a curve of radius 30 m is to be banked so that a car may make the turn at a speed of 13 m/s without depending on friction. what must be the slope of the curve (the banking angle)? (write the angle in degrees)

Question

28-10-2022
Physics

Answered

a curve of radius 30 m is to be banked so that a car may make the turn at a speed of 13 m/s without depending on friction. what must be the slope of the curve (the banking angle)? (write the angle in degrees)

Answer :

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Lanuel Lanuel · Answer 1 · 2022-10-31T07:36:31-04:00

The slope of the curve (the banking angle) is equal to 30 degrees.

How to determine the slope of the curve (the banking angle)?

In this scenario, we can reasonably infer and logically deduce that there are only two (2) forces that are acting on this car and these include the following:

The weight of the car (mg).
The normal force that is exerted by the pavement on this car (Fn).

From the information provided above, we have the following equations:

Fncosθ = mg .......equation 1.

Fnsinθ = mv²/r .......equation 2.

Dividing equation 2 by equation 1, we have:

Tanθ = v²/gr

Substituting the given parameters into the equation, the slope of the curve (the banking angle) is given by;

Tanθ = 13²/(9.81 × 30)

Tanθ = 169/(9.81 × 30)

Banking angle, θ = tan⁻¹(0.575)

Banking angle, θ = 30 degrees.

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