Explanation Given Info: the air resistance force proportional to the square of the bicycle’s speed, heart rate is directly proportional to the mechanical power output, the hart rate is 90 beats per minute when the speed is 22 km/h . The magnitude of the forward static frictional force on the static wheel is equal to the retarding air resistance force if the speed of the cyclist’s speed is a constant. Thus, the expression used to find the power output. P = f sta v f sta is the static frictional force v is the velocity P is the power output Re-write the above equation. P = ( k v 2 ) v = k v 3 (I) k is the proportionality constant The heart rate is proportional to the power output. Thus, R = k ' P (II) k ' is the proportionality constant P is the power output R is the heart rate Substitute equation (I) in (II) to find the heart rate. R = k ' k v 3 Consider R 2 is the heart rate at a speed of v 2 and R 1 is the heart rate at a speed of v 1 . The expression used to the ration of heart rate R 2 and R 1 . R 2 R 1 = k ' k v 2 3 k ' k v 1 3 = ( v 2 v 1 ) 3 R 2 is the heart rate at a speed of v 2 R 1 is the heart rate at a speed of v 1 Re-arrange the expression to find the speed v 2

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ISBN: 9781285761954

Author: Raymond A. Serway, Chris Vuille

Publisher: Cengage Learning

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Chapter 5, Problem 91AP

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Chapter 5, Problem 90AP

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