First slide

Dynamics of uniform and non uniform circular motion

Question

A car, moving at a speed of 54 kmh^-1, is to go round a curved road of radius 30 m. If the curved road is not banked, what must be the coefficient of friction between the tyres and the road for the car to negotiate the curve? Take g = 10 ms^-2

Moderate

Solution

The maximum centripetal force that the friction can provide is $F = μmg = \frac{{mv}^{2}}{R}$
or $μ = \frac{v^{2}}{Rg} = \frac{15 \times 15}{30 \times 10}$
$= 0 .75 (∵ 54 {kmh}^{- 1} = 15 {ms}^{- 1})$

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