A car that is in a frictionless corner with a radius of 5.5 × 102 m. The corner is banked at an angle of 5.7º. find the speed of the car as it rounds the corner .

Answer:

Car is moving in circular road of radius r = 5.5 * 10² m

The road is banked at an angle = 5.7º

Let speed of car when it rounds the corner per road = v

m = mass of the car

Figure is in attached file,

In figure we can see,

mg = Ncosθ

N = mg/cosθ .........equation 1.

Nsinθ will provide the centripetal force to car to move on road corner

Nsinθ = F_c

Nsinθ = mv² / r

Putting the value of N from equation 1

(mg/cosθ ) * sinθ = mv² / r

v² = g*r*tanθ

v = sqrt[9.8*5.5*10² * tan(5.7)

v = 23.194 m/sec

PFA