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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/s
Given: 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)(1μstanθ)
=500×9.8(tan10+0.25)(10.25tan10)
=4900(0.1763+0.25)(10.25×0.1763)=4900(0.4263)10.0441=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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