What is the Maximum Acceleration for Contact of Skidding Bicycle Tires?

[fizics]

Homework Statement

A simplified model of a bicycle of mass M has two tires that each comes into contact with the ground at a point. The wheelbase of this bicycle (the distance between the points of contact with the ground) is w, and the center of mass of the bicycle is located midway between the tires and a height h above the ground. The bicycle is moving to the right, but slowing down at a constant rate. The acceleration has a magnitude a. Air resistance may be ignored. Assume that the coefficient of sliding friction between each tire and the ground is different: μ1 for the front tire and μ2 for the rear tire. Let μ1=2*μ2. Assume that both tires are skidding: sliding without rotating. What is the maximum value of a so that both tires remain in contact with the ground?

Additionally, I'm confused how this case is different from the case that μ1=μ2.

Homework Equations

Friction=μmg
F1*L1=F2*L2

The Attempt at a Solution

I can't find any difference between this case and the "μ1=μ2" one,so I cannot go on.

 

[Andrew Mason]

Homework Statement

A simplified model of a bicycle of mass M has two tires that each comes into contact with the ground at a point. The wheelbase of this bicycle (the distance between the points of contact with the ground) is w, and the center of mass of the bicycle is located midway between the tires and a height h above the ground. The bicycle is moving to the right, but slowing down at a constant rate. The acceleration has a magnitude a. Air resistance may be ignored. Assume that the coefficient of sliding friction between each tire and the ground is different: μ1 for the front tire and μ2 for the rear tire. Let μ1=2*μ2. Assume that both tires are skidding: sliding without rotating. What is the maximum value of a so that both tires remain in contact with the ground?

Additionally, I'm confused how this case is different from the case that μ1=μ2.

Homework Equations

Friction=μmg
F1*L1=F2*L2

The Attempt at a Solution

I can't find any difference between this case and the "μ1=μ2" one,so I cannot go on.

I think that is the answer. Is there any downward force on the rear tire when the condition is met (ie. maximum value of a to keep back wheel on ground). Why would μ2 matter at all? BTW what is the solution for the case in which μ1=μ2?

AM

 

[fizics]

Oh,thank you.I was just not confident enough.The answer to "μ1=μ2" case is wg/2h,which I got it right.But the choices in this case are:
(a)wg/h
(b)wg/3h
(c)2wg/3h
(d)hg/2w
(e)none of the above
The answer is (e),so I can't confirm if what I think is right.