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Mechanics Of Machines Question Paper

Mechanics Of Machines

Course:Bachelor Of Science In Manufacturing Engineering And Technology

Institution: Kenyatta University question papers

Exam Year:2008

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2007/2008
SECOND SEMESTER EXAMINATION FOR THE DEGREE OF
BACHELOR OF SCIENCE (MANUFACTURING ENERGY)
SET 311: MECHANICS OF MACHINES
DATE: Friday 2nd May 2008 TIME: 8.00am – 10.00am
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INSTRUCTIONS:
1.This paper contains three sections and having a total of five questions.
2.You are required to answer three questions only.
3.Answer question one in Section A and any ONE question from each of the
sections B and C.
Question ONE carries 30 marks and the others carry 20 marks each.
Section A (Compulsory Question)

Q1. (a) A point moves with simple harmonic motion. When this point is 0.75m
from the mid path, its velocity is 12m/s and when 2 meters from the
centre of its path, its velocity is 3.5m/s. Determine its.
(i) Angular velocity
(ii) Periodic time
(iii) Maximum acceleration. [15 marks]

(b) A uniform rod shown in fig Q1(b) has a mass of 1.2kg and carries a
concentrated mass of 2.8kg at B. The rod is hinged at A and is maintained
in the horizontal position by a spring of stiffness 2KN/m.
Determine:
(i) the periodic time
(ii) the frequency of the oscillation, neglecting the effect of the mass of
the spring. [10 marks]

(c) A body of mass m controlled by an elastic system of stiffness s is given a
linear displacement x. In terms of gravity g and the static deflection,
determine
(i) the periodic time
(ii) the frequency of the free vibration. [5 marks]

Section B: Answer any ONE question. (20 marks)

Q2.
(a) The time of free vibration of a mass hung from the end of a vertical spring
is 0.8sec. When the mass is stationery, the upper end is made to move
upwards with a displacement y m such that y = 0.018 sin 2t
where t is the time in seconds measured from the beginning of the
motion. Neglecting the mass of the spring and the damping effects,
determine the vertical distance through which the mass is moved in the
first 0.3 sec. [15 marks]

(b) A pendulum of mass m , not concentrated at a point is suspended as
shown in fig Q2(b). The radius of gyration about the centre of gravity a is
k , and the distance of the point of suspension from G is h . If the
pendulum is given a small angular displacement ? determine the periodic
time in terms of k, g and h. [5 marks]

Q3. (a) A mass of 6kg hangs from a spring and makes damped oscillations. The
time of 60 complete oscillations is found to be 20 sec, and the ratio of the
first downward displacement to the sixth is found to be 2.5. Determine
(i) the stiffness of the spring
(ii) the damping force. [10 marks]

(b) A rod is hinged at one end and supported by a spring of stiffness 5KN/M,
at the other end as shown in fig Q3(b). A mass of 7kg is attached at 1/3 of
the length from the hinge and a dashpot having a damping coefficient of
3Ns/m is attached at 2/3 of the length from the hinge.
Determine,
(i) The differential equation for the motion.
(ii) The equivalent mass and the equivalent damping coefficient at the spring
(iii) The frequency of the damped vibration of the system.

Section C: Answer any ONE question

Q4.
(a)Two uniform beams AB, 2m long and together 6kg are hinged at A and supported at B by a single spring of stiffness 5.5KN/m. The beams carries a flywheel D of mass 30kg in bearing 1.2m from A. When in static equilibrium, AB is horizontal.
(i) Find the natural frequency of vibration of system
(ii) If the centre of gravity of the flywheel is 4mm from its axis of rotation, determine the total vertical movement of B when the flywheel rotates at 250 rev/min. [12 marks]

(b) The mass of a vibrating system is 6kg and with a spring stiffness of 4.8N/mm. If the system has a dashpot attached which exerts a force of 40N when the mass has a velocity of 1m/s. Determine
(i) the critical damping coefficient
(ii) damping factor
(iii) logarithmic decrement
(iv) ratio of two consecutive amplitudes. [8 marks]

Q5. (a) Four masses m1, m2, m3 and m4 are 10kg, 15kg, 12kg, and 13kg
respectively. The corresponding radii of rotation are 0.3m, 0.2m, 0.4m
and 0.5m respectively and the angles between successive masses are 35o,
60o and 140o. Calculate the position and magnitude of the balance mass
required if its radius of rotation is 0.3m. [14 marks]

(b) The load on a journal bearing is 160KN due to turbine shaft of 280mm diameter running at 1800 rpm. Assuming the end leakage correction factor is 0.002, determine
(i) the length of the bearing if the allowable bearing pressure is 2N/mm2.
(ii) The amount of heat to be removed by the lubricant per minute if the bearing temperature is 60oC and viscosity of the oil at 60oC is 0.02kg/ms and the bearing clearance is 0.25mm. [6 marks]

Mechanics Of Machines Question Paper

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