How Does Air Resistance Affect Cyclist Power Output?

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The discussion centers on calculating the air resistance force acting on a cyclist moving at a constant speed of 7.0 m/s with a power output of 120 W. Key equations include the power formula P = energy/time and the kinetic energy formula KE = 1/2 mv^2. Participants highlight the relationship between power, work, and force, emphasizing that constant speed implies a balance between the cyclist's exerted force and the air resistance. The challenge lies in determining the frictional force without sufficient variables, prompting further exploration of the definitions of power and work. Understanding these concepts is crucial for accurately calculating the air resistance experienced by the cyclist.
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Homework Statement


The power of a cyclist moving at a constant speed of 7.0 m/s on a level road is 120 W. What is the magnitude of the frictional force (in N) exerted on her (and the bicycle) by the air?


Homework Equations


P=energy/time KE=1/2mv^2


The Attempt at a Solution


Idk i tried but I'm just missing too many variables.. i attempted and got 4.9N
 
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Power is the rate at which work,W, is done i.e. P=\frac{d}{dt}(W)

W=Fs => (you can take it from here) [Note: constant velocity means constant acceleration which means what about the force and hence you should have a new expression for P]
 
jk5389 said:

Homework Statement


The power of a cyclist moving at a constant speed of 7.0 m/s on a level road is 120 W. What is the magnitude of the frictional force (in N) exerted on her (and the bicycle) by the air?


Homework Equations


P=energy/time

Here are two things to consider. The cyclist is working along to propel the bike, so they must be exerting a force, yet they are moving at constant speed. What is the acceleration of the cyclist and bicycle? What is the net force of the cyclist and bicycle? What must be the power being delivered by the air resistance against the cyclist and bike?

Knowing the power brought to bear by the air, you can take apart the definition of power, which is P = energy/time or work/time. What is the definition of work and how do you calculate it? Work can be written as a product of something, so it can be factored. What would be a way to factor the quotient for power in terms of a quantity you know from the problem and a quantity you want to find?
 
Last edited:
rock.freak667 said:
[Note: constant velocity means constant acceleration...

Erm, but not just any constant -- exactly what acceleration?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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