91Ó°ÊÓ

The latent heat of fusion is a critical concept in understanding phase changes. It refers to the amount of heat energy required to change 1 kg of a substance from solid to liquid without changing its temperature. For ice, this value is quite substantial at about 334,000 J/kg. This means when ice melts, it absorbs energy efficiently without a rise in temperature. In the context of the sliding ice block, the kinetic energy lost due to slowing down is converted into the energy needed to melt a small portion of the ice. Understanding latent heat helps us predict how much of a substance will undergo a phase change when a certain amount of energy is applied. In calculations dealing with energy transformation like the one in our problem, the latent heat of fusion allows us to determine the mass of the ice that will transform into water.

Kinetic friction occurs when two objects are in motion relative to each other. In our scenario, the ice block sliding on the horizontal surface encounters kinetic friction, which acts opposite to its motion. This force is responsible for the ice block slowing down, converting its kinetic energy into heat. Frictional forces depend on the nature of the surfaces in contact and the normal force exerting on the object sliding. For ice, this friction is often low due to its smooth nature but still significant enough to cause a conversion of kinetic energy into thermal energy. In this problem, the heat generated due to kinetic friction contributes directly to the melting of the ice.

Energy conversion refers to the process of changing energy from one form to another. In this exercise, the kinetic energy of the moving ice block is converted into thermal energy due to the kinetic friction. This conversion is crucial as it supplies the heat required for the melting process. Initially, the ice block has a certain amount of kinetic energy because of its motion. As it slows down, energy is not lost but transformed into heat energy, which tends to spread along the surfaces in contact. Understanding energy conversion is essential to determine how energy behaves in various systems, enabling us to solve for unknowns like the mass of melted ice.

The melting process is a phase transition where a solid turns into a liquid. For ice, this occurs at 0°C, precisely where kinetic energy loss from friction can provide the necessary heat for the melting process without changing temperature. In our problem, the ice's initial kinetic energy decreases, transforming into thermal energy due to friction. This thermal energy is absorbed by a portion of the ice, facilitating its change from solid to liquid. It should be noted that the mass fraction of ice melting is exceptionally small due to the high energy requirement, encapsulated by the latent heat of fusion. Grasping the melting process is crucial in interpreting how external energy influences physical state changes.