Question

a roadway is designed for traffic moving at a speed of 18 m/s. a curved section of the roadway is a circular arc of 460 m radius. the curved section is temporarily replaced with an unbanked roadway of the same radius. the coefficient of friction of this roadway is 0.40. the maximum safe driving speed for this unbanked, curved section is closest to: 38 m/s 36 m/s 40 m/s 42 m/s 34 m/s

Explanation:

Step1: 向心力公式

汽车在无倾斜弯道上做圆周运动，向心力由摩擦力提供，即 \(F_{向}=f\)。根据向心力公式 \(F_{向}=\frac{mv^{2}}{r}\)，摩擦力公式 \(f = \mu N\)，在水平路面 \(N = mg\)。

Step2: 联立求解速度

联立可得 \(\frac{mv^{2}}{r}=\mu mg\)，化简为 \(v=\sqrt{\mu gr}\)。已知 \(\mu = 0.40\)，\(g = 9.8m/s^{2}\)，\(r = 460m\)，代入可得 \(v=\sqrt{0.40\times9.8\times460}\)。

Step3: 计算速度

\(v=\sqrt{0.40\times9.8\times460}=\sqrt{1803.2}\approx 42m/s\)

Answer:

42 m/s