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A roadway for stunt drivers is designed for racecars moving at a speed of 40 m/s. A curved section of the roadway is a circular arc of 230 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?

Respuesta :

Answer:

Bank angle = 35.34o

Explanation:

Since the road is frictionless,

Tan (bank angle) = V^2/r*g

Where V = speed of the racing car in m/s, r = radius of the arc in metres and g = acceleration due to gravity in m/s^2

Tan ( bank angle) = 40^2/(230*9.81)

Tan (bank angle) = 0.7091

Bank angle = tan inverse (0.7091)

Bank angle = 35.34o

asuwafohjames

The angle at which the roadway is banked is 35.37°.

To calculate the banked angle. we use the formula below.

Formula:

  • tan∅ = mv²/mgr
  • tan∅  = v²/gr.............. Equation 1

Where:

  • ∅ = Banked angle
  • v = velocity of the car race
  • r = radius of the circular arc
  • g = acceleration due to gravity.

From the question,

Given:

  • v = 40 m/s
  • r = 230 m
  • g = 9.8 m/s²

Substitute these values into equation 2

  • tan∅ = 40²/(230×9.8)
  • tan∅ = 1600/2254
  • tan∅ = 0.7098
  • ∅ = tan⁻¹(0.7098)
  • ∅ = 35.37°

Hence, The angle at which the roadway is banked is 35.37°.

Learn more about banked angle here: https://brainly.com/question/18955243