A car weighs 2000 lbs and is making a turn around a banked curve of angle 25 deg

Question

A car weighs 2000 lbs and is making a turn around a banked curve of angle 25 degrees where the coefficient of static friction equals 0.4 and the radius of curvature is 100 feet. What is the maximum and minimum safe driving speeds that the car can go at? [First derive the equation for either the minimum or maximum speeds and then you can switch the signs for the other one. You have to derive one of them; you can't just use a formula] If you are driving 10 ft/sec below the maximum speed, what is the magnitude and direction of fs and the magnitude of N? How fast should you drive so that there is no friction?

Explanation / Answer

Assuming it goes at max speed, then it has tendecy to go upward, so f is down the incline: along incline: mgsin25-(mv^2/r)cos25+f=0 f=uN perpndicular to incline: N=mgcos25+(mv^2/r)sin25 solving for v: by dividing entire equation by cos25,,,,,, v=sqrt[g*r*(tan25+u)/1-utan25) put -u to get minimum speed

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