Question

5.
A circular road of radius 1000 m has banking angle 45°. Find the maximum safe speed of a car having
mass 2000 kg, if the coefficient of friction between tyre and road is 0.5.
(Raj. PET 1997)​

Answer 1

Answer:

100/√3

Explanation:

Please refer to attachment .

Answer 2

Answer:

171.46 m/s.

Explanation:

Given:

• Radius of the circular road, $\rm R=1000\ m$.

• Banking angle of the road, $\theta = 45^\circ$.

• Mass of the car, $\rm M=2000\ kg$.

• Coefficient of friction between tyre and road, $\mu = 0.5$.

The maximum safe speed of the car at the banked road is given by

$\rm v=\sqrt{gr\left( \dfrac{\mu+\tan\theta}{1-\mu\tan\theta} \right)$.

where,

$\rm g$ is the acceleration due to gravity, having value, $\rm g = 9.8\ m/s^2$.

Putting all the values in the above expression, we get,

$\rm v=\sqrt{9.8\times 1000\left( \dfrac{0.5+\tan(45^\circ)}{1-0.5\times \tan(45^\circ)} \right)}=171.46\ m/s.$