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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?

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Answer:

10.897 m/s²

Explanation:

[tex]f_s[/tex] = Slipping force

[tex]F_d[/tex] = Downforce = 3620 N

[tex]\mu[/tex] = Coefficient of static friction = 0.843

m = Mass of car = 678 kg

[tex]f_h[/tex] = Horizontal force = 1270 N

g = Acceleration due to gravity = 9.81 m/s²

[tex]a=\frac{f_s-f_h}{m}\\\Rightarrow a=\frac{\mu(F_D+mg)-f_h}{m}\\\Rightarrow a=\frac{0.843(3620+678\times 9.81)-1270}{678}\\\Rightarrow a=10.897\ m/s^2[/tex]

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

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