THE UNIVERSITY OF HONG KONG

DEPARTMENT OF MECHANICAL ENGINEERING

EXAMINATION

ENGG1205: INTRODUCTION TO MECHANICAL ENGINEERING

December 16, 2016 Time: 9:30 a.m. - 11 :30 a.m.

Attempt any FIVE questions. All questions carry equal marks.

Use answer books of different colors for Section A, Section B and Section C.

Electronic Calculators:

Only approved calculators as announced by the Examinations Secretary can be used in this
examination. It is candidates' responsibility to ensure that their calculator operates
satisfactorily, and candidates must record the name and type of the calculator used on the
front page of the examination script.

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ENGG1205: Introduction to Mechanical Engineering

SECTION A

Al. (a) Sketch the engineering stress-strain graph of a typical non-ferrous, ductile metal
such as aluminium, as obtained from a tensile test. Indicate on the graph the
following parameters:

• Yield stress
• Ultimate tensile stress
• Young modulus

Then, explain in words the meaning of each of the three parameters above.

Explain why in practice it is difficult to precisely identify the yield stress from an
experimental stress-strain curve. Describe the meaning and use of a "proof stress" to
represent the yield strength. (I 0 marks)

(b) An axial tensile force of 1 kN is applied along a tapered bar of circular cross
section. The diameter of the rod is 10 mm at its bigger end, and the angle of taper is
0.1° as shown in Figure Al. Length of rod is 2 m.

{ Taper angle 0.1°

1 kN
. \ 1 kN
--

=-.:: ==============1-~ 2m ~ lOmm

Figure Al

(i) Calculate the average values of the tensile stress over the cross sections at the
bigger and smaller ends of the rod. (6 marks)

(ii) Given that the Young modulus of the rod is 80 GPa, estimate the elastic
elongation of the rod under the applied load of 1 kN. [Hint: divide the rod into
infinitesimal slabs and apply Hooke's law to each slab, followed by
integration.] (4 marks)

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ENGG 1205 : Introduction to Mechanical Engineering

A2. (a) Within Griffith' s concept for the critical stress required to cause a crack to
propagate, show that the condition for crack propagation is

where the terms have their usual meanings. (10 marks)

(b) "Materials can be strengthened by various means."

(i) Explain the above statement in the context of aircraft grade of aluminium
alloys. What are the strengthening mechanism in such materials, compared to
pure aluminium which has very low strength? (5 marks)

(ii) Explain the same statement in the context of glass reinforced plastics. Why is
it that a seemingly weak material such as glass can be used to strengthen
plastics? What form of glass is used, and how are such "glass reinforced
plastics" usually made? (5 marks)

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ENGG1205: Introduction to Mechanical Engineering

SECTIONB

B 1. Figure B 1 shows a linkage with two revolute joints. The length of link 1 is f 1 and that
of link 2 is f 2 • The angular displacements of joint 1 and joint 2 are 81 and 82
respectively.

(a) Express the coordinates of the end-effector (xe, Ye) in terms of f 1 , f 2, 81 and 82.
(2 marks)

(b) Derive the expressions relating the x- and y-components of the end-effector velocity
Xe, Ye with joint velocities 01 , 02 . (4 marks)

(c) Use the Principle of Virtual Work or otherwise, relate the joint torques 't1 and 't2 to
the x- and y-components of the force exerted by the end-effector, Fx and Fy.
(4 marks)

(d) Given that £ 1 = 0.8m, f 2 = 0.6m, work out the two configurations that the end-
effector is located at (l.069m, 0.830m). (6 marks)

(e) For each of the configurations worked out in (d), calculate the joint torques when
the required force components at the end-effector are Fx = 20N and Fy= 35N.
(4 marks)

Figure Bl

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ENGG1205: Introduction to Mechanical Engineering

B2. (a) Pulse-width modulation is used to control the voltage applied to a DC motor. The
DC supply is 36V and PWM frequency is 5 kHz. For a duty cycle of 75%, work out
toN and toFF. Calculate the average voltage applied across the motor terminals.
(4 marks)

(b) With suitable sketches, show the arrangement for a H-bridge circuit and explain
how the direction of rotation of a motor can be changed. (2 marks)

(c) The linkage shown in Figure B2 has a revolute joint connected to a prismatic joint.
a is a constant.

(i) Express the coordinates of the end-effector (xe, Ye) in terms of d, f , e and a.
(2 marks)

(ii) Determine the Jacobian matrix relating the end-effector velocity components
[ie, y:J with the joint velocities [d and B]. (4 marks)

(iii) By working out the inverse of the Jacobian matrix or otherwise, express the
joint velocities [ d and e] in terms of the components of the end-effector
velocity [Xe , y:]. (4 marks)

(iv) For this linkage, sketch the singular configurations. (4 marks)

Figure B2

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ENGG1205: Introduction to Mechanical Engineering

SECTIONC
Take density of water= 1,000 kg/m3, acceleration due to gravity= 9.81 m/s2 •

Cl. (a) How does the viscosity or effective viscosity of a fluid depend on the stress when
the fluid is Newtonian, shear thinning, or shear thickening? (3 marks)

(b) Briefly describe the cause and effect of cavitation. (6 marks)

(c) State the Archimedes principle. (3 marks)

(d) As is shown in Figure Cl, a spherical object of diameter d 0 is made up of Material

Hint: the volume of a sphere = ~ x diameter' . (8 marks)

Material A
ofrelative
density r Hollow core of
diameter de

~---do

Figure Cl

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ENGG1205 : Introduction to Mechanical Engineering

C2. This problem is to check the stability against sliding of an object of a rectangular
( 0.5 m x 1.2 m) cross section resting on a 15° slope, as shown in Figure C2. The object
has a density 2.5 times that of water. Behind the object (AB) is a gap filled with water to
the top of the gap. Owing to roughness, the contact between the bottom of the object
(BC) and the slope is not watertight. Water seeps through very fine crevices between the
contact surfaces of the object and the slope. The water pressure acting on AB and BC is
assumed to be linearly distributed, as shown in the figure, where the pressure at A and C
is zero. Consider a 1 m long of the object in the following analysis.

(a) Assuming hydrostatics in the gap, find the water pressure at B. (2 marks)

(b) Calculate the resultant hydrostatic force acting on the back (AB) of the object.
(4 marks)

(c) Calculate the resultant force due to water pressure acting on the bottom (BC) of the
object. (4 marks)

(d) It is given that the only force preventing the object from sliding is the friction
between the object and the slope, for which the average coefficient of friction is 0.5.
Draw a free body diagram to show all forces acting on the object. Then, determine
whether or not the object will slide down the slope. (10 marks)

I \
I \
.....---',
', \
1..,--",
' \

\ \
I \
B ,...--
\
______ _____
____

----£-- l_ ____ ---- ----

Figure C2

-END OF PAPER-

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