A car moves on a horizontal unbanked circular road of radius 40 m. The coefficient of static friction between tyres and road is 0.5. Take g = 10 m/s². If the maximum safe speed is v_max = 10√N m/s, find N.
Physics · Circular Motion · friction and circular motion
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Question

A car moves on a horizontal unbanked circular road of radius 40 m. The coefficient of static friction between tyres and road is 0.5. Take g = 10 m/s². If the maximum safe speed is v_max = 10√N m/s, find N.

Physics · Circular Motion · friction and circular motion

G1 Physics · Accepted Answer

On a flat circular road, static friction supplies the centripetal force. At the limiting condition, mv_max²/r = μmg. Therefore v_max² = μrg = 0.5×40×10 = 200. Hence v_max = 10√2 m/s, so N = 2.