Rolling resistance force for a 75gram vehicle

[Isti0503]

Homework Statement

Estimate the rolling resistance force for a 75gram vehicle with axle friction coefficient of 0.2 if the wheel is 40mm diameter and the axle 2mm diameter.

I am having trouble with applying the axle friction coefficient. I could not find a similar problem online.
Basically we know that the smaller the radius of the circle the more tangential force is needed to produce the same torque (axle and the wheel). However, after I am not sure what to do with the axle friction coefficient.

 

[haruspex]

What is the normal force at the axle?
What is the frictional force at the axle?
What is the frictional torque that creates?
What force at the rim will overcome that torque?

 

[Isti0503]

Ok so the normal force would be just mg, the frictional torque that creates would be the tangential force at the axle times the radius of the axle, the force that will overcome that torque is basically the radius of the wheel times the tangential force to the rim right?
What do you mean by the frictional force at the axle? Would that just be the coefficient of axle friction given (0.2)?

 

[jbriggs444]

What do you mean by the frictional force at the axle? Would that just be the coefficient of axle friction given (0.2)?

The coefficient of friction is a pure number. A ratio. It does not have the right units to be a force.

You've said that the normal force at the axle is mg. If the coefficient of friction at the axle is 0.2, what is the force of friction at the axle?

 

[Isti0503]

Well the force of friction will be the coefficient times mg. Right?

 

[jbriggs444]

Well the force of friction will be the coefficient times mg. Right?

Right.

 

[Isti0503]

Alright but then out off those two forces (at the rim, and the frictional force), which force am I looking for?

 

[jbriggs444]

Alright but then out off those two forces (at the rim, and the frictional force), which force am I looking for?

You tell us. It is your homework problem.

You claimed to be looking to determine frictional torque. You have all the information needed to calculate it.

 

[Isti0503]

So if I use those formulas I will get:
F=Uk*mg*(r1/r2).

So r1 is the radius of the axle and r2 radius of the wheel.

 

[jbriggs444]

So if I use those formulas I will get:
F=Uk*mg*(r1/r2).

So r1 is the radius of the axle and r2 radius of the wheel.

Yes.

 

[Isti0503]

Alright thank you.