A racing car travels on a track (without banking) ABCDEFA (Fig). ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The coefficient of friction on the road is µ = 0.1. The maximum speed of the car is 50 m s–1. Find the minimum time for completing one round.

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Alok Kumar Singh | Contributor-Level 10

6 months ago

This is a Long Answer type Questions as classified in NCERT Exemplar

Explanation – centripetal force, F= mv²/r= f= $μ N = μ m g$

V= $\sqrt[]{μ r g}$

For path ABC path length =3/4 (2 $π 2 R$ )= $3 π R = 3 π (100) = 300 π$

V₁= $\sqrt[]{μ 2 R g} = \sqrt[]{0.1 * 100 * 10} = 1.414 m / s$

So t= 300 $\frac{π}{1.414} = 66.6 s$

For path DEF path length = $\frac{1}{4} (2 π R) = 50 π$

V₂= $\sqrt[]{μ R g} = \sqrt[]{0.1 * 100 * 10} = \frac{10 m}{s}$

So t₂= 50 $\frac{π}{10}$ = 15.7s

For path CD and FA

Path length =R+R= 200m

T= 200/50= 4s

Total time = 66.6+15.7

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