Calculating Velocity & Kinetic Energy of Bicycle Racer Rolling Downhill

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In summary, the conversation discusses the scenario of a bicycle racer going downhill at 11.0m/s when one of the wheels, weighing 2.25kg and modeled as a thin-walled cylinder with a diameter of 85.0cm, falls off at a height of 75.0m above the foot of the hill. The conversation then focuses on finding the velocity and total kinetic energy at the bottom of the hill. The formula Kf=1/2Mv^2+1/2(I)w^2 is used to calculate the final kinetic energy, with the initial velocity being 11.0m/s and the radius of the cylinder being 0.425m. The moment of inertia (I)
  • #1
bigtymer8700
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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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  • #2
No, that looks correct.
 
  • #3
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
 
  • #4
am i messing up on calculating the ang velocity (w)?
 

FAQ: Calculating Velocity & Kinetic Energy of Bicycle Racer Rolling Downhill

What is velocity and how is it calculated?

Velocity is a measure of the speed and direction of an object. It is calculated by dividing the change in distance by the change in time. In the case of a bicycle racer rolling downhill, velocity can be calculated by dividing the distance traveled downhill by the time it took to travel that distance.

What is kinetic energy and how is it calculated?

Kinetic energy is the energy an object possesses due to its motion. It is calculated by multiplying the mass of the object by the square of its velocity, and then dividing by two. In the case of a bicycle racer rolling downhill, kinetic energy can be calculated by using the mass of the racer and the velocity calculated in the previous step.

What factors affect the velocity and kinetic energy of a bicycle racer rolling downhill?

The factors that affect velocity and kinetic energy include the mass of the bicycle and rider, the steepness of the hill, and any external forces such as friction or air resistance. The steeper the hill and the lighter the bike and rider, the faster the velocity and greater the kinetic energy will be.

How does the velocity and kinetic energy change as the bicycle racer goes down the hill?

As the bicycle racer goes down the hill, their velocity will increase due to the force of gravity pulling them downhill. This increase in velocity will also result in an increase in kinetic energy. The change in velocity and kinetic energy will depend on the steepness of the hill and other factors mentioned in the previous question.

How can the velocity and kinetic energy of a bicycle racer be used to improve performance?

The velocity and kinetic energy of a bicycle racer can be used to improve performance by optimizing factors such as the weight of the bike and rider, aerodynamics, and the angle of the hill. By understanding the relationship between these factors and velocity/kinetic energy, a racer can make strategic decisions to improve their performance on downhill sections of a race.

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