Question

# The friction coefficient between a road and the type of a vehicle is 4/3. Find the maximum incline the road may have so that once had brakes are applied and the wheel starts skidding, the vehicle going down at a speed of 36 km/hr is stopped within 5 m.

Solution

## Given, initial velocity of the vehicle, u = 36 km/h = 10 m/s final velocity of the vehicle, v = 0 s = 5 m, $\mathrm{\mu }=\frac{4}{3}$, g = 10 m/s2 Let the maximum angle of incline be $\theta$. Using the equation of motion From the free body diagram R − mg cos θ = 0 ⇒ R = mg cos θ                     (1) Again, ma + mg sin θ − μ R = 0 ⇒ ma + mg sin θ − μmg cos θ = 0 ⇒ a + g sin θ − μg cos θ = 0 ⇒ 30 + 30 sin θ − 40 cos θ = 0 ⇒ 3 + 3 sin θ − 4 cos θ = 0 ⇒ 4 cos θ − 3 sin θ = 3 On squaring, we get 16 (1 − sin2 θ) = 9 + 9 sin2 θ + 18 sin θ 25 sin2 θ + 18 sin θ − 7 = 0 Therefore, the maximum incline of the road, θ = 16°.PhysicsHC Verma - IStandard XI

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