Solve Centripetal Motion: Find Fnet | Physics Calculations

In summary, the net radial force at the finish line is the product of the cyclist's mass and the radius of the circular course. The net tangential force is the opposite of the net radial force.
  • #1
SA32
32
0
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 Fnet acting on the bicycle as it crosses the finish line?

Find Fnet, 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, Fnet = Fcentripetal = 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!
 
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  • #2
SA32 said:
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 Fnet acting on the bicycle as it crosses the finish line?

Find Fnet, 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, Fnet = Fcentripetal = 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?
 
  • #3
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!
 

Related to Solve Centripetal Motion: Find Fnet | Physics Calculations

1. What is centripetal motion?

Centripetal motion is the circular motion of an object around a central point, caused by a force directed towards the center of the circle. This force is necessary to keep the object moving in a circular path.

2. How do you find the net force in centripetal motion?

To find the net force in centripetal motion, you need to use the formula Fnet = mv^2/r, where Fnet is the net force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.

3. What is the difference between centripetal force and centrifugal force?

Centripetal force is the force that keeps an object moving in a circular path, while centrifugal force is the apparent outward force experienced by an object in circular motion. Centrifugal force is a fictitious force and does not actually exist, it is simply a result of the object's inertia.

4. Can you use the same formula to find the net force in all types of centripetal motion?

Yes, the formula Fnet = mv^2/r can be used to find the net force in all types of centripetal motion, as long as the motion is circular. This formula is also known as the centripetal force equation.

5. What are some real-life examples of centripetal motion?

Some real-life examples of centripetal motion include the movement of planets around the sun, the motion of a car around a curve, and the rotation of a spinning top. Any object or body that moves in a circular path experiences centripetal motion.

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