David is driving his prius on the freeway and reaches his exit. The exit has a...

David is driving his prius on the freeway and reaches his exit. The exit has a radius of curvature of 25 m and is banked at 38 degrees. How fast can David travel around the curve on a dry day (where the coefficient of friction between his tires and the road is 1)? How fast can he travel around the curve on a rainy day (when the coefficient of friction between his tires and a wet road is 0.75)? Give your in miles per hour. Show all work and explain each step.

Expert Solution

When considering the effects of friction on the system, which way the friction force is pointing. When calculating a maximum velocity for our automobile, friction will point down the incline and towards the center of the circle. Therefore we must add the horizontal component of friction to that of the normal force. The sum of these two forces is our new net force in the direction of the center of the turn (the centripetal force):

Once again, there is no motion in the vertical direction, allowing us to set all opposing vertical forces equal to one another. These forces include the vertical component of the normal force pointing upwards and both the car's weight and vertical component of friction pointing downwards:

By solving the above equation for mass and substituting this value into our previous equation we get:

Solving for v we get:

This equation provides the maximum velocity for the automobile with the given angle of incline, coefficient of static friction and radius of curvature. By a similar analysis of minimum velocity, the following equation is rendered:

U can get more detailed reference from

http://en.wikipedia.org/wiki/Banked_Turns

genius_generous answered 1 year ago

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