A solid aluminum sphere has a radius of 0.50 m and a temperature of75 o C. The s

Question

A solid aluminum sphere has a radius of 0.50 m and a temperature of75 oC. The sphere is then completely immersed in apool of water whose temperature is 25 oC. Thesphere cools, while the water temperature remains nearly at 25oC, because the pool is very large. The sphere isweighed in the water immediately after being submerged (before itbegins to cool) and then again after cooling to 25oC. (a) Which weight is larger? Why? (b) UseArchimedes' principle to find the magnitude of the differencebetween the weights.

Explanation / Answer

a) Which weight is larger? Why?
The sphere, after in cools, will shrink. That will increse itsdencity as the volume will decrease. The decrease in teh voluemewill lower the amount of water displaced, decreasing the buoyantforce Fb  . Since the weight in water isWw is the difference between weight of the sphereWs and buoyant force Fb  . Ws - Fb = Ww   the weight Ww in water will go up as the sphere'svoluem is going down. the weight Ww in water will go up as the sphere'svoluem is going down. (b) Use Archimedes' principle to find the magnitude ofthe difference between the weights. Ww = Ws - Fb1 - (Ws -Fb2 ) = Fb2 -  Fb1= g(V2 - V1) since V= 4/3 r3   Ww = g(4/3 r23    - 4/3 r13 ) Ww = (4/3)g(r23    - r13 ) where r = r2 - r1 r2 - r1 =r1T  where -coeficient of liner expansion of aluminum T   = 75 - 25 = 50 deg and r2= r1+r1T r2 - r1 =r1T  where -coeficient of liner expansion of aluminum T   = 75 - 25 = 50 deg and r2= r1+r1T r2=   r1 (1 +T ) Now just substitute and solve for Ww Let me know if you have any problems. Let me know if you have any problems.

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