A skier, moving at 8m/s, slides to a stop on a level surface while moving 64m. Assuming her mass to be 60kg, what is the coefficient of friction between her skies and the snow?
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Welcome to Math SE. In the future, please post your thoughts and work on the problem in order to make it a quality question. – zahbaz Feb 05 '19 at 05:54
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Also, if an answer works out for you, please click the "checkmark" next to your desired answer. This helps close the question for record keeping on the site. – zahbaz Feb 05 '19 at 18:28
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Hint: Use conservation of energy. – amd Feb 05 '19 at 21:55
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Let's say the skier is headed in the positive $x$ direction. Draw a free body diagram. The only non-negligible force in this direction will be due to friction, which we assume is constant: $f = -\mu N = -\mu m g$. By Newton's 2nd law, the sum of all forces in this direction gives $m a = -\mu m g$. This simplifies to $\mu = -a/g$. You need to find the acceleration. Use $v_f^2 - v_0^2 = 2a\Delta x$ to get $a = -v_0^2/2\Delta x$, giving a solution
$$\mu = v_0^2 / 2g\Delta x \approx 0.05 $$
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