while at roller derby While at the roller derby the other night, I measured the

Question

while at roller derby While at the roller derby the other night, I measured the oval track as having two straight sections, each 70 feet long. The track was 15 feet wide. The two circular ends of the track had an inside radius of 15 feet and an outside radius of 30 feet. Assume that a skater chooses to go all around the track along the very inside edge as fast as possible without skidding, maintaining the same speed on the straight portions as around the curved ends. Assume that another skater chooses to go all around the track along the very outside edge as fast as possible without skidding, also maintaining her same speed on the straight portions as around the curved ends. Which skater has the shortest lap time What are these two lap times? Assume a value of 0.6 for the coefficient of friction and note that there is no bank to the track, it is horizontal and flat.

Explanation / Answer

For circular motion,

the centriperal force = mv^2/r

In our question, the force of friction will provide the necessary centripetal force

So, umg = mv^2/r

where u = coefficient of friction = 0.6

So, ug = v^2/r

So, v = sqrt(u*r*g)

For the inner radius, r = 15 feet = 4.57 m

So, vinner = sqrt(0.6*4.57*9.8) = 5.18 m/s

For outer radius, r = 30 feet = 9.14 m

So, vouter = sqrt(0.6*9.14*9.8) = 7.33 m/s

So, the lap time for inner track = (2*pi*4.57+2*21.34)/5.18 = 13.8 s

lap time for outer track =  (2*pi*9.14+2*21.34)/7.33 = 13.66 s

So, the outer lap time is shorter

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