91Ó°ÊÓ

Kinetic energy is the energy an object possesses due to its motion. In the case of our sliding ice block, the kinetic energy comes from the block's mass and velocity. When an object is in motion, its kinetic energy can be calculated using the formula:\[ KE = \frac{1}{2} m v^2 \]where \(m\) is the mass of the object and \(v\) is its velocity. This equation tells us that kinetic energy is dependent on both the mass of the object and the square of its velocity. This means that a small increase in speed can cause a significant increase in kinetic energy.
Consider the ice block example: Initially, it moves with a velocity of \(7.3 \, \text{m/s}\), giving it significant energy. As it slows to \(3.5 \, \text{m/s}\), its kinetic energy decreases. This lost energy does not vanish; it converts into other forms, such as heat, which plays a crucial role in the melting process of ice.

Latent heat of fusion is the heat energy required to change a unit mass of a substance from solid to liquid without changing its temperature. For ice, this value is defined as \(334,000 \, \text{J/kg}\).This value is exceptionally high, which means a significant amount of energy is needed to melt ice, despite the temperature staying constant at \(0^\circ \text{C}\). In our exercise, when the kinetic energy of the ice block is converted to heat, it facilitates the melting of a portion of the ice. The equation we use is:\[ Q = m_{ice} \, L_f \]where \(Q\) is the heat energy absorbed (from the lost kinetic energy), \(m_{ice}\) is the mass of the ice to melt, and \(L_f\) is the latent heat of fusion. By rearranging the equation to solve for \(m_{ice}\), we can find how much of the ice melts based on the energy available.

Melting of ice is a phase change where ice (solid) transforms into water (liquid) without a change in temperature. This process occurs at a constant temperature of \(0^\circ \text{C}\) because the energy is used in breaking the bonds between water molecules within the ice to form liquid water.Here's how it applies in our ice block exercise:

• As the ice block slows down, it loses kinetic energy.
• This lost energy is converted into heat which contributes to the melting process.
• The latent heat of fusion quantifies exactly how much energy is required to convert a certain mass of ice into water, with no temperature change.

Therefore, even a slight reduction in the speed of the ice block can release enough energy to melt a small amount of ice, as seen in the precise calculations given. Understanding the melting process helps underline the broader principle that energy, while transferring from one form to another, is conserved throughout physical processes.