Question

A roadway for stunt drivers is designed for racecars moving at a speed of 88 m/s. A curved section of the roadway is a circular arc of 550 m radius. The roadway is banked so that a vehicle can go around the curve with the friction force from the road equal to zero. At what angle is the roadway banked?

a. 57

b. 53

c. 51

d. 55

e. 49

Answer 1

ans is d) 55

The short answer: use the equation v = sqrt(rg*tan(theta)) and solve for theta. The v is velocity, r is the radius of the track, and g is the acceleration due to gravity.


To see why this equation works, draw a right triangle with the car on the hypotenuse. There's the mg force vector pointing straight down from the car, and the normal force vector perpendicular to the hypotenuse, or the road.

-In a banked turn with no friction, there is no acceleration in the vertical direction, so the sum of the vertical components is zero: (normalForce)*cos(theta) = mg.

-In the horizontal direction, the only component comes from the centripetal force: netForce = centripetalForce = (normalForce)*sin(theta) = (mg/cos(theta))*sin(theta) = mg*tan(theta).

-Since netForce = centripetalForce: mg*tan(theta) = (mv^2)/r.

g* tan (theta) = 88^2 / 550

theta = 55.161205971624