What is the theoretical maximum distance for a rotating wheel with added weight?

[supamanc]

Homework Statement

this is not really a homework question, but it would make a good one!. i posted it in the classical mechanics forum, but did not seem to get much help

i have a two wheel rims, 50mm thick, (ouside radius 500mm, inside 475mm) connected by 8 horizontal spokes. between two of the spokes on opposite sides of the wheel are basket holders, such that the wheel is in perfect balance, and when a weight is dropped in one basket the wheel revolves and moves forwards, dropping the weight when it reaches the bottom of the wheel (the other basket is for symmetry/balance) by using a 2.2 kg weight i have had the wheel roll an average of 55m (61.3 max!) it takes 2.4 secs to complete one revolution, giving an RPM of 25

my question is how can i work out the theoretical maximum distance i should be able to get from the weight?

Homework Equations

not really sure, this is what i am trying to find! i know
I = 1/2m(r12 + r2²)
angular velocity = v * r
do not know how to work out friction, or how to take it into account

The Attempt at a Solution

I am not studying physics, and have very little knowledge of it, bar what my internet research has turned up, so i really do not have a clue where to start. some relevant formulas or a link to a good instructional site would be appreciated, thank you

 

[chaoseverlasting]

Basically friction is directly proportional to the weight of the object. When the wheel rolls, it experiences rolling friction (as opposed to sliding friction). What you're essentially doing is converting the potential energy of the weight into the kinetic energy of the wheel.

Since the outside radius of the wheel is 0.5 m, the potential energy of the weight is 2.2*9.8*0.5 (mgh where m is the mass of the wheel, g is the constant of gravitation and h is the height of the object). This is converted into kinetic energy given by K=\frac{1}{2}Iw^2, where w is the angular velocity of the wheel.

You are going to have to determine the coefficient of friction to get a theoretical expression for the maximum distance traveled. Do you have a general idea of what you need to do?

 

[supamanc]

mmmmm let's see!
i now know the kinetic energy of the wheel, and by calculating the energy required for one revolution, i can calculate the maximum possible number of revs, thus the maximum possible distance, without friction.

i need the find the coefficient of rolling friction for wood on concrete. my wheel rims are 6mm thick, and combined with the weight of the wheel, i should be able to find the friction, yes? (dont know how yet though)

by then combining the two equations and solving for when k=0, i can work out my max distance with friction? hope this sounds reasonable!

ps, thank you for the help so far!