Banked curve in a rear engine car

[swraman]

This is for a vehicle dynamics class; it is more than just a banked curve problem. I am not sure what we have to calculate...the professor never went over this.

Homework Statement

A Porsche 911 is traveling around a circular track of diameter 400m at a constant 30 m/s without using any steering. Due to what should have been an obvious engineering error, the engine in the Porsche is placed behind the rear wheels. Assume 60 % of the vehicles weight is on the rear tires. Assume the vehicles mass is 1000 kg, its wheelbase is 2.2 meters, and the cornering stiffness of the tires is 10,000N/rad. What angle is the track banked at?

Homework Equations

not sure...

The Attempt at a Solution

well I thing that the force on the outer front and back wheel will be more than the force on the inner two wheels. so the back outer tire will have the most force on it.

I really have no idea where to go. Id appreciate any help.

Thanks

 

[Valkarie]

!You need to use the equation F=mv^2/r, where m is the vehicle's mass, v is the speed of the vehicle and r is the radius of the curve. You can then find the centripetal force on the rear tires by multiplying the vehicle's weight by 0.6 (since 60% of the weight is on the rear tires). The angle of banking is then found by equating this centripetal force to the maximum cornering force of the tires (which is 10,000N/rad).

 

[Mene]

it is important to approach problems like this with a systematic and analytical mindset. The first step would be to gather all of the relevant information and equations that can help us solve this problem.

Based on the given information, we can determine that the Porsche is experiencing a centripetal force as it travels around the circular track. This force is provided by the friction between the tires and the track, and it is necessary to keep the car moving in a circular path.

To calculate the angle of the banked track, we can use the equation:

θ = tan^-1 [(v^2)/(rg)]

Where:
θ = angle of the banked track
v = velocity of the car
r = radius of the track
g = acceleration due to gravity

In this case, we are given the velocity (30 m/s) and the radius (400m) of the track. We can also assume a value for the acceleration due to gravity (9.8 m/s^2).

Next, we need to determine the centripetal force acting on the car. This can be calculated using the equation:

Fc = mv^2/r

Where:
Fc = centripetal force
m = mass of the car
v = velocity of the car
r = radius of the track

We are given the mass of the car (1000 kg) and the velocity (30 m/s). However, we need to determine the radius of the track. To do this, we can use the wheelbase and the angle of the banked track to calculate the radius using trigonometry.

Once we have the radius and the centripetal force, we can substitute these values into the first equation to solve for the angle of the banked track.

Additionally, we can also calculate the normal force acting on each tire using the equation:

N = mg cosθ

Where:
N = normal force
m = mass of the car
g = acceleration due to gravity
θ = angle of the banked track

We can use this information to determine the specific forces acting on each tire and how they contribute to the overall stability of the car as it travels around the banked curve.

In conclusion, this problem requires a thorough understanding of circular motion, forces, and trigonometry. By carefully analyzing the given information and using relevant equations, we can determine the angle of the banked track and gain insights into the dynamics of a rear-engine car on a banked curve