Chapter 14, Problem 32P

To determine

Mass of melted ice

Answer to Problem 32P

Solution:

$0.00\text{27 kg}$

Explanation of Solution

Given Info:

Mass of ice skater is 64 kg moving at 7.5 m/sec. Ice is at a temperature 0°C. 50% of the heat generated by friction is absorbed by ice.

Formula used:

Heat for melting is given by

$Q=mL$

Where L is latent heat

Kinetic energy is given by

$KE=\frac{1}{2}m{v}^2$

Calculation:

Half the kinetic energy gets used to melt the ice. Ice is at its melting point

So,

$\begin{array}{l}0.5\times \frac{1}{2}{m}_s{v}^2=m_{ice}L\\ 0.5\times \frac{1}{2}\times 64\text{kg}\times {(}^{7.5}=m_{ice}(3.33\times {10}^5\text{J/kg})\\ m_{ice}=0.0027\text{kg}\end{array}$