Drag force and friction force

[makeAwish]

Homework Statement

For a touring bicyclist the drag coefficient C(where f of air = 0.5CApv^2) is 1.04, the frontal area A is 0.462 , and the coefficient of rolling friction is 4.60×10−3. The rider has mass 53.0kg, and her bike has mass 11.1kg.
Note: p is density of air (1.2kg/m^3)

To maintain a speed of 11.7m/s on a level road, what must the rider's power output to the rear wheel be?

The attempt at a solution

Total force = friction force + drag force
Power = total force x velocity = 459.6W

which is not correct.

 

[LowlyPion]

I would calculate it the same way, but with more precision. I got an answer close but possibly enough dissimilar?

 

[nlightner]

I would like to provide a more detailed explanation of the concepts involved in this problem and how to correctly solve it.

Firstly, drag force and friction force are two important forces that act on an object moving through a fluid (such as air) or on a surface. Drag force is the resistance force that opposes the motion of an object through a fluid and is dependent on the object's shape and size, the density of the fluid, and the velocity of the object. On the other hand, friction force is the resistance force that opposes the motion of an object on a surface and is dependent on the nature of the surface and the normal force acting on the object.

In this problem, the touring bicyclist is experiencing both drag force and friction force while maintaining a speed of 11.7m/s on a level road. The drag force is given by the equation Fd = 0.5CApV^2, where C is the drag coefficient, A is the frontal area, p is the density of air, and V is the velocity. The friction force is given by Ff = μN, where μ is the coefficient of rolling friction and N is the normal force.

To find the power output of the rider to maintain this speed, we need to find the total force acting on the rider and her bike. The total force is the sum of the drag force and the friction force. So, we can write the equation as Ftotal = Fd + Ff.

Substituting the given values, we get Ftotal = 0.5(1.04)(1.2)(0.462)(11.7)^2 + (4.60x10^-3)(64.1)(9.8) = 459.6N.

Now, to calculate the power output, we need to multiply the total force by the velocity, which gives us P = Ftotal x V = 459.6 x 11.7 = 5377.32W.

However, this is the total power output required to maintain the speed of 11.7m/s. To find the power output to the rear wheel, we need to take into account the efficiency of the bike and the rider. Let's assume an efficiency of 90%, which means that only 90% of the power output is actually being used to maintain the speed. So, the power output to the rear wheel would be P = 5377