Question

A racecar of mass 500 kg is going around a curve of radius 15.0 m, banked at 45∘ . The car has a coefficient of static friction with the track which is 0.200. The car also has a rear wing which produces downforce—“negative lift” due to airflow over the wing, which pushes the car into the track. The downforce is given by ? = ?v² , where ? = 10 kg/m. Find the minimum and maximum speeds between which the car can take the curve without skidding.

Answer 1

Case 1 ; For maximum speed

For maximum speed , the frictional force will act downwards because the car wants to go up the road .

Following diagram represents all the forces acting on the car

here , we have purposely resolved the components of the forces, along the line AB for easier calculation of normal force , N

Now, let us again resolve the components of all the forces acting on the car ( but this time in horizontal and vertical direction )

Our focus will only be on the horizontal component of the forces;

Case 2 ; For minimum velocity

In this case just reverse the direction of frictional force and solve in a similar fasion as case 1