A block of ice at 0 degrees C, whose mass is initially 40.0 kg, slides along a horizontal surface, starting at a speed of 5.26 m/s and finally coming to rest after traveling 22.5 m. Compute the mass of ice melted (in grams) as a result of friction between the ice and the horizontal surface.

To compute the mass of ice melted as a result of friction, we need to first determine the amount of kinetic energy lost by the block of ice.

The initial kinetic energy (KE_i) of the block of ice can be calculated using the formula:

KE_i = (1/2) * mass * velocity^2

Given:
Mass of the ice block (m) = 40.0 kg
Initial velocity (v_i) = 5.26 m/s

Substituting these values into the formula:

KE_i = (1/2) * 40.0 kg * (5.26 m/s)^2

Next, we can calculate the final kinetic energy (KE_f) of the block of ice. Since the block comes to rest, the final velocity (v_f) is 0 m/s.

Using the same formula:

KE_f = (1/2) * mass * velocity^2

Substituting the values:

KE_f = (1/2) * 40.0 kg * (0 m/s)^2

The kinetic energy lost (KE_lost) can be calculated as the difference between the initial and final kinetic energies:

KE_lost = KE_i - KE_f

Substituting the respective equations:

KE_lost = [(1/2) * 40.0 kg * (5.26 m/s)^2] - [(1/2) * 40.0 kg * (0 m/s)^2]

Now, we need to realize that the energy lost as kinetic energy is converted into other forms, such as heat. In this case, it is converted into melting ice.

The amount of ice melted can be calculated using the concept of specific latent heat of fusion (L) for ice. This is the amount of heat energy required to change a unit mass of a substance from solid to liquid state without changing its temperature.

The formula for calculating the amount of ice melted is:

Mass of ice melted (m_melted) = KE_lost / L

However, we need to pay attention to the units. The given mass is in kilograms, but we need to convert it to grams before calculating the mass of ice melted, as we want the answer in grams.

Therefore, the final calculation becomes:

Mass of ice melted (in grams) = (KE_lost / L) * 1000

You would need to have the value of the specific latent heat of fusion (L) for ice to compute the final mass of ice melted.