Question

A 866 kg car is traveling at 16.7 m/s around a banked curve with a radius
of 50 m. At what angle would the car have to be banked so that no
friction is required?

Answer 1

Answer: $29.64 \°$

Explanation:

The expression to calculate the angle $\theta$ of an ideally banked curve in which friciton is not needed is:

$\theta=tan^{-1}(\frac{V^{2}}{r.g})$

Where:

$V=16.7 m/s$ is the car's velocity

$r.=50 m$ is the radius of the curve

$g=9.8 m/s^{2}$ is the acceleration due gravity

As you may see, this angle does not depend on the mass of the car.

Solving with the given values:

$\theta=tan^{-1}(\frac{(16.7 m/s)^{2}}{(50 m)(9.8 m/s^{2})})$

Finally:

$\theta=29.64 \°$