On a cold winter day, a 1 kg aluminum sphere at an initial temperature of 0.00 C

Question

On a cold winter day, a 1 kg aluminum sphere at an initial temperature of 0.00 C is dropped from the top of the Empire State Building, which is 443 m tall. The sphere lands in a frozen puddle of water below, also at a temperature of 0.00 C. If all of the sphere's initial potential energy goes into melting the ice, how much ice is melted? On a cold winter day, a 1 kg aluminum sphere at an initial temperature of 0.00 C is dropped from the top of the Empire State Building, which is 443 m tall. The sphere lands in a frozen puddle of water below, also at a temperature of 0.00 C. If all of the sphere's initial potential energy goes into melting the ice, how much ice is melted?

Explanation / Answer

m = 1 kg ; h = 443 m ;

At this height the potential energy of the sphere is:

PE = m g h

PE = 1 x 9.8 x 443 = 4341.4 J

This PE of sphere is taken by the ice to melt.

PE = M(ice) x Lf + M(ice) x Ci x (Ti - Tf)

4341.4 J = M(ice) x 3.33 x 10^5 J/kg

M(ice) = 4341.4/3.33 x 10^5 = 0.013 kg

Hence, M(ice) = 0.013 kg = 13 g

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