Engineering Mechanics

Chapter 32 : Motion of Vehicles „„„„„ 661

1·15 RF – 0·51 RF= 1·6 RR

∴ RR=

0·64

0·4

1·6

F

F

R

= R

Substituting this value of RR in equation (i),

RF + 0·4 RF= 7840 or 1·4 RF = 7840

∴ RF=

7840

5600 N

1· 4

=

and FF= 0·6 RF = 0·6 × 5600 = 3360 N ...(iv)

Since this force of friction is equal to the accelerating force therefore equating equations (ii)
and (iv),

800 a= 3360

∴ a=^2

3360

4·2 m/s

800

= Ans.

(iii) Maximum possible acceleration when the car has four wheel drive

We know that as the car has four wheel drive, therefore the force of friction will act on both the
pairs of wheels. Now the total force of friction.

FF + FR= 0·6 (RF + RR) = 0·6 × 7840 = 4704 N ...(v)
Since the total force of friction is equal to the accelerating force, therefore equating equations
(ii) and (v),

800 a= 4704

∴ a=

(^4704) 5·88 m/s 2
800
= Ans.
32.6.BRAKING OF A VEHICLE
The term ‘brake’ may be defined as a device to apply artificial frictional resistance, to a
moving body, in order to retard or stop it. In a moving vehicle, the brakes are applied either on the
pair of rear wheels, front wheels or on both pairs of the front and rear wheels. Now we shall discuss
the braking of a vehicle in all the cases one by one.

1. Braking on rear pair of wheels only. It is a common way of braking the vehicle, in which
   frictional force acts in the rear pair of wheels only.


2. Braking on front pair of wheels only. It is a very rare way of braking the vehicle, in
   which the frictional force acts in the front pair of wheels only.


3. Braking on both the pair of wheels. It is the most common way of braking the vehicle, in
   which the frictional force acts on both the rear and front pair of wheels.
   In all the above mentioned three types of braking, the frictional force acts in the backward
   direction (i.e.,opposite to the tractive force or direction of motion of the vehicle). A little consideration
   will show, that the braking distance (i.e., distance in which the vehicle is brought to rest after the
   application of brakes) will be the least when the brakes are applied on both the pair of wheels. It is due
   to this reason that the brakes are applied on both the pairs of wheels (or sometimes termed as all the
   four wheels of a four-wheeled vehicle) these days. Such vehicles are generally used in hilly areas or
   army operations.