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# dec09 - THE UNIVERSITY OF HONG KONG BACHELOR OF ENGINEERING...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG BACHELOR OF ENGINEERING: LEVEL 1 EXAMINATION FOUNDATIONS OF ENGINEERING MECHANICS (ENGGlOlO) Date: December 9, 2009 Time: 2:30 pm. — 5:30 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 FIVE questions. All questions carry the same marks. Use answer books of different colours for Section A (Pink) and Section B (Green). 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. Foundations of Engineering Mechanics (ENGGIOIO) Page 2 SECTION A A1. Figure A1 Shows a simpliﬁed sketch of the mechanism used to raise the bucket of a bulldozer. The bucket and its contents weigh 10 kN and have a centre of gravity at H. Arm ABCD has a weight of 2 kN and a centre of gravity atB; arm DEFG has a weight of 1 kN and a centre of gravity at E. The weight of the hydraulic cylinders can be ignored. (a) Draw a free body diagram for the complete mechanism. Hence, determine the force in the horizontal cylinder CJ. (5 marks) (b) Draw a free body diagram for the bucket and its contents. Hence, determine the force in the horizontal cylinder E1. (4 marks) (c) Draw a free body diagram for arm DEFG. Determine all the forces acting on this arm for the position shown. (11 marks) Figure A1 (P.T.O.) Foundations of Engineering Mechanics (ENGGlOlO) Page 3 A2. (a) (b) Two wooden planks, each 12 mm thick and 225 mm wide, are connected by the dry mortise joint, as shown in Figure A2(a). Assume that the wood used shears off along its grain when the average shear stress exceeds 8 MPa. (i) Sketch the failure mode of the joint. (2 marks) (ii) Determine the magnitude of P at which the joint fails. (5 marks) Figure A2(a) The structure shown in Figure A2(b) consists of two rods AB and BC, which have cross-sectional areas 400 and 800 m2, reSpectiver. (i) Assume that one of the rigid walls is removed; determine the total elongation of the rods when the temperature is increased by 50 oC. (2 marks) (ii) Hence, or otherwise, determine the axial forces in the rods when the temperature is increased by 50 °C. (7 marks) (iii) Further to part “ii”, determine the displacement of location B. Assume that the coefﬁcient of thermal expansion and elastic modulus of the two rods are 10'5 / CC and 200 GPa, respectively. (4 marks) C A B 400 mm ' 400 mm Figure A2(b) (P.T.O.) Foundations of Engineering Mechanics (ENGGIOIO) Page 4 A3. A motor driving a tapered high strength aluminum alloy tube AB and a solid circular high strength aluminum alloy bar BC at 10 Hz as shown in Figure A3. The diameter of the tapered tube AB varies linearly from point A having a diameter of 60 mm to point B having a diameter of 30 mm, and the tube has constant thickness of 5 mm. The solid bar BC has a constant diameter of 30 mm. A gear at C is connected at the end of the bar for the purpose of driving machinery. The tube AB and the bar BC have a maximum shear stress of 205 MPa. The shear modulus of elasticity of the aluminum alloy is 28 GPa. (a) What is the maximum power P of the motor should be driven without exceeding the maximum shear stress? (10 marks) (b) If the motor delivers 10 kW of power, what is the angle of twist ¢AC (in degrees) between the motor at A and the gear at C. In this part of the question, the polar moment of inertia of the tube AB can be represented by an approximate formula It [(100]3 t IP05): 4 where d(x) is the diameter as a function of x, and t is the thickness of the tube. (10 marks) (13.10.) Foundations of Engineering Mechanics (ENGGIOIO) Page 5 SECTION B B1. As shown in Figure Bi, the two crates are connected through a belt which runs over a pulley with grooved wheel surface such that the belt does not slip around the wheel. The wheel is made of a uniform circular disk of mass mw=10 kg and a certain radius rw. The masses of the crates are m; = 30 kg and ma = 20 kg, and the coefﬁcients of friction between crate A and the inclined surface are as = 0.2 (static) and ,uk 3 0.1 (dynamic), respectively. The second moment of mass for the uniform wheel is calculated as 1w = I rzdm = muff/2 . Note that the numeric value of rw is not needed in calculation. (3) Draw free-body diagrams for crate A and crate B separately when the crates move. (5 marks) (b) Prove that the crates do move. 7 (5 marks) (0) Determine the acceleration of the crates. Hint: there are different belt tensions at the two sides of the pulley wheel. (10 marks) Figure BI (13.10.) Foundations of Engineering Mechanics (ENGGIOIO) Page 6 Take density of water = 1,000 kg/m3, acceleration due to gravity = 9.81 III/52. B2. (a) Shown in Figure B2(a) is a tank containing water and mercury. Draw the distributions of hydrostatic pressure acting on the plane surfaces denoted by AB, BC, CD, DE and EF. (5 marks) A D E B C F Figure B2(a) (b) Shown in Figure BZ(b) is a rectangular gate CD, which is hinged at the top and has no support elsewhere. To keep equilibrium, a moment has to be applied at the hinge. .1:2:;fryer-mam,»am,-:w¢€mmaat§saasmagi: 2 m sectional View front‘view Figure B2(b) (i) Draw a free body diagram of the gate. (2 marks) (ii) Find the magnitude of the resultant hydrostatic force on the gate. (5 marks) (iii) Determine the depth of the centre of pressure. (4 marks) (iv) Calculate the moment to be applied at the hinge to keep the gate in equilibrium. Is the moment clockwise-or counter-clockwise? (4 marks) (1)10.) Foundations of Engineering Mechanics (ENGGIOIO) Page 7 B3. As is shown in Figure B3, 3 ﬂow-metering device consists of a stagnation probe at- station 2 and a static pressure tap at station 1. The cross-sectional area of the tube at station 2 is one-half that at station 1, where the diameter of the tube is 10 cm. Air with a density 1.2 lag/m3 ﬂows through the duct. A water manometer is connected between the stagnation probe and the pressure tap, and a reading of 1 cm is measured. (a) (b) (d) (e) (1) 10 cm Figure B3 Draw a sketch to describe the ﬂow near the stagnation probe. (3 marks) By continuity, relate the velooities at the two stations. (2 marks) By Bernoulli equation, relate the pressure at station 1 to the velocity at station 2. (4 marks) Hence, using the manometer reading, evaluate the pressures and velocities at stations 1 and 2. (6 marks) Calculate the force acting on the convergent part of the duct. _ (5 marks) - ND OF PAPER -7 ...
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