A bicyclist coasts without pedaling down an incline that makes an angle of 4o with the horizontal at a steady speed of 13 m/s. If the mass of the cyclist and the bike combined is 76 kg, use k-work (not Newton’s second law) to estimate the force of friction that must be acting on the bicyclist. (Hint: Think about what happens during a time interval of 1 s.)

Question

A bicyclist coasts without pedaling down an incline that makes an angle of 4o with the horizontal at a steady speed of 13 m/s. If the mass of the cyclist and the bike combined is 76 kg, use k-work (not Newton’s second law) to estimate the force of friction that must be acting on the bicyclist. (Hint: Think about what happens during a time interval of 1 s.)

Answer 1

whats the answer?

Answer 2

To estimate the force of friction acting on the bicyclist, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. In this case, since the bicyclist is coasting down an incline at a steady speed, the work done by friction is equal to the change in kinetic energy.

Let's break down the problem step by step to find the solution:

1. First, we need to calculate the change in height (Δh) that the bicyclist descends during a time interval of 1 second. To do this, we can use the trigonometric relationship between the angle of the incline and the vertical change in height:

sin(θ) = Δh / L

Where θ is the angle of the incline (4 degrees) and L is the length of the incline. Since we don't know the length of the incline, we can consider it as the hypotenuse of a right triangle with Δh being the opposite side and L being the adjacent side.

By rearranging the equation, we have:

Δh = L * sin(θ)

2. Next, we can calculate the change in potential energy (ΔPE) using the formula:

ΔPE = m * g * Δh

Where m is the mass of the bicyclist and the bike combined (76 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and Δh is the change in height.

3. Since the bicyclist is coasting at a steady speed, there is no change in kinetic energy. Therefore, the work done by friction (W_friction) must be equal to the negative change in potential energy:

W_friction = -ΔPE

4. Finally, we can calculate the force of friction (F_friction) by dividing the work done by friction by the distance traveled (L):

F_friction = W_friction / L

We can solve for F_friction by substituting the values obtained in the previous steps.

This approach calculates an estimate for the force of friction based on the work-energy principle. However, note that the actual force of friction may be influenced by various factors, such as air resistance and rolling resistance, which are not considered in this simplified estimation.