The friction coefficient between a road and the tyre of a vehicle is 4/3. Find the maximum incline the road may have so that once hard brakes are applied and the wheel starts skidding, the vehicle going down at a speed of 36 km/hr is stopped within 5 m.
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a= 0− (10^2 /2) ×5
a= 10 m/s^2
R−mgcosθ=0
from the free body diagram
ma+mgθ−μR=0 −−−−−−−−−−−−−−−−(1)
ma+mgθ−μmgθ=0
a+gsinθ−μgcosθ=0
10+ (10×sinθ) − 4/3 ×10θ =0
30+30sinθ−40θ=0
3+3sinθ−4θ=0
4cosθ−3θ=3
squaring we get
=4 √(1−sin²θ) =9+9sin²θ+18sinθsinθ
=18+ √[18²−4(25)×(−7) / (2×25)]
sinθ= (−18+32)/50
= 14/50
=0.28
θ=sin⁻¹[0.28] =16∘
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