Bicycle rider down a hill (Dynamics)

[Femme_physics]

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

 

[FourierFaux]

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...

 

[FourierFaux]

Working out the forces in this instance, though it can be done... might lead to ulcers.

 

[I like Serena]

Perhaps you could check your formula table?
I seem to be missing a few squares?!

 

[BruceW]

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

 

[Femme_physics]

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!