The minimum coefficient of static friction between the pavement and the tires is 0.156.
Minimum coefficient of static friction
The minimum coefficient of static friction is calculated by applying Newton's second law of motion in determining the net force.
[tex]F_c = Wsin(\theta) + \mu_s W cos(\theta)\\\\\frac{mv^2}{r} = mg sin(\theta) + \mu_s mg cos(\theta)\\\\\mu_s mg cos(\theta)\ = \frac{mv^2}{r} - mg sin(\theta) \\\\\mu _ s = \frac{mv^2 \ - \ mgr sin(\theta)}{mg rcos(\theta)}[/tex]
where;
- m is the mass = 1200 kg
- v is the speed = 65 km/h = 18.1 m/s
- r is the radius = 100 m
- g is gravity
- θ = 10.4 ∘
[tex]\mu _ s = \frac{1200 \times 18.1^2 \ - \ 1200 \times 9.8 \times 100 sin(10.4)}{1200 \times 9.8 \times 100 \times cos(10.4)}\\\\\mu_s = 0.156[/tex]
Thus, the minimum coefficient of static friction between the pavement and the tires is 0.156.
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