Question

A curve of radius 55.1 m is banked so that a car of mass 1.6 Mg traveling with uniform speed 61 km/hr can round the curve without relying on friction to keep it from slipping on the surface. 1.6 Mg µ ≈ 0 θ At what angle is the curve banked? The acceleration due to gravity is 9.8 m/s 2 . Answer in units of deg.

Answer 1

Answer:

θ = 28°

Explanation:

For this exercise We will use the second law and Newton, let's set a System of horizontal and vertical.

X axis

      Fₓ = m a

      Nₓ = m a

Where the acceleration is centripetal

      a = v² / r

The only force that we must decompose is normal, let's use trigonometry

      sin θ = Nₓ / N

      cos θ = $N_{y}$ / N

      Nₓ = N sin θ

      $N_{y}$ = N cos θ

Let's replace

     N sin θ = m v² / r

Y Axis

     $N_{y}$ - W = 0

     N cos θ = mg

Let's divide the two equations of Newton's second law

     Sin θ / cos θ = v² / g r

     tan θ = v² / g r

     θ = tan⁻¹ (v² / g r)

We reduce the speed to the SI system

      v = 61 km / h (1000 m / 1 km) (1h / 3600 s) = 16.94 m / s

Let's calculate

     θ = tan⁻¹ (16.94 2 / (9.8 55.1)

     θ = tan⁻¹ (0.5317)

     θ = 28°