Chapter 5: Q20. (page 133)

Highway curves are marked with a suggested speed. If this speed is based on what would be safe in wet weather, estimate the radius of curvature for an unbanked curve marked 50 km/h. Use Table 4-2 (coefficients of friction).

Short Answer

Expert verified

The radius of curvature for an unbanked curve marked with 50 km/h is estimated to be 28.1 m.

Step by step solution

Step 1. Understanding the concept of centripetal force

The centripetal force acts on the objects that travel with a constant speed in a circular path in order to keep them moving in circular motion.This force acts on an object towards the center of the circle around which it is moving.

The centripetal force $(F_{R})$ on an object of mass m moving with speed v in a circle of radius r is given as:

$F_{R} = \frac{m v^{2}}{r}$

Step 2. Identification of the given information

The maximum speed of the vehicle allowed at the unbanked curve is,

$v = 50 km / h = (\frac{50 km}{1 h}) \times (\frac{1000 m}{1 km}) \times (\frac{1 h}{60 \min}) \times (\frac{1 \min}{60 s}) = 13.89 m / s$ .

From the table, the coefficient of friction of the rubber on the wet concrete is, $μ = 0.7$ .

Step 3. Estimation of the radius of curvature for an unbanked curve

Here, centripetal force $(F_{R})$ to a vehicle is provided by the frictional force $(μ N)$ .

Therefore, the centripetal force can be given as,

$\begin{matrix} F_{R} = μ N \\ \frac{m v^{2}}{r} = μ m g \\ r = \frac{v^{2}}{μ g} \end{matrix}$

On putting the given values, you will get:

$\begin{matrix} r = \frac{{(13.89 m / s)}^{2}}{(0.7) (9.8 m / s^{2})} \\ = 28.1 m \end{matrix}$

Thus, the estimated radius of curvature of the unbanked road is 28.1 m.

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Highway curves are marked with a suggested speed. If this speed is based on what would be safe in wet weather, estimate the radius of curvature for an unbanked curve marked 50 km/h. Use Table 4-2 (coefficients of friction).

Short Answer

Step by step solution

Step 1. Understanding the concept of centripetal force

Step 2. Identification of the given information

Step 3. Estimation of the radius of curvature for an unbanked curve

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