Chapter 32 : Motion of Vehicles 659
32.5.DRIVING OF A VEHICLE
We have already discussed in Arts. 32.3 and 32.4 the motion of a vehicle due to the tractive
force. We have also discussed the two popular cases i.e., when the tractive force passes through the
centre of gravity of the vehicle and when the tractive force passes through a point, other than its centre
of gravity.
As a matter of fact, both these cases are only of academic interest. In actual practice, the
tractive force, produced by the engine, is converted into rotary motion, which drives the pair of
wheeels. These wheels, in turn, make the vehicle to move. It will be interesting to know that almost all
the vehicles are driven either by the rear pair of wheels or both the pairs of wheels. But from the
academic point of view, we shall discuss the driving of vehicles in the following cases one by one :
- Driving of vehicle by the rear pair of wheels. It is the most common way of driving the
vehicles, in which the rotary motion of the engine is coupled with the rear pair of wheels
only. - Driving of vehicle by the front pair of wheels. It is a very rare way of driving the vehicles,
in which the rotary motion of the engine is coupled with the front pair of wheels only. - Driving of vehicle by both the pair of wheels. It is also a rare way of driving the vehicles,
in which the rotary motion of the engine is coupled with both the pairs of wheels. This
types of driving is, generally, adopted in case of jeeps and military vehicles, which are
used in hilly or difficult areas only.
In all the above mentioned three types of driving, the frictional force acts in the backward
direction (i.e. opposite to the tractive force or direction of motion of the vehicle) on the pair of
wheels, which drive the vehicle.
Example 32.4. A motor car of mass 800 kg has a wheel base of 2·75 m with centre of gravity
is 0·85 m above the ground and 1·15 m behind the front axle. Calculate the maximum possible
acceleration of the car, if the coefficient of adhesion between the tyres and ground is 0.6 and when
the car has (i) rear wheel drive; (ii) front wheel drive ; and (iii) four wheel drive.
Solution. Given: Mass of the motor car (M) = 800 Kg; Distance between the centre of the
axles (d) = 2·75 m; Height of the c.g. of the car above the ground (h) = 0·85 m; Distance of c.g. from
front wheel (x 1 ) = 1·15 m; Distance of c.g. from Rear wheel (x 2 ) = 2·75 – 1·15 = 1·6 m and coefficient
of friction (μ) = 0·6.
(i) Maximum possible acceleration when the car has rear wheel drive
Fig. 32.4.
Let RF= Reaction on the front pair of wheels,
RR= Reaction on the rear pair of wheels, and
a= Maximum possible acceleration of the car.