a 75kg skater is travelling at 15m/s stops suddenly on the ice. If the ice is at 0 degrees and it is assumed that all of the skaters energy is converted to heat, how much ice does he melt? (latent heat of fusion for water is 3.3x10^5 J/kg)
Assume all of the kinetic energy,
(1/2) M V^2 = 8438 J, is used to melt the ice. Divide that energy by the latent heat of fusion, 3.3x10^5 J/kg. The answer will be in kg.
0,02556818182kg
To calculate how much ice the skater melts, we need to find the amount of heat energy converted from the skater's kinetic energy into melting the ice.
1. Start by calculating the skater's initial kinetic energy using the formula:
KE = 0.5 * m * v^2
where KE is the kinetic energy, m is the mass of the skater, and v is the velocity of the skater.
Plugging in the values, we have:
KE = 0.5 * 75 kg * (15 m/s)^2
= 0.5 * 75 kg * 225 m^2/s^2
= 8437.5 J
So, the skater's initial kinetic energy is 8437.5 joules.
2. Next, to determine the amount of ice melted, we need to know the latent heat of fusion for water, which is given as 3.3 x 10^5 J/kg.
The latent heat of fusion represents the amount of energy required to change one kilogram of a substance from solid to liquid without a change in temperature. In this case, it is the ice melting into water.
3. Divide the skater's initial kinetic energy by the latent heat of fusion to find the amount of ice melted:
Amount of ice melted = KE / latent heat of fusion
Amount of ice melted = 8437.5 J / (3.3 x 10^5 J/kg)
Amount of ice melted ≈ 0.0256 kg
Therefore, the skater would melt approximately 0.0256 kilograms (or 25.6 grams) of ice when they stop suddenly on the ice.