Question

a. Find the angle of banking for a highway curve of 90 m radius designed to accomodate cars travelling at 160 kph if the coefficient of friction between the tires and the road is 0.5 .
b. What is the rated speed of the curve?

Answer 1

Answer on question #79846, Physics / Mechanics

a. Find the angle of banking for a highway curve of $90\mathrm{m}$ radius designed to accommodate cars travelling at 160 kph if the coefficient of friction between the tires and the road is 0.5.

b. b. What is the rated speed of the curve?

Solution

A projection on the axis X: $N \cdot \sin \alpha + \mu N \cdot \cos \alpha = \frac{mv^2}{R}$

A projection on the axis Y: $N \cdot \cos \alpha + \mu N \cdot \sin \alpha - mg = 0$

From here: $tg\alpha = \frac{v^2 - \mu gR}{v^2\mu + gR} = 0.81$

$\alpha = 39{}^{\circ}$

Max. speed of the curve is 160 kph

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