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16 November, 03:51

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?

+3
Answers (1)
  1. 16 November, 07:44
    0
    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
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