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 678-kg car is 0.843. What is the magnitude of the maximum acceleration at which the car can speed up without its tires slipping when a 3620-N downforce and an 1270-N horizontal air resistance force act on it?

Answer 1

10.897 m/s²

Step-by-step explanation:

`f_s` = Slipping force

`F_d` = Downforce = 3620 N

`\mu` = Coefficient of static friction = 0.843

m = Mass of car = 678 kg

`f_h` = Horizontal force = 1270 N

g = Acceleration due to gravity = 9.81 m/s²

`a=(f_s-f_h)/(m)\\\Rightarrow a=(\mu(F_D+mg)-f_h)/(m)\\\Rightarrow a=(0.843(3620+678* 9.81)-1270)/(678)\\\Rightarrow a=10.897\ m/s^2`

Hence, magnitude of the maximum acceleration is 10.897 m/s²