Answer: The car's centripetal acceleration is 8.64 m/s² and the minimum coefficient of friction necessary is 0.88.
Explanation:
The formula for centripetal acceleration is given as:
[tex]\dfrac{v^{2} }{r}[/tex], where:
Plugging in the given values for v and r:
[tex]\frac{22^{2} }{56}[/tex] = 8.64
The car's centripetal acceleration is 8.64 m/s².
To calculate the minimum coefficient of static friction between the tires and the road necessary for the car to round the curve without stopping, we can set the friction force equal to the net force, which is calculated by multiplying the car's mass by its centripetal acceleration.
[tex]F_{fr} =ma[/tex]
The force of friction is given by the formula:
[tex]F_{fr} =[/tex] μmg
We can replace μmg for the force of friction:
μmg = ma
We can then cancel out the m's:
μg = a
Plugging in the values of g (9.81 m/s²) and a (8.64 m/s²):
μ(9.81) = 8.64
μ = [tex]\frac{8.64}{9.81}[/tex]
μ = 0.88
The minimum coefficient of friction necessary is 0.88.
Learn more about centripetal forces here: https://brainly.com/question/43980939
