Bicycle rider down a hill (Dynamics)

In summary, the conversation discusses a problem involving a bicycle rider starting at the top of a hill and rolling freely in a circular path. The task is to calculate the speed of the rider at the bottom point and the reaction force acting on the bike at that point. The discussion also mentions the use of energy conservation to solve the problem. The final solution involves calculating the velocity and then using it to find the required centripetal force.
  • #1
Femme_physics
Gold Member
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Homework Statement



http://img822.imageshack.us/img822/5347/byccc.jpg

A bicycle rider starts his motion from the top of the hill A at an initial velocity (Vo). From that point, the bicycle roll freely (without using pedals) in a the circular path.

A) Calculate the speed of the rider at bottom point B
B) Calculate the reaction force (N) acting on the bike at point B

Comment: Ignore friction and presume the rider is a point mass.

(The rest of the info is in the pic I uploaded)


The Attempt at a Solution



Again, getting weird/impossible outcomes


http://img94.imageshack.us/img94/324/fyfyasdasdasda.jpg

http://img690.imageshack.us/img690/927/trigg.jpg
 
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  • #2
What is the Potential Energy at the top of the hill?
What is the Kinetic Energy at the top of the hill?

What is the Potential Energy at the bottom of the hill?
What is the Kinetic Energy at the bottom of the hill?

Set up Energy Equation:

(Total energy at top of Hill) = (Total energy at bottom of hill)

Try setting the potential energy at the bottom of the hill as zero and see what you get...

You can have the whole equation set up in one line...
 
  • #3
Working out the forces in this instance, though it can be done... might lead to ulcers.
 
  • #4
Perhaps you could check your formula table?
I seem to be missing a few squares?! :confused:
 
  • #5
yeah, Femme_Physics - In the second image, you've calculated the final speed of the bike using energy conservation, but both of those velocities in the equation should be squared. Which is why it comes out with the wrong answer.
Once you get the right value for velocity, you can calculate the required centripetal force. And this will equal N-W because these forces are both in a radial direction when the cyclist is at the bottom of the circle
 
  • #6
Okay, I did it with squared values and I got the correct answer.

Vb = 18.19 m/s

As far as N goes...piece a cake :)

http://img849.imageshack.us/img849/94/nnnasdas.jpg

Working out the forces in this instance, though it can be done... might lead to ulcers.
Really?
How could it be possibly easier to solve it with energy? This was pretty facile if you ask me! :)

Thanks, everyone!
 
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1. What is the force that propels a bicycle rider down a hill?

The force that moves a bicycle rider down a hill is gravity. Gravity is the force of attraction between two objects, in this case, the rider and the Earth. The rider's weight and the slope of the hill determine the strength of the gravitational force.

2. How does the rider's position affect the speed while going down a hill?

The rider's position plays a significant role in determining the speed while going down a hill. The more aerodynamic the rider is, the less air resistance they will face, resulting in a higher speed. Additionally, leaning forward can shift the rider's center of mass, making them more stable and able to maintain a higher speed.

3. What is the role of friction in a bicycle rider going down a hill?

Friction is the force that opposes motion between two surfaces in contact. While going down a hill, friction plays a crucial role in slowing down the rider. The friction between the tires and the road, as well as air resistance, act as a braking force, allowing the rider to control their speed and come to a stop.

4. How does the weight of the rider affect the dynamics of going down a hill?

The weight of the rider is a crucial factor in the dynamics of going down a hill. The rider's weight determines the strength of the gravitational force, which accelerates the rider down the hill. A heavier rider will experience a greater gravitational force and, therefore, a higher acceleration and speed compared to a lighter rider.

5. What are the safety measures to consider while going down a hill on a bicycle?

There are several safety measures to consider while going down a hill on a bicycle. These include wearing a helmet and other protective gear, checking the brakes and tires before riding, maintaining a safe speed, and using hand signals to communicate with other riders and drivers. It is also important to be aware of potential hazards, such as uneven surfaces or obstacles, and to always follow traffic laws and regulations.

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