A 75 -kg cross-country skier glides over snow as in Figure...

A 75 -kg cross-country skier glides over snow as in Figure P11.29. The coefficient of friction between skis and snow is $0.20$. Assume all the snow beneath his skis is at $0^{\circ} \mathrm{C}$ and that all the internal energy generated by friction is added to snow, which sticks to his skis until it melts. How far would he have to ski to melt $1.0 \mathrm{~kg}$ of snow?

Key Concepts

Energy Conservation

The principle of energy conservation states that energy in a closed system is neither created nor destroyed but can only change form. In problems like the one presented, mechanical energy lost to friction is completely transformed into thermal energy, which is then used to cause the phase change (melting) of the material. This principle is vital for setting up energy balance equations in various physical scenarios.

Coefficient of Friction

The coefficient of friction is a dimensionless scalar value that quantifies the ratio of the frictional force resisting an object's motion to the normal force pressing the surfaces together. It is essential for calculating how much force will be lost to friction when an object moves along a surface, which directly impacts the mechanical energy available for conversion into heat.

Work Done by Friction

Work done by friction is the energy transferred when frictional forces oppose the motion of an object over a distance. This work, expressed as the product of the friction force and the distance traveled, represents the energy dissipated as heat. In energy conversion problems, this frictional work is set equal to the energy required to induce a phase change, demonstrating the transformation from mechanical energy to thermal energy.

Latent Heat of Fusion

Latent heat of fusion is the amount of energy required per unit mass to change a substance from a solid to a liquid state at its melting point, without any change in temperature. This concept is fundamental in thermodynamics when analyzing how absorbed energy can cause a phase change, such as melting, emphasizing the energy needed to break molecular bonds rather than increasing temperature.

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