What is the maximum speed that a car can safely move on a horizontal road
| April 10, 2021 | education
What is the maximum speed that a car can safely move on a horizontal road at a bend with a radius of 81 m, if the coefficient of friction of the wheels on the road is 0.4?
R = 81 m.
g = 10 m / s2.
μ = 0.4.
Vmax -?
Let’s write 2 Newton’s law in vector form: m * a = Ftr + N + m * g.
ОХ: m * a = Ftr.
OU: 0 = N – m * g.
N = m * g.
The sliding friction force Ftr is determined by the formula: Ftr = μ * N = μ * m * g.
The centripetal acceleration a is expressed by the formula: a = Vmax ^ 2 / R.
m * Vmax ^ 2 / R = μ * m * g.
Vmax = √ (μ * g * R).
Vmax = √ (0.4 * 10 m / s2 * 81 = 18 m / s.
Answer: the maximum safe speed of the car when cornering is Vmax = 18 m / s.
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