Question

Air rushing over the wings of high-performance race cars generates unwanted horizontal air resistance but also causes a vertical downforce, which helps cars hug the track more securely. The coefficient of static friction between the track and the tires of a 552-kg car is 0.967. What is the magnitude of the maximum acceleration at which the car can speed up without its tires slipping when a 3150-N downforce and an 1300-N horizontal air resistance force act on it?

Answer 1

We need the horizontal acceleration so,
ax=Fx/m

Since Fx, or the horizontal forces acting on the car is composed of the air resistance and the force of static friction,
ax=(fs-1300N)/m

Looking for fs(static friction):
fs=us*N

N=mg+3150N
=(552kg)(9.8)+3150N
=8559.6N

fs=(0.967)(8559.6N)
=8277.13N

Solving for ax:
ax=(8277.13-1300N)/553
ax=12.54m/s2