Description
A 62-kg cross-country skier glides over snow as in the figure below. The coefficient of friction between skis and snow is 0.16. 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 2.5 kg of snow?
Explanation & Answer
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mass=62 kg
friction coefficient =0.16
Q=mL
L-latent heat for ice=3*10^5 j/kg
Q=2.5 x 3 x 10^5
Q=7.5 x 10^5 j
so the friction energy can find as fallows
W=Fs-------------(1)
but
F=friction coefficient x R where R is the reactant force
so
F=0.16 x 62 x 9.81
F=97.32N
subustitute for (1)
W=97.32 x S
but W=work=Q
so W=Q=7.5 x 10^5j
then
7.5 x 10^5=97.32 x S
s=7.5 x 10^5/97.32 which is
s=7706.5 m
so he has to ski 7706.5 m
Thank you.
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