THE UNIVERSITY OF HONG KONG

DEPARTMENT OF MECHANICAL ENGINEERING

ENGG1205: INTRODUCTION TO MECHANICAL ENGINEERING

December 7, 2013 Time: 2:30p.m. -4:30p.m.

Attempt any FIVE questions. All questions carry equal marks.

Use answer books of different colours 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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ENGG 1205: Introduction to Mechanical Engineering

SECTION A

Al. (a) In the structure shown in Figure Al, linkage AC is an elastic tie rod with Young
modulus 80 GPa, cross-sectional area 50 mm2 , and an unstretched length of 2 m. It
is connected to the ceiling at A via a double-shear pin joint, and the pin there has a
failure shear stress of 250 MPa. Linkage BD is rigid but it is glued to the ceiling at
B via an elastic lap joint, and the glue material has a shear modulus of 1 GPa, a
thickness of 10 mm and a lap-joint area of 100 mm2 • The beam supported by the
two linkages is rigid and weighs 5 kN, and it carries an additional load of 10 kN as
shown. The original lengths of both AC and BD, before they are assembled.into the
structure, are both 2 m.

(i) Calculate the elongation of linkage AC, as the structure is assembled and the
load applied.

(ii) Calculate the minimum cross-sectional area required for the pin at A.

(iii) Calculate the displacement of point D, as the structure is assembled and the
load applied.

(iv) Judging from the properties given above, what are the likely materials for the
linkage AC, the pin at A, and the glue at B?
(10 marks)

Elastic glue layer

10 mm thick, glue
area 100 mm2

Side view of double-

shear pin joint at A Initial length 2 m,
cross-section 50 mm2
J l1omm
Side view oflap-joint at B

2 m long

1m 0.5 m 0.5 m

5kN 10kN

Figure A1

[Qn. Al is cont'd on P.3]

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ENGG1205: Introduction to Mechanical Engineering

Al. Cont'd

(b) Sketch the atomic arrangement in a semi-crystalline polymer. (2 marks)

(c) Distinguish between thermo-plastic and thermo-set polymers, and describe their
stress-strain behaviour. (3 marks)

(d) Draw sketches of an edge dislocation and a screw dislocation. Explain how they
correspond to plastic deformation in a metal. Why is aircraft grade of aluminium
much stronger than pure aluminium? (5 marks)

A2. (a) Show that for brittle materials such as ceramics, the stress required to propagate a
crack is inversely proportional to the square root of the crack size. (8 marks)

(b) On the basis of (a), explain why fibre forms of glass can be much stronger than bulk
pieces of glass. Sketch the stress-strain behaviour of these two types of glass, and
clearly label the fracture point. (4 marks)

(c) Explain how glass can be used to strengthen polymers. What are the advantages of
such polymer-based composites over pure polymers? Suggest a method by which
such glass-polymer composites can be made. (4 marks)

(d) A through-thickness crack of tip-to-tip length 20 mm is present in a large-area

ceramic plate with a thickness of 10 mm. The plate is subjected to tensile stress of
10 MPa, and has Young modulus of 300 GPa, and surface energy of I Jm·2 •
Calculate the net energy change if the crack is to propagate by I mm. (4 marks)

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ENGG1205: Introduction to Mechanical Engineering

SECTIONB

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

(a) Express the coordinates of the end-effector (xe, Ye) in terms of £ 1 , £ 2 , 81 and 8 2 .
(2 marks)

(b) Derive the expressions relating the x- andy-components of the end-effector velocity
e,
:i:e, Ye with joint velocities 82 • (6 marks)

(c) By working out the inverse of the Jacobian matrix or otherwise, express the joint
velocities e,
82 in terms of the end-effector velocity components :i:e, Ye· (8 marks)

(d) Sketch the linkage configurations in which the expressions in (c) do not give a
solution. (4 marks)

End Effecter

(;:)

Joint 1 X
0
LinkO

Figure Bl

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ENGG 1205: Introduction to Mechanical Engineering

B2. Figure B2 shows a linkage with a prismatic joint supported on a revolute joint. The
extension of the prismatic joint is d and the angular displacement of the revolute joint is
e.

(a) Express the coordinates of the end-effector (x, y,) in tenns of d and e. (2 marks)

(b) Derive the expressions relating the x- andy-components of the end-effector velocity
x,, y, with joint velocities d. and e. (6 marks)

(c) Use the Principle of Virtual Work or otherwise, relate the joint force (F) and joint
torque ( r) to the x- and y-components of the force exerted by the end-effector, Fx
and Fy. (8 marks)

(d) If the prismatic joint and the revolute joint are actuated by d.c. motors, how can one
control the force and torque exerted by the motors? (4 marks)

Figure B2

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ENGG 1205: Introduction to Mechanical Engineering

SECTIONC
2
Take density of water= 1,000 kg/m 3 , acceleration due to gravity= 9.81 m/s •

Cl. (a) Define the term 'viscosity'. (2 marks)

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

(c) What is the effect of temperature on the viscosity of a fluid? (2 marks)

(d) Briefly describe the cause and effect of cavitation. (4 marks)

(e) Draw a sketch to show the contact angle at a liquid-gas-solid interface. At what
contact angles is a liquid called wetting or non-wetting? (3 marks)

(f) What are the two fundamental physical laws that govern fluid flow? (2 marks)

(g) When half submerged in water, a spherical object of homogeneous material will
have an apparent weight equal to two-thirds of its weight in air. What is the relative
density of the material of the object? (4 marks)

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ENGG1205: Introduction to Mechanical Engineering

C2. Figure C2 shows a section view of a tank containing water of 6 m depth. The wall of the
tank is installed with a quadrant circular gate AB, which can freely rotate about the hinge
at A and is kept closed by a horizontal force F applied at B. The gate is 10 m long, and its
back is exposed to the atmosphere. The weight of the gate and friction in the hinge may
be neglected.

(a) Calculate the magnitude of the horizontal component of the resultant force acting on
AB. (5 marks)

(b) Calculate the magnitude of the vertical component of the resultant force acting on
AB. (5 marks)

(c) Find the magnitude and the inclination of the resultant hydrostatic force acting on
AB. (5 marks)

(d) Determine the minimum horizontal force Fthat is required to hold the gate closed.
(5 marks)

4m

2m
F

Figure C2

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