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A circular racetrack of radius 300m is banked at an angle of 15^(@). If the coefficient of friction between the wheels of a race - car and the road is 0.2, what is the (a) optimum speed of the race - car to avoid wear and tear on its tures, and (b) maximum. Permissible speed to avoid slipping ? |
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Answer» Solution :On a banked road, the horizontal component of the NORMAL force and the frictional force contribute to provide centripetal force to KEEP the car moving on a circular turn without SLIPPING. At the OPTIMUM speed, the normal reaction.s component is enough to provide the needed centripetal force, and the frictional force is not needed. The optimum speed `upsilon_(0)` is given by `upsilon_(0)=(Rg tan theta)^(1//2)` Here `R=300 m, theta = 15^(@), g=9.8 ms^(-2)` `upsilon_(0)=(Rg tan theta)^(1//2)=(300xx9.8xx tan15^(@))^(1//2)`. On simplification, `upsilon_(0)28.1 ms^(-1)`. The maximum permissible speed `upsilon_(max)` is given by `v_(max)=sqrt((Rg(tan theta+mu))/((1-mu tan theta)))` `= sqrt((300xx9.8xx(tan 15^(@)+0.2))/((1-0.2 tan 15^(@)))` On simplification `upsilon_(max)=38.1 ms^(-1)`. |
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