This problem has four parts to this. I will type the questions for each of these four parts along with additional info about this problem in the "Description" below.

Question

A car is driving along a level and unbanked circular track of diameter d = 0.94 km at a constant speed of v = 21.7 m/s.

Part a) Write an expression for the magnitude of the acceleration of the car in terms of the given parameters.

Part b) What is the magnitude, in meters per squared second, of the acceleration of the car?

Part c) Write an expression for the minimum coefficient of friction between the car's tires and the road that is required in order to keep the car going in a circle in terms of the given parameters.

Part d) What is the value of the minimum coefficient of friction between the car's tires and the road that is required in order to keep the car going in a circle?

Answer 1

a) a_c = V² / r where r = d/2

b) a_c = 21.7² m^{2 / s}2/ 470 m = 1001.9 m / s²

c) μMg = MV² / r, μ = V² / rg where M is mass of the car (cancels out), g the gravitational constanct, r the radius of curvature already determined, μ the coefficient of friction.

d.) μ = 21.7² m²/s² / 470 m x 9.8 m/s² = 0.10 minimum coefficient of friction.