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Question

# A circular road course track has a radius of 500 m and is banked to 10∘. If the coefficient of friction between the road and tyre is 0.25, compute (i) the maximum speed to avoid slipping (ii) optimum speed to avoid wear and tear of the tyres. [Take tan10∘=0.1763]

A
46.74 m/s, 29.39 m/s
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B
30 m/s, 24 m/s
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C
74.46 m/s, 23.39 m/s
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D
50 m/s, 44 m/s
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Solution

## The correct option is A 46.74 m/s, 29.39 m/sGiven: radius of curve = r=500 m, Angle of banking =θ=10∘, and coefficient of friction =μ=0.25,g=9.8 m/s2, To find safe velocity = v=?, To avoid wear and tear, vsp=? Maximum speed to avoid slipping: In this case, centripetal force is provided by horizontal component of both normal reaction and friction (i.e there will be wear and tear) vmax=√rg(tanθ+μs)(1−μstanθ) =√500×9.8(tan10∘+0.25)(1−0.25tan10∘) =√4900(0.1763+0.25)(1−0.25×0.1763)=√4900(0.4263)1−0.0441=√20890.9559 ∴vmax=√2185=46.74 m/s Maximum speed to avoid wear and tear: In order to avoid wear and tear, centripetal force for making the turn has to provided by the horizontal component of normal reaction alone. (i.e no friction) vopt=√rgtanθ=√500×9.8×tan10∘ =√500×9.8×0.1763=29.39 m/s

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