To test the performance of its tires, a car

travels along a perfectly flat (no banking) cir-

cular track of radius 564 m. The car increases

its speed at uniform rate of

u du = 3.62 m/s?

dt

until the tires start to skid.

If the tires start to skid when the car reaches

a speed of 35 m/s, what is the coefficient of

static friction between the tires and the road?

0.43

Explanation:

Sum of forces in the y direction:

∑F = ma

N - mg = 0

N = mg

There are friction forces in two directions: centripetal and tangential. The centripetal acceleration is:

ac = v² / r

ac = (35 m/s) ² / 564 m

ac = 2.17 m/s²

The total acceleration is:

a = √ (ac² + at²)

a = √ ((2.17 m/s²) ² + (3.62 m/s²) ²)

a = 4.22 m/s²

Sum of forces:

∑F = ma

Nμ = ma

mgμ = ma

μ = a / g

μ = 4.22 m/s² / 9.8 m/s²

μ = 0.43