A ski that is placed on snow will stick to the snow. However, when the ski is mo

Question

A ski that is placed on snow will stick to the snow. However, when the ski is moved along the snow, the rubbing warms and partially melts the snow, reducing the coefficient of kinetic friction and promoting sliding. Waxing the ski makes it water repellent and reduces friction with the resulting layer of water. A magazine reports that a new type of plastic ski is especially water repellent and that, on a gentle 210 m slope in the Alps, a skier reduced his top-to-bottom time from 64.0 s with standard skis to 44.0 s with the new skis. Determine the magnitude of his average acceleration with (a) the standard skis and (b) the new skis. Assuming a 3.80

Explanation / Answer

S = 210 m

t1 = 64

a)

S = 0 + .5at^2 = .5*a*64^2

a = .1025 m/s^2

b)

S = 0 + .5at^2 = .5*a*44^2

a = 0.2169 m/s^2

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downward force along the slope due to gravitational force = mgsin(theta)

upward force along the slope due to friction = u*mgcos(theta)

average acceleration = gsin(theta) - u*gcos(theta)

c)

.1025 = 9.8 (sin(3.8) - ucos(3.8))

soving we get coefficient of friction u = 0.056

d)

similary for new skis

0.2169 = 9.8 (sin(3.8) - ucos(3.8))

u = .0442

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