Solve Centripetal Motion: Find Fnet | Physics Calculations

[SA32]

Hi there, I was wondering if anyone could help me with a centripetal motion question.

"A cyclist competes in a one-lap race around a flat, circular course of radius r. Starting from rest and speeding up at a constant rate throughout the race, the cyclist covers the entire course in a time Δt. The mass of the bicycle (including the rider) is m. What is the magnitude of the net force F_net acting on the bicycle as it crosses the finish line?

Find F_net, the magnitude of the net force acting on the cyclist at the finish line.
Express the net force in terms of r, Δt, m, and π."

My thinking was as follows:

In circular motion, F_net = F_centripetal = mv²/Δt

I also know that v=2πr/Δt

Substituting the latter equation into the former, I get (m*4π²r)/Δt²

However, I am being told that my answer is "off by a multiplicative factor". I worked through a series of hints for this problem with a friend, only to come up with the same answer. Any help is appreciated!

 

[PhanthomJay]

Hi there, I was wondering if anyone could help me with a centripetal motion question.

"A cyclist competes in a one-lap race around a flat, circular course of radius r. Starting from rest and speeding up at a constant rate throughout the race, the cyclist covers the entire course in a time Δt. The mass of the bicycle (including the rider) is m. What is the magnitude of the net force F_net acting on the bicycle as it crosses the finish line?

Find F_net, the magnitude of the net force acting on the cyclist at the finish line.
Express the net force in terms of r, Δt, m, and π."

My thinking was as follows:

In circular motion, F_net = F_centripetal = mv²/Δt

I also know that v=2πr/Δt

Substituting the latter equation into the former, I get (m*4π²r)/Δt²

However, I am being told that my answer is "off by a multiplicative factor". I worked through a series of hints for this problem with a friend, only to come up with the same answer. Any help is appreciated!

First you have a typo in the F_c equation, it's mv^2/r, which you have correctly applied though. Your error comes in your equation for v. You have calculated his average speed using that formula. Since his initial speed is 0, what's his final speed at the finish line?

 

[SA32]

Oops! Now I feel stupid.

This is non-uniform circular motion... so I need to find the net radial force and the net tangential force than use the Pythagorean Theorem to solve for Fnet.

Thanks for pointing that out!