Serway & Jewett — Circular Motion and Other Applications of Newton's Laws: Problem 8

A driver is suing the state highway department after an accident on a curved freeway. The driver lost control and crashed into a tree located a short distance from the outside edge of the curved roadway. The driver is claiming 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 the tree. You have been hired as an expert witness for the defense, and have been requested to use your knowledge of physics to testify that the radius of curvature of the roadway is appropriate for the speed limit. State regulations show that the radius of curvature of an unbanked roadway on which the speed limit is 65 mi/h must be at least 150 m. You build an accelerometer, which is a plumb bob with a protractor that you attach to the roof of your car. An associate riding in your car with you observes that the plumb bob hangs at an angle of 15.0° from the vertical when the car is driven at a safer speed of 23.0 m/s on the curve in question. What is your testimony regarding the radius of the curve?