Car on a ramp with uneven weight distribution

[itzhard]

Homework Statement

A car is on a ramp of angle theta with the horizontal with the front of the car pointing up the ramp. Its weight distribution is uneven so that more of its weight is towards the rear of the car therefore the center of mass is closer to the rear of the car. The car is very special in that the front wheel does not experience friction while the rear wheel is experiencing kinetic friction. The center of mass is also a height H above the ground. The car is in equilibrium. I was wondering if you have the car pointing downhill instead, will that change the angle theta to keep the car in equilibrium?

Relative equations
Moment = ΣFiXi

The Attempt at a Solution

I have tried calculating the moment at the center of mass by including the normal forces from each of the wheels, and the frictional force from the rear wheel. I believe the moments in both situations are the same and therefore the angle should be the same to keep the car in equilibrium.

 

[haruspex]

I have tried calculating the moment

Then I assume the equilibrium issue is in respect of tipping over.
You need more information on the geometry of the vehicle, specifically, how far the mass centre is from the axles.
To avoid worrying about friction, take moments about the rear wheels' point of contact with the ground.

 

[NascentOxygen]

the rear wheel is experiencing kinetic friction.

So it's moving?

The car is in equilibrium.

That surely means the car is being held stationary by its brakes. So it's not moving?

 

[CWatters]

It says kinetic friction so the wheels are spinning/slipping?

Presumably the friction force acting up the slope is what counters the component of gravity acting down the slope keeping things in equilibrium.

If the car faces down rather than up the slope the weight on the driving wheels will change.