2. an iceskater of mass 100 kg starts to glide at 10 m/s and comes to rest. how much ice is melted? assume that half the heat generated by friction is absorbed by the ice and that the ice is at its melting point.
Heat from skater* .5 = Lf*massice.
1/2 massskater*100*.5= Lf*massicemelted.
Put lf in units of joules/kg
To solve this problem, we need to calculate the amount of heat generated by friction, and then use that to determine the mass of ice melted. Let's break down the steps:
1. Calculate the heat generated by friction:
- The formula for heat generated by friction is given by: Heat = μ * m * g * d
(where μ is the coefficient of friction, m is the mass of the skater, g is the acceleration due to gravity, and d is the distance traveled)
- In this case, the skater starts at 10 m/s and comes to rest, so the distance traveled is determined by the deceleration. Let's assume a constant deceleration over a certain distance. We'll use the kinematic equation: v_final^2 = v_initial^2 + 2 * a * d
(where v_final is the final velocity, v_initial is the initial velocity, a is the acceleration, and d is the distance traveled)
- Since the skater comes to rest, v_final = 0, v_initial = 10 m/s, and a = (-v_final^2) / (2 * d)
- Substitute these values into the equation and solve for d:
0 = 10^2 + 2 * (-a) * d
100 = -2ad
d = 50 / a
- Now we have the distance traveled, and we can substitute it into the heat equation.
2. Determine the mass of the ice melted:
- Given that half the heat generated by friction is absorbed by the ice, we can write: Heat from skater * 0.5 = Lf * mass_ice
(where Lf is the latent heat of fusion and mass_ice is the mass of ice melted)
- Rearrange the equation to solve for mass_ice:
mass_ice = (Heat from skater * 0.5) / Lf
3. Convert the latent heat of fusion to the appropriate units:
- The latent heat of fusion (Lf) represents the amount of heat energy required to change the state of 1 kg of substance from solid to liquid. It has units of joules per kilogram (J/kg). Therefore, we don't need to convert it.
4. Substitute values and calculate:
- Plug in the values calculated in step 1 for the heat from the skater and the value of Lf into the equation from step 2 to find the mass of ice melted.
Following these steps, you should be able to determine how much ice is melted.