Work, Energy and Power question

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SUMMARY

The discussion centers on a physics problem involving a cyclist's power output and the effects of air resistance on different terrains. The cyclist experiences maximum velocities of v on level ground, 1/2v uphill, and av downhill. The incorrect assumption made in the calculations was that air resistance is proportional to the square of the speed (kv^2), while it is actually proportional to the speed (kv). The correct interpretation leads to the conclusion that the value of a is √(7/4).

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  • Understanding of basic physics concepts such as work, energy, and power.
  • Familiarity with forces acting on objects in motion, specifically in cycling scenarios.
  • Knowledge of how air resistance affects velocity and power output.
  • Ability to manipulate algebraic equations to solve for unknown variables.
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  • Review the principles of dynamics related to cycling and resistance forces.
  • Study the relationship between power, force, and velocity in physics.
  • Learn about the effects of different types of resistance (linear vs. quadratic) on motion.
  • Explore advanced problems involving forces on inclines and their impact on maximum velocity.
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of problem-solving in dynamics related to cycling and resistance forces.

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Homework Statement


A cyclist develops constant power when cycling. The air resistance is proportional to the speed of cycling. When he cycles on level ground, the maximum velocity he can attain is v. When he cycles up a slope, his maximum velocity is 1/2v. If he cycles down the same slope, his maximum velocity is av. Ask what is the value of a.


Homework Equations





The Attempt at a Solution


The cyclist exerts the same amount of force on the bike at all velocity,thus

On level ground: F = kv2

cycling up a slope: F = 1/4kv2 + mgsinθ
kv2 = 1/4kv2 + mgsinθ
mgsinθ = 3/4kv2

cycling down the slope: kv2 + 3/4kv2 = k(av)2
a2 = 7/4
a = (7/4)1/2

But this is not the correct answer. Can anyone tell me where did I go wrong?
 
Physics news on Phys.org
You assumed that the air resistance was proportional to the square of the speed (kv^2), when it is given that it is proportional to the speed (kv).
 

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