Determining the total distance a solid sphere will roll.

[smalveh]

Hi guys.

I'm trying to calculate the total distance a marble (I'm modeling it as non-deformable solid sphere) will travel along a flat cardboard surface (I'm also assuming the cardboard does not deform).
The sphere will initially be propelled by a known external force, it can be assumed that the sphere will not slip.
I've tried figuring this out by calculating the rolling resistance that acts on the marble as it moves across the surface, but it seems that this is not possible without knowing the coefficient of rolling resistance between the marble and the cardboard surface.
I'm quite sure I could figure out the total distance if I knew the magnitude of the friction acting on the sphere because I also know the speed at which the marble is launched.
I know the coefficient of static friction between the two surfaces as well if that helps in any way.

Any way thanks for your help.

 

[Nate810]

The total distance the marble will travel is dependent on the coefficient of rolling friction between the marble and cardboard surface. You can calculate this coefficient by finding the ratio between the force required to keep the marble rolling at a constant speed and the weight of the marble. The coefficient of static friction between the two surfaces will not help in this case because it does not account for how much friction is generated when the marble is rolling.