Question

A 58-kg cross-country skier glides over snow as in the figure below. The coefficient of friction between skis and snow is 0.24. Assume all the snow beneath her skis is at 0°C and that all the internal energy generated by friction is added to snow, which sticks to her skis until it melts. How far would she have to ski to melt 1.5 kg of snow?

Answer 1

The skier needs to glide 397.72 meters to melt 1.5 kg of snow.

Friction work: The skier's weight (58 kg) experiences frictional force (0.24 friction coefficient) while gliding. This friction work turns into thermal energy, which melts snow.

Energy balance: The work done against friction (friction force x distance) equals the heat needed to melt 1.5 kg of snow (latent heat of fusion of ice x mass).

Melting equation: Substitute the values: (58 kg x 0.24 x distance) = (334 kJ/kg x 1.5 kg).

Distance calculation: Solving for the distance, we get: distance = 334 kJ/kg x 1.5 kg / (58 kg x 0.24) = 397.72 meters.