2019-03-01_Physics_Times

13. Motion of a vehicle at a turn

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9. Friction

When two bodies are kept in contact,

electromagnetic forces act between the charged

particles (molecules) at the surfaces on the bodies.

Thus, each body exerts a contact force of the other.

The direction of the contact force acting on a

particular body is not necessarily perpendicular to

the contact surface. We can resolve this contact

force into two components, one perpendicular to

the contact surface and the other parallel to it.

The perpendicular component is called the normal

contact force or normal force ( N) and the parallel

component is called friction ( ).f

Therefore, if R is contact force then

R f N^2 ^2

10. Magnitude of Kinetic and Static

Friction

(I) Kinetic friction

The magnitude of the kinetic friction is

proportional to the normal force acting between

the two bodies.

fkkN

Where N is the normal force. The proportionality

constant k is called the coefficient of kinetic

friction

(II) Static friction

The magnitude of static friction is equal and

opposite to the external force exerted, till the

object at which force is exerted is at rest.

This means it is a variable and self adjusting

force. However, it has a maximum value called

limiting friction.

fmaxsN

The actual force of static friction may be smaller

than sN and its value depends on other forces

acting on the body. The magnitude of frictional

force is equal to that required to keep the body

at relative rest.

0  f fs smax

Here s is called coefficient of static friction

and k is called coefficient of kinetic friction.

11. Angle of Friction ()

When a body is in contact with a surface, the angle

made by the resultant of normal reaction and the

limiting friction with the normal reaction is called

Angle of Friction.

9. Friction

10. Magnitude of Kinetic and Static

Friction

11. Angle of Friction

12. Angle of Repose

13. Motion of a vehicle at a turn

tan fL tan smg

N mg



  

  tan^1  s

The greater angle of friction the greater is the value

of coefficient of friction.

( )

Angle of repose is the minimum angle of the

rough inclined plane for which body placed on it

may just start sliding down.

Let θ be the angle of inclination of a rough

inclined plane,  be the angle of repose, m be

the mass of the body and μ be the coefficient of

friction.

mgsin  smgcostan  s

  tan^1  s

When   ; the block remains at rest on the

inclined plane.

When   ; the block reamins at rest on incline

plane and it is at the range of slipping

When   , sliding will start.

(I) Motion of a vehicle on an unbanked rough

road:

Then, max

2

S

mv

mg

r

 or

2

max

S

v

r

g



vmax Srg.

.

.

.