Maximum attainable coefficient of static friction

[canza]

Homework Statement

Hi, I'm having trouble with this question. I don't seem to get this at all. I hope you guys can help me on this.

Before 1960, it was believed that the maximum attainable coefficient of static friction for an automobile tire was less than 1. Then, about 1962, three companies independently developed racing tires with coefficients of 1.6. Since then, tires have improved, as illustrated in this problem. According to the 1990 Guinness Book of Records, the shortest time in which a piston-engine car initially at rest has covered a distance of one-quarter mile is 4.96 s. This record was set by Shirley Muldowney in September 1989.

Assume that, as in the figure, the rear wheels lifted the front wheels off the pavement. What minimum value of µs is necessary to achieve a time of 6.04 s?

 

[Carid]

Why do they speak of the front wheels lifting off the ground?

We have a distance, a time, an initial velocity; can you work out the average acceleration?

What's the average forward force?

What's the normal reaction to the car's weight?

What's the kinetic frictional force?

If we don't want the wheels to spin what condition must hold?

I hope this helps you get some traction

 

[PhanthomJay]

Why do they speak of the front wheels lifting off the ground?

Rear wheel drive, where all of the car's weight is supported by the normal force from the rear tires. The rotation of the vehicle is due to the eccentricity of the driving friction force (at the rear wheels) relative to the c.g of the car, creating a torque which causes the car to rotate off its front wheels and pivot about its rear wheels.

 

[Mr.Amin]

The knowledge that the front tires are lifted indicates torque which is directly related to the static friction acting on the tires. If the figure tells you the angle of lift, what missing information can you compute to determine average acceleration?

 

[Carid]

PhantomJay and Mr. Amin

My question about the wheels was rhetorical. I think it's in the question just so all the weight of the car is on the rear wheels. Nothing fancy!

 

[Mr.Amin]

Fair enough.
Let's assume that the front tires "barely" leave the ground. This implies the rear tires DO NOT slip. Now since you know that the vehicle starts from rest, (1) what does the position equation look like? (2) From a term in this equation what term says anything about...force?

 

[PhanthomJay]

PhantomJay and Mr. Amin

My question about the wheels was rhetorical. I think it's in the question just so all the weight of the car is on the rear wheels. Nothing fancy!

I agree!