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Unformatted text preview: THE UNIVERSITY OF HONG KONG BACHELOR OF ENGINEERING: LEVEL 1 EXAMINATION FOUNDATIONS OF ENGINEERING NIECHANICS (ENGGI 0 10) Date: December 10, 2008 Time: 9:30 am. — 12:30 pm. This paper contains SIX questions (THREE in Section A and THREE in Section B). Full
marks can be obtained by the correct solutions to FOUR questions (of which TWO must be
from Section A and TWO from Section B). All questions carry the same marks. Use answer books of different colours for Section A (Pink) and Section B (Green). Electronic Calculators: Candidates taking examinations that permit the use of calculators may use any calculator
which fulﬁls the following criteria: (a) it should be selfcontained, silent, batteryoperated and pocketsized; (b) it should have numeraldisplay facilities only and should be used only for the purpose of
calculation; (0) it should not have any printing device, alphanumeric keyboard, or graphic display; and (d) it should not contain any recorded data or program. It is the candidate’s responsibility to ensure that the calculator operates satisfactorily and the
candidate must record the name and type of the calculator on the front page of the
examination scripts. Lists of permitted/prohibited calculators will no longer be made
available to candidates for reference, and the onus will be on the candidate to ensure that the
calculator used will not be in violation of the criteria listed above. Foundations of Engineering Mechanics (ENGGlOl O) Page 2 SECTION A A1. A hydrauliclift table is designed for vehicle inspection, as shown in Figure A1. The
lifting is controlled by a hydraulic actuator, which exerts forces at F. The liﬁ table is supported by two linkages at B and D. Assume that the weight of the automobile is
18 RN. (a) Draw a freebody diagram for the lift table. Hence, determine the forces at B and D. (12 marks)
(b) Draw a freebody diagram for the linkage AFB. (4 marks)
(0) Determine the force on the piston rod EF. (6 marks) (d) Determine the pressure in the hydraulic actuator, which has an internal diameter of
100 mm. (3 marks) Figure Al (1)110.) Foundations of Engineering Mechanics (ENGGIOlO) Page 3 A2. (a) A wood tension member with a 70 mm x 110 mm rectangular cross section will be (b) fabricated with an inclined glue joint (450 3 ¢ 3 90°) at its mid—section, as shown in
Figure A2(a). If the allowable stresses for the glue are 5.0 MPa in tension and
2.9 MPa in shear, determine 0)
(ii) the optimum angle ¢ for the joint; and
the maximum safe load P for the member. (5 marks)
(4 marks) Figure A2(a) Show that when a truss of cross sectional area A, coeﬁicient of thermal expansion at, length L and elastic modulus E is subjected to a tensile force F and temperature change T, its elongation is: 5=££+GLT A E (4 marks) Figure A2(b) shows a bimetallic temperature sensor, which is designed to have a
short steel tube of outer diameter 65 mm and inner diameter 60 mm surrounding a
solid copper rod of 50 mm diameter. At 20°C, the rod and the tube have the same
length and are unstressed. If a load of 80 kN is placed on top of the rod and
cylinder, determine (0 the stresses in the two components when the whole assembly is subject to a
temperature change of 45°C; and (9 marks) (ii) the temperature at which the copper rod would take up all the loading.
(3 marks) Assume that the moduli of elasticity of steel and copper are 207 GPa and 104 GPa,
respectively, and the corresponding coefﬁcients of thermal expansion are 12x10'6/°C and 18.5x10'6 /°c.
80kN rigid plate I
copper rod E rigid plate Figure A2(b) Steel
tube (P.T.O.) Foundations of Engineering Mechanics (ENGGlOlO) Page 4 A3. A tapeer bar AB of solid circular cross section is loaded by a distributed torque t= 800
kNm/m along the longitudinal axis of the bar, as shown in Figure A3. In addition, the
bar is also loaded by a constant torque T = 300 kNm at the end A. The bar is not
subjected to stress concentration at A. The bar is ﬁxed at one end and free at the other
end. The diameter of the bar varies linearly from end B having a maximum diameter of
500 mm to end A having a minimum diameter of 200 mm. The bar AB is made of steel
and has a shear modulus of elasticity G = 80 GPa. Determine the angle of twist
(in degrees) between the ends of the bar. (25 marks) T= 300 kNm Cross section
1000 mm t= 800 kNm/m Figure A3 (1210.) Foundations of Engineering Mechanics (ENGGl 010) B1. (a) (b) (0) Page 5 SECTION B A disk of radius R rolls on the ground at angular speed co as shown in Figure B1(a).
A bar (AB) of length 2R is pulled along the ground by the disk by a hinge on the
disk edge at point A. Determine the speed of another end of the bar on the ground, point B, and the clockwise rotational speed of the bar, coAB, for the moment when
the angular position of the hinge is at 9=1t/4. (12 marks) 7/ c§ B Figure B 1 (a) Suppose you are designing a monorail transportation system that will travel at
velocity V and you decide that the angle 6, shown in Figure B1(b), that the cars
swing out from the vertical when they go through a turn must not be larger than 30".
If the turns in the track consist of circular arcs of constant radius R, what is the
minimum allowable value of R? (7 marks) Figure B 1 (c) Figure B1(b) A car is driven along a hill with ups and downs as shown in Figure B1(c). The car
speed is V and the road curvature is such that the local radius is R. Please draw a
simple free body diagram for the car, which includes the driver, with all forces
acting on the car labelled, and state whether the friction force on the road affects
the weight the driver feels for the given V and R. (6 marks) (P.T.O.) Foundations of Engineering Mechanics (ENGGlOlO) Page 6 Take density of water = 1,000 kg/m3, acceleration due to gravity = 9.81 m/s2. BZ. A long, solid cylinder of radius 1 m, which is freely hinged at point A, is used as an
automatic gate for a water reservoir, as shown in Figure B2. When the water level
reaches 5 m, the cylindrical gate opens by turning about the hinge A. Consider a 1 m run
of the cylinder. (a) Determine the horizontal component of the total hydrostatic force acting on the
curved surface AB. (6 marks) (b) Determine the vertical component of the total hydrostatic force acting on the curved surface AB. (6 marks)
(0) Hence, evaluate the magnitude and direction of the resultant hydrostatic force acting
on the curved surface AB. (6 marks)
(d) Find the weight per unit length of the cylinder. (7 marks) Figure B2 (P.T.O.) Foundations of Engineering Mechanics (ENGGlOlO) Page 7 B3. As shown in Figure B3, water is discharged from an open tank of 0.5 m width via a
0.2 m diameter circular duct to the atmosphere. On assuming that the water level in the
tank is steady and horizontal, and using the control volume as indicated, (a) show how the continuity and Bernoulli equations can be applied to ﬁnd the
velocities 141 and u;, and (13 marks) (b) ﬁnd the horizontal component of the force exerted by the ﬂowing water on the
outﬂow structure. (12 marks) State any further assumptions made in your analyses. control volume are“ Figure B3  END OF PAPER  ...
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