CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A turn of radius 20 m is banked for the vehicle going at speed of 36 km/hr. If the coefficient of static friction between the road and the tyre is 0.4. What of the following speeds are possible such that the vehicle neither slips down nor skids up ?


A
20 km/hr
loader
B
30 km/hr
loader
C
40 km/hr
loader
D
50 km/hr
loader

Solution

The correct options are
A 20 km/hr
B 30 km/hr
C 40 km/hr
Speed of vehicle (v) = 36 km/hr = 10 m/sec
Let θ be the angle at which the road is banked.

Let us find out all the forces that are acting on this moving vehicle

(i) Mg in downward direction 

(ii) N (normal reaction) acting perpendicular to the surface of road

(iii) pseudo force acting in radially outward direction

(iv) frictional force acting parallel to the road, either in inward or outward direction 

Case 1:
To avoid slipping of the vehicle 
In this case friction will act in outward direction


Let us now resolve all the forces in the direction along the surface and perpendicular to the surface.
 
Now we get , 
N=Ma sinθ+Mgcosθ.......(i)

Mgsinθ=μN+Ma cosθ...(ii)

To calculate θ we know 

tanθ=ag

tanθ=v2rg

tanθ=(10)220g = 0.5........(iii)

Put (iii) in (ii) and (i) we get 
Vmin=106 m/s = 14.7 km/h

Case 2:

To avoid vehicle from skidding up

In this case friction will act inward direction.



Again resolve the forces along the surface and perpendicular to the surface.

μN+mg sinθ=ma3 cosθ.......(v)

N=ma3 sinθ+mg cosθ.....(vi)

a3=v2maxr...(vii)
on solving (v), (vi) and (vii) this we get 

vmax= 44.1 km/h

Options A, B and C are correct

Physics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image