CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


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, μ=43, g = 10 m/s2

Let the maximum angle of incline be θ.

Using the equation of motion
a=v2-u22s=0-1022×5 =-10 m/s2

From the free body diagram

Rmg 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
10+10 sin θ-43×10 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
41-sin2 θ=3+3 sin θ
On squaring, we get
16 (1 − sin2 θ) = 9 + 9 sin2 θ + 18 sin θ
25 sin2 θ + 18 sin θ − 7 = 0
sin θ=18+182-425 -72×25            =-18+3250=1450=0.28             Taking positve sign onlyθ=sin-1 0.28=16°
Therefore, the maximum incline of the road, θ = 16°.

Physics
HC Verma - I
Standard XI

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
Same exercise questions
View More


similar_icon
People also searched for
View More



footer-image