Question

Curves on some test tracks and racecourses are very steeply banked. This banking, with the aid of tire friction and very stable car configurations, allows the curves to be taken at very high speed. If the speed of the car is 46.4 m/s at which a 52.3m radius curve banked at angle theta degree(road is frictionless). What is angle theta

Answer 1

Answer:

$\theta =76.61^0$

Explanation:

given,

speed of the car = 46.4 m/s

Radius of the curve = 52.3 m

banked at an angle = θ = ?

now car is moving in the circular path

so,

computing the horizontal component and vertical component

$R Sin \theta = \dfrac{mv^2}{r}$...........(1)

vertical

$R cos \theta = m g$..................(2)

dividing equation (1) from (2)

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

$tan \theta = \dfrac{46.4^2}{52.3 \times 9.8}$

$\theta =tan^{-1}(4.2)$

$\theta =76.61^0$