(^664) A Textbook of Engineering Mechanics
(iii) Distance covered by the automobile in coming to stop, if the brakes are applied on both the pair
of wheels
Let s 2 = Distance covered by the automobile in coming to stop.
We know that when the brakes are applied on both the pairs of wheels, then the total force of
friction,
FF + FR= 0·2 (RF + RR) = 0·2 × 39 200 = 7840 N
This total force of friction stops the automobile in a distance of s 3 meters. Therefore work
done by the force
Force × Distance = 7840 s 3 N-m ...(vi)
We know that kinetic energy of 312 500 N-m [as per equation (ii)] of the automobile is
absorbed by the force of friction in travelling through a distance s 3. Therefore equating equations
(ii) and (vi),
312 500 = 7840 s 3
∴ s 3 =
312 500
39·9 m
7840
= Ans.
EXERCISE 32.1
- An army vehicle of mass 2 tonnes has two pairs of wheels of 1 m radius. Each pair of wheel,
including its components, has a mass of 400 kg and radius of gyration as 0·25 m. The centre to
centre distance of the two wheels is 2·5 m and the c.g. of the vehicle is in the middle of the two
wheels. Find the reactions of the two pairs of wheels, if the tractive force of the vehicle is 10
kN, acting 300 mm below the c.g. of the vehicle. [Ans. RF = 9·45 kN; RR = 10·15 kN] - An industrial vehicle of mass 1 tonnes is moving on a newly constructed road whose coefficient
of friction is 0·55. Determine the maximum possible acceleration of the vehicle, if it is driven
by both the pairs of wheels. [Ans. 4·9 m/s^2 ] - A motor car of mass 500 kg has a wheel base of 2·5 m with its centre of gravity 0·75 m above
the ground level and 1·5 m behind the front axle. If the coefficient of friction between the
tyres and the road is 0·3, find the maximum possible acceleration of the car, when it is driven by
the rear pair of wheels only. [Ans. 5·52 m/sec^2 ] - A 1500 kg automobile travelling at 72 km.p.h. is brought to rest by the application of brakes on
all the four wheels. If the coefficient of friction offered by the brakes is 0·35, how far the
automobile will travel before it is brought to stop. [Ans. 72·4 m] - A passenger van of mass 2·5 tonnes is travelling at 54 km.p.h. on a level road. The wheel base
of the van is 3 m and its centre of gravity is 1 m above the road surface. The c.g. is 1·75 m
behind the front axle. If the coefficient of friction offered by the brakes is 0·7, find the distance
covered by the van before coming to stop, when the brakes are applied on both the pairs of
wheels. [Ans. 16·4 m]
32.7. MOTION OF VEHICLES ON AN INCLINED PLANE
We have already discussed in the last articles about the motion of vehicle on level tracks only.
The examples of motion of vehicles on an inclined plane may also be solved in the same way.
Note: When the vehicle is going up the inclined plane, there will be some resistance due to
inclination, in addition to the braking resistance. Similarly, when the vehicles is coming down the
inclined plane, then there will be some additional force due to gravity to move the vehicle.