A car negotiates a banked curve of radius R, banking angle θ and tyre-road static friction coefficient μₛ. The maximum safe speed is:
Options

Question

A car negotiates a banked curve of radius R, banking angle θ and tyre-road static friction coefficient μₛ. The maximum safe speed is:

G1 Physics · Accepted Answer

For maximum speed, friction acts down the bank. Resolve N and limiting friction μₛN: horizontal inward equation Nsinθ+μₛNcosθ=mv²/R; vertical balance Ncosθ-μₛNsinθ=mg. Divide equations to obtain v²/(Rg)=(tanθ+μₛ)/(1-μₛtanθ). Hence option D.