Question

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

Answer 1

Answer:

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

$L_{f} = 3.33\times 10^{5}\ J/kg$ = Latent Heat of fusion

Thus from eqn (1) and (2):

$s = \frac{ML_{f}}{\mu_{k}mg}$

$s = \frac{5\times 3.33\times 10^{5}}{0.50\times 64\times 9.8}$

s = 5.309 km