A solid aluminum sphere has a radius of 2.07 m and a temperatureof 82.6 °C. The

Question

A solid aluminum sphere has a radius of 2.07 m and a temperatureof 82.6 °C. The sphere is then completely immersed in a pool ofwater whose temperature is 25.4 °C. The sphere cools, while thewater temperature remains nearly at 25.4 °C, because the poolis very large. The sphere is weighed in the water immediately afterbeing submerged (before it begins to cool) and then again aftercooling to 25.4 °C. Use Archimedes' principle to find themagnitude of the difference between the weights.

Number Units N

Explanation / Answer

the buoyant force acting on the sphere is B = fluid * g * V fluid = 1000 kg/m3 g = 9.8 m/s2 V = (4/3)r3 where r = 2.07 m the weight of the sphere is w = m * g = sphere * V * g the magnitude of the difference between theweights W = (B - w) = (fluid * g * V -sphere * V * g) = V * g *(fluid - sphere) sphere = 2698 kg/m3 V = (4/3)r3 where r = 2.07 m the weight of the sphere is w = m * g = sphere * V * g the magnitude of the difference between theweights W = (B - w) = (fluid * g * V -sphere * V * g) = V * g *(fluid - sphere) sphere = 2698 kg/m3

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