Final answer:
To find how much ice melts due to a 64-kg ice-skater stopping, calculate the initial kinetic energy, take 50% that is absorbed by the ice, and divide by the latent heat of fusion. The result is approximately 2.7 grams of ice melted.
Step-by-step explanation:
To calculate how much ice melts when a 64-kg ice-skater glides to a stop from a speed of 7.5 m/s, we need to determine the energy dissipated by friction and how much of that energy is used to melt the ice. The skater's initial kinetic energy (KE) can be calculated using the formula KE = ½ mv^2, where m is the mass and v is the velocity. Here, KE becomes ½ × 64 kg × (7.5 m/s)^2.
The next step is to realize that 50% of this energy is absorbed by the ice. This energy is what will potentially melt the ice. To find the mass of the ice melted, we use the formula: mass = energy / latent heat of fusion. The latent heat of fusion of ice is 334,000 J/kg.
Therefore, if 50% of the skater's energy goes into melting ice, we first calculate the KE which is 1800 joules (J). Half of this energy is 900 J. Dividing 900 J by the latent heat of fusion, we get the mass of ice melted. Thus, mass of ice melted is 900 J / 334,000 J/kg, which equals approximately 0.0027 kg or 2.7 grams of ice.