# Power of a cyclist physics problem

• jk5389
In summary: The cyclist is moving at a constant speed, but they're also accelerating. So you need to find the acceleration of the cyclist and bicycle, and then use that to calculate the power being exerted by the air resistance.]
jk5389

## 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

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?

## 1. How does the power of a cyclist affect their speed?

The power of a cyclist directly affects their speed by determining how quickly they can overcome the resistance forces, such as air resistance and friction, and move forward. The greater the power output, the faster the cyclist will be able to travel.

## 2. What factors contribute to the power output of a cyclist?

The power output of a cyclist is determined by several factors, including their physical fitness, muscle strength and endurance, body position on the bike, and the gear ratio they are using. Environmental factors such as wind speed, terrain, and temperature can also impact power output.

## 3. How does air resistance affect the power of a cyclist?

Air resistance, also known as drag, is a major factor that affects the power of a cyclist. As the cyclist moves through the air, they must overcome the resistance caused by the air pushing against them. The greater the air resistance, the more power the cyclist must use to maintain their speed.

## 4. How does the gear ratio impact the power of a cyclist?

The gear ratio chosen by a cyclist can greatly impact their power output. A lower gear ratio, such as a smaller chainring and larger rear cog, allows the cyclist to pedal at a higher cadence with less resistance, resulting in less power output. On the other hand, a higher gear ratio, with a larger chainring and smaller rear cog, requires more power output to maintain the same speed.

## 5. What is the relationship between power and energy in cycling?

Power and energy are closely related in cycling, as power is the rate at which energy is expended. The more power a cyclist produces, the more energy they are using to maintain their speed. This can also be seen in the calculation of work done, where work (energy) equals power multiplied by time.

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