The Daytona 500 stock car race is held on a circular track that is approximately 2.25 miles long, and the turns are banked at an angle of 32.5°. It is currently possible for cars to travel through the turns at a speed of about 189 miles per hour. Assuming that these cars are on the verge of slipping into the wall of the race track (since they are racing!), find the coefficient of static friction between the tires and the track.

Question

The Daytona 500 stock car race is held on a circular track that is approximately 2.25 miles long, and the turns are banked at an angle of 32.5°. It is currently possible for cars to travel through the turns at a speed of about 189 miles per hour. Assuming that these cars are on the verge of slipping into the wall of the race track (since they are racing!), find the coefficient of static friction between the tires and the track.

I was thinking that if I used square root (gr x (uscos + sin/cos-ussin))= v
...but I am not sure how to solve for mu_s

Any help would be great!

Answer 1

The tyres they use are friction ready, so they usually bank the turn at 14.8 degrees

Answer 2

A singly charged ion of unknown mass moves in a circle of radius 13.5 cm in a magnetic field of 5.4 T. The ion was accelerated through a potential difference of 1.0 kV before it entered the magnetic field. What is the mass of the ion?

Answer 3

To find the coefficient of static friction (μs), we can start by analyzing the forces acting on the car as it navigates the turn.

At the maximum speed before slipping, the centripetal force acting on the car is equal to the maximum static friction force that the tires can provide. The centripetal force is given by the equation:

Fc = mv^2 / r

Where:
- Fc is the centripetal force
- m is the mass of the car
- v is the velocity of the car
- r is the radius of the turn

Now, the maximum static friction force can be calculated using:

Fs = μs * m * g

Where:
- Fs is the maximum static friction force
- μs is the coefficient of static friction
- m is the mass of the car
- g is the acceleration due to gravity

We can equate the centripetal force and the maximum static friction force:

mv^2 / r = μs * m * g

The mass of the car cancels out, leaving:

v^2 / r = μs * g

Now, let's solve for μs:

μs = v^2 / (r * g)

Given the following information:
- v = 189 mph (convert to ft/s: v = 189 * 5280 / 3600 ft/s)
- r = 2.25 miles (convert to ft: r = 2.25 * 5280 ft)
- g = 32.2 ft/s^2 (approximate value for acceleration due to gravity)

Substituting these values into the equation, we get:

μs = (189 * 5280 / 3600)^2 / (2.25 * 5280 * 32.2)

Simplifying the equation gives us the value of μs:

μs ≈ 1.135

So, the coefficient of static friction between the tires and the track is approximately 1.135.