Engineering Mechanics

(^652) „„„„„ A Textbook of Engineering Mechanics
32.2.TYPES OF MOTIONS OF VEHICLES
Though there are many types of vehicles and their motions, yet the following are important
from the subject point of view :

1. Motion of a vehicle along a level track, when the tractive force passes through its centre
   of gravity.


2. Motion of a vehicle along a level track, when the tractive force passes through a point,
   other than its centre of gravity.
   In addition to these types of motions, we shall also discuss the driving of vehicles, braking of
   vehicles and motion of vehicles on an inclined plane in this chapter.

32.3.MOTION OF A VEHICLE ALONG A LEVEL TRACK WHEN THE TRACTIVE

FORCE PASSES THROUGH ITS CENTRE OF GRAVITY

Fig. 32.1. Forces passing through centre of gravity.

Consider a four-wheeled vehicle moving along a level track. Let the tractive force (P) tending

to move the vehicle to the right, pass through the centre of gravity (G) of the vehicle as shown in

Fig. 32.1.

Let M= Total mass of the vehicle,

m= Mass of the two pair of wheels and their axles,

k= Radius of gyration of the wheels,

I= Total mass moment of inertia of both the pair of wheels

and their axles (such that I = mk^2 )

r= Radius of the wheels,

h= Height of centre of gravity (G) of the vehicle above the road

level,

a= Linear acceleration of vehicle due to tractive force,

α= Angular acceleration of the wheels,

RF and RR= Reactions at the pair of front and rear wheel respectively,

2 x= Horizontal distance between the reactions, and

F= Force of friction acting at each pair of wheels (such that

total force of friction is 2F).

For simplicity, let us consider, front and back pair of wheels as symmetrical about the

vertical axis dividing the wheels. Now let us apply two equal and opposite forces of magnitude

2 F, parallel to the force of friction and through the centre of gravity (G) of the vehicle as shown

in Fig. 32.1.