Question #2225

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

Expert's answer

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">

<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">

## Comments

Assignment Expert04.04.11, 18:18You are welcome

Caycie Rance01.04.11, 16:52Great help! Thanks!

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