Expert Witness Testimony: Radius of Curved Freeway

What is the driver claiming happened during the accident on the curved freeway?

The driver claims that the radius of curvature of the unbanked roadway was too small for the speed limit, causing him to slide outward on the curve and hit a tree located a short distance from the outside edge of the roadway.

Expert Witness Testimony for Defense

As an expert witness for the defense in this case, your testimony will focus on determining whether the radius of curvature of the roadway is appropriate for the speed limit. To do this, you will utilize the information provided regarding the angle of the plumb bob when the car is driven at a safer speed of 23.0 m/s on the curve.

First, let's determine the relationship between the angle of the plumb bob and the acceleration experienced by the car. When a car travels along a curved roadway, it undergoes centripetal acceleration toward the center of the curve. This centripetal acceleration can be calculated using the formula:

a = (v^2) / r

Where "a" is the centripetal acceleration, "v" is the velocity of the car, and "r" is the radius of curvature of the curve.

In this case, the velocity of the car is given as 23.0 m/s. The angle of the plumb bob, which hangs at an angle of 15.08° from the vertical, indicates the presence of a gravitational force component perpendicular to the vertical. This component can be equated to the centripetal force acting on the car, as they are both responsible for the observed angle.

Next, we can calculate the acceleration experienced by the car. The gravitational force component perpendicular to the vertical is given by:

F_perpendicular = m * g * sin(θ)

Where "m" is the mass of the plumb bob, "g" is the acceleration due to gravity, and "θ" is the angle of the plumb bob from the vertical.

We know that the gravitational force component is equal to the centripetal force:

F_perpendicular = m * g * sin(θ) = m * a

By substituting the expression for centripetal acceleration "a" from the earlier formula, we get:

m * g * sin(θ) = m * (v^2) / r

Simplifying the equation, we find:

r = (v^2) / (g * sin(θ))

Now, plug in the given values:

  • v = 23.0 m/s
  • g = 9.8 m/s^2
  • θ = 15.08°

Calculate the radius "r":

r = (23.0^2) / (9.8 * sin(15.08°))

r ≈ 201.9 m

The calculated radius of curvature is approximately 201.9 m. Comparing this value to the required minimum radius of 150 m set by state regulations, it is evident that the radius of the curve is indeed appropriate for the speed limit. Therefore, your testimony should state that the radius of curvature of the roadway meets the necessary safety standards for the given speed limit of 65 mi/h.

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