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

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SUMMARY

The discussion focuses on the relationship between cycling speed, drag force, and energy expenditure. Given a cyclist and bicycle mass of 60kg and an initial speed of 5 m/s with a drag force of 10N, the energy used to travel 1 km is calculated as 10 kJ. When the speed is doubled to 10 m/s, the drag force increases by a factor of four due to the velocity-squared relationship, significantly increasing energy expenditure. The discussion also raises questions about power expenditure when encountering a headwind while slowing down.

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  • Knowledge of how drag force relates to speed, specifically the v-squared relationship.
  • Basic principles of energy expenditure in cycling dynamics.
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justunme
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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) ?
 
Last edited:
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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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