The following data refers to a vehicle:

Mass of the vehicle=1600kg
Number of wheels =4
Moment of inertia of each wheel=3.2kgm2
Diameter of each wheel=650mm
Mass of engine rotating parts=60kg
Radius of gyration of engine rotating parts=90mm
Transmission efficiency=85%
Gear ration from engine to back axle=6

The resistance to motion is given by (180 + 0.84V2) and the engine torque available is given by (90 – 0.048V2), where V is the linear speed of the vehicle in m/s.

Determine:

The power of the vehicle when velocity is 18m/s.(11 marks)
The time taken for the vehicle to increase speed from 18m/s to 24 m/s.(5 marks)
The distance covered during the acceleration(4 marks)

a) i) State TWO conditions necessary for complete dynamic balance for a shaft carrying several masses.
ii) State any FOUR effects of unbalanced forces in a machine having several rotating parts.(4 marks)

b) Four masses A,B,C and D are carried on a shaft with their centers of mass 150mm, 200mm, 700mm and 600mm respectively. The masses are such that A=9kg, B=18kg, C=21kg and D=14kg. The distance of the planes of rotation measured from mass A are anticlockwise from A are B=3m, C=5m and D=7m respectively. The angular position of B,C and D measured anticlockwise from A, are 750, 1600 and 2400 respectively. Two balance masses are fitted as follows: one, midway between A and B, whose centre of mass from the shaft axis is 110mm; and the other is fitted mid-way between C and D, whose centre of mass from the shaft axis is 90mm.

Determine the values of the balance masses and their angular positions with respect to A. show the position of the masses on an end view. (16marks)

SECTION B: STRENGTH OF MATERIALS

Answer any ONE question from this question.

The following data refers to an open – coiled helical spring:

Pitch of the coils=27mm
Number of coils=12
Mean coil diameter=54mm
Diameter of wire=8mm
Modulus of elasticity spring material=208GN/m2
Modulus of rigidity of spring material=72GN/m2
The spring is subjected to a pure axial twisting moment of 9M-m.

Determine:

The resulting angle of twist. (8 marks)
The extension produced. (31/2 marks)
The bending stress in the surface of the wire. (41/2 marks)
The shear stress in the surface of the wire. (4 marks)

a) i) State any FOUR assumptions made in the theory of torsion.
ii) Show that the strain energy ‘u’ stored in a solid shaft of diameter ‘d’, length ‘l’ and modulus of rigidity G, when subjected to pure torque T, is given by the expression:

u=T2 x Volume of the shaft
4G
where T is the maximum shear stress. (7 marks)

b) A composite shaft is used to transmit 380KW at a speed of 750 rev/min. The composite shaft is made by passing a solid cylindrical shaft of 65mm diameter and 1.8m long, 65mm and 75mm internal and external diameters respectively. They are then rigidly joined together at their ends. The solid shaft is made of steel and the hollow shaft is made of brass.

Determine:
The maximum and minimum stresses in the two shafts.
The angle of twist.
The total strain stored:
Take G for brass=35GN/m2
and G for steel=78 GN/m2 (13 marks)

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