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Question

On a highway, the maximum speed of vehicles is 50 m/s. The material of the road provides a coefficient of static friction μs=0.35. If the highway has a circular turn with a radius of curvature 90 m, then what should be the banking angle (θ) for this turn to ensure safe driving ?

A
tan1(2.24)
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B
tan1(1.23)
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C
sin1(2.26)
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D
cos1(1.26)
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Solution

The correct option is B tan1(1.23)
For maximum safe speed v=50 m/s, the vehicle will have a tendency to skid up the incline, hence friction
(fmax=μN) will act down the incline to ensure no slipping.


From equation of dynamics:
Nsinθ+fmaxcosθ=mvmax2r....(i)
where fmax=μN.......(ii)
Ncosθfmaxsinθ=mg.......(iii)

Dividing (i) by (iii):
sinθ+μscosθcosθμssinθ=v2maxrg
tanθ+μs1μstanθ=v2maxrg
Dividing by cosθ on L.H.S and solving for tanθ gives:-
tan θ=(v2maxgr)μs1+(μsv2maxgr)
=50210×900.351+0.35×50210×90=1.23
or, θ=tan1(1.23)

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