Air rushing over the wings of high-performance race cars generates unwanted horizontal air resistance but also causes a vertical downforce, which helps the cars hug the track more securely. The coefficient of static friction between the track and the tires of a 650-kg race car is 0.92. What is the magnitude of the maximum acceleration at which the car can speed up without its tires slipping when a 4334-N downforce and an 1160-N horizontal-air-resistance force act on it?
13.36 m/s^2
To determine the maximum acceleration at which the car can speed up without its tires slipping, we need to consider the forces acting on the car.
In this case, we have two forces acting on the car: the downforce (acting vertically downwards) and the horizontal air resistance force.
First, let's calculate the net force acting on the car in the horizontal direction. Since we want the maximum acceleration without slipping, the net force should be equal to the maximum frictional force.
The net horizontal force can be calculated as follows:
Net horizontal force = Horizontal air resistance force
In this case, the horizontal air resistance force is given as 1160 N.
Next, let's calculate the maximum frictional force. The maximum frictional force is determined by the coefficient of static friction, which is given as 0.92, and the normal force.
The normal force can be calculated as follows:
Normal force = Weight of the car - Downforce
The weight of the car can be calculated using the equation:
Weight of the car = mass of the car * acceleration due to gravity
The mass of the car is given as 650 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Now, substitute the values into the equation:
Weight of the car = 650 kg * 9.8 m/s^2
Once you have the weight of the car, you can calculate the normal force by subtracting the downforce (given as 4334 N) from the weight.
Now that you have the normal force, you can calculate the maximum frictional force using the equation:
Maximum frictional force = coefficient of static friction * normal force
Substitute the values into the equation:
Maximum frictional force = 0.92 * normal force
Now that you have calculated both the net horizontal force and the maximum frictional force, you can set them equal to each other:
Net horizontal force = Maximum frictional force
1160 N = 0.92 * normal force
Solve for the normal force:
Normal force = 1160 N / 0.92
Once you have the normal force, you can calculate the maximum acceleration using the formula:
Maximum acceleration = net horizontal force / mass of the car
Substitute the values into the equation:
Maximum acceleration = 1160 N / 650 kg
Now, calculate the magnitude of the maximum acceleration.