How Does Doubling Speed Affect Energy Use Against Drag in Cycling?

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Doubling the speed of a cyclist from 5 m/s to 10 m/s significantly increases the drag force, as drag is proportional to the square of the velocity. At 5 m/s, the drag force is 10N, resulting in an energy expenditure of 10 kJ for traveling 1 km. When speed is doubled, the drag force increases to 40N, leading to a higher energy requirement for the same distance. Additionally, when slowing down to 5 m/s while facing a headwind of 5 m/s, the total effective speed becomes 10 m/s, and the power expended can be calculated based on the increased drag. Understanding these dynamics is crucial for optimizing energy use in cycling against drag.
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In this problem assume that all of the energy expended goes into working against drag. Assume that F is proportional to v-squared exactly & that the air is motionless with respect to the ground. Suppose a cyclist and the bicycle have a combined mass of 60kg and is moving a 5m/s.

A) If the drag force on the cyclist is 10N, how much energy does the cyclist use in traveling 1 km?

B) If speed is doubled to 10 m/s, how much energy is used in traveling 1 km?

C) Upon slowing down to 5 m/s, we hit a head wind of 5 m/s, How much power is being expended?

2. Homework Equations

W = Fd

P = W/change in time3. The Attempt at a Solution

A) W = 10N x 1km = 10 kj

B) ?

C) ?
 
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Hi justunme and welcome to PF. For part (B), if the speed is doubled does the drag force change? If so, by what factor?
 
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