Calculating Velocity & Kinetic Energy of Bicycle Racer Rolling Downhill

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Homework Help Overview

The discussion revolves around a bicycle racer who experiences a mechanical failure while descending a hill. The problem involves calculating the final velocity and kinetic energy of a wheel modeled as a thin-walled cylinder, given initial conditions such as speed and height.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of energy conservation principles, specifically the relationship between kinetic and potential energy. There are attempts to calculate initial and final kinetic energies, as well as questions regarding the calculation of angular velocity and its implications for the final velocity of the wheel.

Discussion Status

The discussion includes various attempts to calculate kinetic energy and velocity, with some participants confirming the correctness of initial approaches. Questions remain about the calculation of angular velocity and its integration into the overall energy conservation equation.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is an emphasis on ensuring the correct application of formulas related to rotational motion and energy conservation.

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A bicycle racer is going downhill at 11.0m/s when, to his horror, one of his 2.25kg wheels comes off when he is 75.0m above the foot of the hill. We can model the wheel as a thin-walled cylinder 85.0cm in diameter and neglect the small mass of the spokes.

I need to get the velocity at the bottom of the hill and KEtotal at the bottom

I know Kf=1/2Mv^2 + 1/2(I)w^2

Vo=11m/s
M=2.25kg
r=.425m

I know I=MR^2
I=.4064kg*m^2

would you use Ki+Ui=Kf+Uf to get w? or is there another way?
 
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No, that looks correct.
 
here was my attempt
Ki=136.125J
Ui=1653.75J
Kf=1/2mv^2+ 1/2Iw^2
Uf=0

for I am stuck on Kf
Its a thin cylinder so I=MR^2 for w did i calculate it correct? v=wr so 11/.425= 25.8rad/s
Ki +Ui=Kf + Uf
so 136.125J +1653.75J= 1/2mv^2 + .4064*(25.8)^2 +0

from here i solved for the v i plugged in 2.25kg into m and i got 38.8m/s as Vf
 
am i messing up on calculating the ang velocity (w)?
 

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