A 64-kg ice-skater moving at 7.5 m/s glides to a stop. Assuming the ice is at and that 50% of the heat generated by friction is absorbed by the ice, how much ice melts?
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This is Giancoli Answers with Mr. Dychko. All of the kinetic energy that the ice skater initially has is going to get dissipated as heat. So, the total heat produced by their stopping is the change in kinetic energy. So, that's K final minus K initial. And we're just concerned with magnitude. So, let's just forget about this negative sign there and it'll make this, even though that K final is 0, we'll just make this 1/2 mass times initial velocity squared. So, that's 1/2 times 64 kilograms times 7.5 meters per second, initial speed squared, which is 1800 joules. Now, the amount of heat absorbed by the ice is 50% of that. So, 1,800 times 0.5 which is 900 joules. And if all that energy goes into change in the phase of the ice, it's going to be equal to mass times the latent heat of fusion. We can divide both sides by L to calculate the mass or the amount of water that must have melted. So, it's 900 joules divided by 333 times 10 to the 3 joules per kilogram, latent heat of fusion for water-ice. And that's about 2.7 grams.
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