Halliday, Resnick & Walker — Temperature, Heat, and the First Law of Thermodynamics: Problem 101

Ice skating. A long-standing explanation of ice skating (Fig. 18.38) is that the ice is slippery beneath the skate because the weight of the skater creates sufficient stress (pressure) beneath the skate to melt the ice, thus lubricating the skate-ice contact area. At temperature \( T = -1^\circ\text{C} \), the pressure required to melt ice is \( 1.4 \times 10^7 \text{ N/m}^2 \). At that temperature, if a skater with weight \( F_g = 800 \text{ N} \) stands evenly on both skates, with each contact area \( A = 14.3 \text{ mm}^2 \), what is the stress \( \sigma \) beneath each skate? (The result appears to support the pressure-melting explanation of ice skating, but the catch is that this is a static calculation whereas ice skating involves moving skates, perhaps rapidly. More promising explanations involve friction melting of the ice by a skate, with the skate not contacting the ice but being supported by meltwater beneath it.)