Answer to Question #2225 in Mechanics | Relativity for Caycie Rance

Question

A 2000 kg car is traveling on a banked curved icy road without sliding. The velocity of the car is 30 m/s and the road is banked at an angle of 20 degrees. What is the radius of curvature of the road?

I really need to know HOW to do it... not just the answer

Answer 1

The support reaction must be ballansed by the vector sum of the weight and the centrifugal acceleration:

<img src="/cgi-bin/mimetex.cgi?%5Ctan%7B20%5E%7B%5Ccirc%7D%7D%20=%20%5Cfrac%7Bmv%5E2%7D%7BR%5Ccdot%20mg%7D%20=%5Cfrac%7B30%5E2%7D%7BR%5Ccdot%2010%7D%20%5C%5C%20R%20=%20%5Cfrac%7B900%7D%7B10%20%5Ctan%7B20%5E%7B%5Ccirc%7D%7D%7D=%20247.27%20%5C%20m" title="\tan{20^{\circ}} = \frac{mv^2}{R\cdot mg} =\frac{30^2}{R\cdot 10} \\ R = \frac{900}{10 \tan{20^{\circ}}}= 247.27 \ m">