What is the minimum radius of curvature of the curve?

• gap0063
In summary, a civil engineer is tasked with designing a curved section of roadway that must meet specific conditions, including a minimum radius of curvature. With a coefficient of static friction of 0.1 between the road and rubber, the car must not slide into the ditch when at rest and must not skid on the outside of the curve at speeds less than 80 km/h. The road is also banked at an angle of 5.71059 degrees. The equation v^2 = ugr can be used to calculate the minimum radius of curvature, taking into account the effect of friction.
gap0063

Homework Statement

A civil engineer is asked to design a curved
section of roadway that meets the following
conditions:
With ice on the road, when the coefficient of
static friction between the road and rubber is
0.1, a car at rest must not slide into the ditch
and a car traveling less than 80 km/h must
not skid to the outside of the curve. The road is banked at an angle of 5.71059 degrees
What is the minimum radius of curvature of
the curve?

Homework Equations

I thought the equation to use was v^2= gr tan (theta)

The Attempt at a Solution

the equation is used above gave me a wrong answer

If you use that equation, you won't be taking into account the effect of friction. Since the coefficient of friction is provided to you, you can use it in the equation u=v^2rg, where u is the coefficient. That might work for the case when the car is moving at 80km/hr(take care of the units...if r is in m, then convert v into m/s. I know its silly but it happens a lot).

Last edited:

What is the minimum radius of curvature of the curve?

The minimum radius of curvature of a curve is the smallest radius of a circle that can fit perfectly at any point on the curve without any gaps or overlaps.

Why is the minimum radius of curvature important?

The minimum radius of curvature is important because it determines the smoothness and sharpness of a curve. A smaller radius of curvature means a sharper curve, while a larger radius of curvature means a smoother curve.

How is the minimum radius of curvature calculated?

The minimum radius of curvature is calculated by taking the derivative of the curve equation and finding the radius of the circle that fits the curve at that point.

What factors can affect the minimum radius of curvature?

The minimum radius of curvature can be affected by the shape and complexity of the curve, as well as any external forces or constraints acting on the curve.

Can the minimum radius of curvature be negative?

No, the minimum radius of curvature cannot be negative. A negative radius of curvature would imply that the curve is curving in the opposite direction, which is not possible.

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