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A circular racetrack of radius 300 m 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 tyres, and (b) maximum permissible speed to avoid slipping ?

Answer» <html><body><p></p>Solution :On a <a href="https://interviewquestions.tuteehub.com/tag/banked-2460103" style="font-weight:bold;" target="_blank" title="Click to know more about BANKED">BANKED</a> 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 `v_0` is given by Eq.<br/>`v_0 = (Rg tan <a href="https://interviewquestions.tuteehub.com/tag/theta-1412757" style="font-weight:bold;" target="_blank" title="Click to know more about THETA">THETA</a>)^(1//2)` <br/>Here `R = 300 m , theta = 15^@ , g =9.8 <a href="https://interviewquestions.tuteehub.com/tag/ms-549331" style="font-weight:bold;" target="_blank" title="Click to know more about MS">MS</a>^(-2) ` , we have <br/> `v_0 = 28.1 ms^(-1)` <br/>The <a href="https://interviewquestions.tuteehub.com/tag/maximum-556915" style="font-weight:bold;" target="_blank" title="Click to know more about MAXIMUM">MAXIMUM</a> permissible speed `v_(<a href="https://interviewquestions.tuteehub.com/tag/max-546895" style="font-weight:bold;" target="_blank" title="Click to know more about MAX">MAX</a>) ` is given by eq. <br/>`v_(max) = (Rg (mu_s + tan theta)/(1 -mu_s tan theta))^(1//2) = 38.1 ms^(-1)`</body></html>


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