Answer:
<em>The coefficient of static friction = 0.392</em>
Explanation:
When the tire starts to skirt, The net force on the car is equal to the maximum friction.
F = μR................ Equation 1
R = mg.............. Equation 2
F = ma ............ Equation 3
Substituting equation 2 and 3 into Equation 1
ma = μmg.
a = μg
μ = a/g................................... Equation 4
Where F = frictional Force, μ = Coefficient of frictional force, R = normal reaction. a = total acceleration of the car. g = acceleration due to gravity.
<em>Note: The tangential acceleration is perpendicular to the radius. The total acceleration is</em>
a = √(a₁² + a₂²)........................ Equation 4
Where a₁ = tangential acceleration of the tire, a₂ = centripetal acceleration of the car.
a₁ = 2.96 m/s²
a₂ = v²/R..................... Equation 5
Where v = speed of the car = 36.1 m/s, R = radius of the circular part traveled by the car = 532 m
Substituting into equation 5
a₂ = 36.1²/532
a₂ = 1303.21/532
a₂ = 2.45 m/s².
Therefore,
a = √(2.45²+2.96²)
a = √(6.0025 + 8.7612)
a = √14.764
a = 3.84 m/s².
Substituting into equation 4
μ = 3.84/9.8
<em>μ = 0.392.</em>
<em>Thus the coefficient of static friction = 0.392</em>
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