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Kinetic energy is the energy an object has due to its motion. For an ice-skater moving on the ice, this energy depends on both the mass of the skater and their speed. The formula to calculate kinetic energy is: \[KE = \frac{1}{2}mv^2\]where \( m \) is the mass and \( v \) is the speed. In our example, the ice-skater weighs 64 kg and is moving at 7.5 m/s. Using the formula, we calculate:* \( KE = \frac{1}{2} \times 64 \times (7.5)^2 \)* \( KE = 0.5 \times 64 \times 56.25 \)* \( KE = 1800 \text{ J} \)This means the ice-skater initially possesses 1800 Joules of kinetic energy. As the skater stops, this energy gets converted mainly into heat due to friction between the skates and the ice.

When the ice-skater glides to a stop, the kinetic energy is transformed into thermal energy because of friction. It's essential to understand where this energy goes. Friction on ice assumes that not all energy is used to melt the ice. In this scenario, 50% of the generated heat is absorbed by the ice. This is calculated as:\[Q = 0.5 \times KE\]For our skater:* \( Q = 0.5 \times 1800 \)* \( Q = 900 \text{ J} \)Thus, 900 Joules of heat are absorbed by the ice, which contributes to the melting process.

The latent heat of fusion is the amount of heat energy required to change a substance from solid to liquid at its melting point, without changing its temperature. For ice, this value is given as 334,000 J/kg. To calculate the mass of ice that melts, we use the formula:\[m = \frac{Q}{L_f}\]where \( m \) is the mass of melted ice, \( Q \) is the heat absorbed, and \( L_f \) is the latent heat of fusion.Applying the values from our problem:* \( m = \frac{900}{334,000} \)* \( m \approx 0.0027 \text{ kg} \)Therefore, approximately 0.0027 kg of ice melts due to the heat absorbed. This illustrates the concept of latent heat effectively, showing how even a small amount of absorbed energy causes a phase change from solid to liquid.