contestada

At what angle should the roadway on a curve with a 50m radius be banked to allow cars to negotiate the curve at 12 m/s even if the road way is icy (and the frictional force is zero)

Respuesta :

onyebuchinnaji

Answer:

The banking angle of the road is 16.38 degrees.

Explanation:

Given:

Radius of the roadway on curve, R = 50 m

velocity of the moving car, V = 12 m/s

The banking angle can be calculated by using the formula below:

If there's no frictional force, then net force is equal to centripetal force.

MgTanΦ = (MV^2)/ R

TanΦ = V^2 / gR

Where;

Φ is the banking angle

g is acceleration due to gravity

TanΦ = (12 x 12) / (9.8 x 50)

TanΦ = 0.2939

Φ = arctan (0.2939)

Φ = 16.38 degrees

Therefore, the banking angle of the road is 16.38 degrees.

fichoh

The angle at which the road should be banked on the curve without reliance on friction should be 16.38°.

Given the Parameters :

  • Radius, r = 50 m
  • Velocity, V = 12 m/s
  • Acceleration due to gravity constant, g = 9.8 m/s²

To avoid reliance on friction, such that, frictional force = 0 ; the angular position of the roadway could be obtained using the centripetal relation :

  • [tex] \theta = tan^{-1} \frac{v^{2}}{rg} [/tex]

Substituting the parameters into the equation :

  • [tex] \theta = tan^{-1} \frac{12^{2}}{50 \times9.8} [/tex]

  • [tex] \theta = tan^{-1} \frac{144}{490} [/tex]

  • [tex] \theta = tan^{-1} (0.2938775) = 16.376[/tex]

Therefore, the roadway on the curve should be banked at angle of 16.38°.

Learn more :https://brainly.com/question/1869806?referrer=searchResults

Otras preguntas