Answer to Question #101776 in Mechanics | Relativity for Ely

Question

(a driver is suing the state highway department after a 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 expertwitness for the defense, and have been requested to use your knowledge in physics to testify that the radisu of curvature of the roadway is appropriate for the speed limit . State regulations show that the radius of curvature of an unbaked roadway on which the speed limit 65mi/h must be at least 150m You build accelerometer which is a plumb bob with a protractor that you attach to the roof of your car. An associate rididing in your car witth you observes that the plumb bob hangs at an angle 15 degree from the vertical when the car is driven at safer speed of 23m/s the radius of the curve?

Answer 1

Speed of the car =65 mi/hour

Radius of the curve = 150 m

angle of inclination $=15^o$

v=23m/sec

Now applying the force balance concept,

$mg \sin\theta= \dfrac{mv^2\cos15^\circ}{R}$

$R=\sqrt{\dfrac{v^2\cos15^\circ}{g\sin15^\circ}}=13.8m$

As per the first condition,

$R=\sqrt{\dfrac{65\times 0.44\times 3.7}{9.8}}=17.37m$

So, here the radius was sufficient to prevent to slipping.