Question

To practice Problem-Solving Strategy 6.1: Circular motion A highway curve with radius R = 274 m is to be banked so that a car traveling v = 25.0 m/s will not skid sideways even in the absence of friction. At what angle should the curve be banked?

Answer 1

Answer:

The curve should be banked at an angle of 13 degrees.

Explanation:

We have,

Radius of a highway curve is 274 m

Speed of car on this curve is 25 m/s

Let $\theta$ is the banking angle. On a banked curve, the angle of safe diving is given by following expression.

$\tan\theta=\dfrac{v^2}{Rg}$

g = 10 m/s²

Plugging all the values in above formula,

$\tan\theta=\dfrac{(25)^2}{274\times 9.8}\\\\\theta=\tan^{-1}\left(\dfrac{(25)^{2}}{274\times9.8}\right)\\\\\theta=13^{\circ}$

So, the curve should be banked at an angle of 13 degrees.