$A = 1.96 	ext{ m}^2$$The minimum area of the ice floe is 1.96 m^2.

Determine the Minimum Area of a Flat Ice Floe 1