Motion and force along a curved path-angle of curves?

[a18c18]

Homework Statement

An automobile club plans to race a 740 kg car at the local racetrack. The car needs to be able to travel around several 175 m radius curves at 85 km/h. What should the banking angle of the curves be so that the force of the pavement on the tires of the car is in the normal direction? (Hint: What does this requirement tell you about the frictional force?)

Homework Equations

a=v^2/r
Tcos(theta)=mv^2/r
F=ma

The Attempt at a Solution

Friction must equal 0?

 

[Mattowander]

Correct. So draw a free body diagram for the situation.

Here is a hint : Resolve the normal force into x and y components. One of these components should equal the weight of the car, the other should provide the required centripetal force towards the center of the track.

 

[baba89]

As a scientist, it is important to understand the concept of motion and force along a curved path. In this scenario, the car is traveling along a curved path at a constant speed of 85 km/h. This means that the car is experiencing a centripetal acceleration, which can be calculated using the equation a=v^2/r, where v is the speed and r is the radius of the curve.

However, the question also mentions the need for the force of the pavement on the tires to be in the normal direction. This means that the frictional force between the tires and the pavement must be equal to 0, as any non-zero friction would result in a force that is not purely in the normal direction.

To achieve this, the banking angle of the curves must be adjusted accordingly. This can be calculated using the equation Tcos(theta)=mv^2/r, where T is the weight of the car, m is its mass, and theta is the banking angle. By setting the frictional force equal to 0, we can solve for theta and determine the required banking angle for the curves.

In conclusion, understanding the principles of motion and force along a curved path is crucial in determining the appropriate banking angle for a car to travel at a given speed on a curved track. By taking into account the centripetal acceleration and the need for the force to be in the normal direction, we can calculate the necessary banking angle to ensure a safe and successful race.