Question

A 64 kg cross-country skier glides over snow. Thecoefficient

of friction between skis and snow is 0.50. Assumeall the snow
beneath his skis is at 0 degrees C and that all theinternal energy
generated by friction is added to snow, whichsticks to his skis
until melted. How far would he have to skito melt 5.0 kg of
snow?

Answer 1

The distance traveled by the skier is 5.309 km

Solution:

As per the question:

Mass of the skier, m = 64 kg

Coefficient of friction between the ski and the snow,
`\mu_(k) = 0.50`

Mass of snow, M = 5.0 kg

Now,

To calculate the distance, 's' traveled by the skier, in order to melt 5.0 kg of snow:

We know that:

`f = \mu_(k)N`

where

`\mu_(k)` = coefficient of friction

N = Normal Reaction

N = mg

Thus

`f = \mu_(k)mg` (1)

Also,

`fs = ML_(f)` (2)

where

`L_(f) = 3.33* 10^(5)\ J/kg` = Latent Heat of fusion

Thus from eqn (1) and (2):

`s = (ML_(f))/(\mu_(k)mg)`

`s = (5* 3.33* 10^(5))/(0.50* 64* 9.8)`

s = 5.309 km