Please, please, help with this question about centripetal motion! Thank you in advance.

Question

An engineer is trying to determine the maximum speed at which a 800kg car can travel around a curve (picture a car travelling in a circular motion around a center point). The coefficient of friction between the wheels and the road is 0.7. Answer questions for the case when the car is traveling at the maximum speed.

number of forces in plane: 3

centripetal force: friction

Are all forces balanced? no

What is the magnitude of the turning friction? ___ N

What is the centripetal net force on the car? ___ N

What is the car's centripetal acceleration? ___ m/s²

At what maximum speed can the car navigate the curve? ___ m/s

Answer 1

Let

m = 800 kg be the mass of the car,

f = 0.7 be the coefficient of friction,

g = 9.81 m/s² be gravitational acceleration,

r (unknown) be the radius of the curve,

v (to be computed) be the car's maximum speed.

The car's weight is mg, and the force of friction is

F = mgf

That is the maximal centripetal force that the track can provide.

By Newton's Second Law with centripetal force F the car experiences centripetal acceleration

a = F/m = gf

This centripetal acceleration satisfies

a = v²/r

Therefore

v = √(gfr).

To calculate the velocity v you need to know the radius.

In contrast, you can get numerical values for the other quantities without knowing the radius.