A block of ice at 0°C whose mass initially is m = 12.5 kg slides along a horizontal surface, starting at a speed vo = 4.10 m/s and finally coming to rest after traveling a distance d = 10.07 m. Compute the mass of ice melted as a result of the friction between the block and the surface. (Assume that all the heat generated owing to friction goes into the block of ice.)

Question

A block of ice at 0°C whose mass initially is m = 12.5 kg slides along a horizontal surface, starting at a speed vo = 4.10 m/s and finally coming to rest after traveling a distance d = 10.07 m. Compute the mass of ice melted as a result of the friction between the block and the surface. (Assume that all the heat generated owing to friction goes into the block of ice.)

i thought i had to use friction but it doesn't give me the coefficient of friction.

Answer 1

work done: 1/2 m v^2

compute that.

Then, heat = work done= massice*Hf

Answer 2

To solve this problem, you need to apply the concept of the conservation of mechanical energy. Since the block comes to rest, all of the initial kinetic energy of the block is converted into thermal energy due to friction.

First, let's calculate the initial kinetic energy of the block using the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Given:
Mass of the block (m) = 12.5 kg
Initial velocity (v0) = 4.10 m/s

Substituting these values into the formula, we can find the initial kinetic energy:

Initial Kinetic Energy (KE0) = (1/2) * 12.5 kg * (4.10 m/s)^2

Next, since the block comes to rest, all of the initial kinetic energy is converted into thermal energy. We can assume that this thermal energy melts a certain mass of ice.

To calculate the mass of ice melted, we need to use the concept of latent heat of fusion, which is the amount of energy required to convert a solid into a liquid without changing its temperature.

The formula for the amount of heat energy required to melt a substance is:

Heat Energy (Q) = mass * latent heat of fusion

In this case, the substance being melted is the ice block, and we assume all the heat generated by friction goes into the ice. Therefore, we can equate the initial kinetic energy to the heat energy:

KE0 = Heat Energy (Q)

Now, let's calculate the initial kinetic energy (KE0) using the given values:

KE0 = (1/2) * 12.5 kg * (4.10 m/s)^2

After obtaining the value of KE0, you can now calculate the mass of ice melted (mass) using the formula:

mass = KE0 / latent heat of fusion

To find the latent heat of fusion of ice, you can use the value of 334,000 J/kg. Substituting the calculated value of KE0 and the latent heat of fusion into the formula, you can solve for the mass of ice melted.