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Unformatted text preview: THE UNIVERSITY OF HONG KONG BACHELOR OF ENGINEERING: LEVEL 1 EXAMINATION FOUNDATIONS OF ENGINEERING MECHANICS (ENGGlOlO) Date: May 20, 2010 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 each Section). All questions carry the same marks. 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 (ENGGlOlO) Page 2 A1. (a) (b) SECTION A Prove that the forces taken by a pinjointed member with two pins only are always
along the line joining the two pin holes. ‘ (4 marks) Figure A1 shows a simpliﬁed scissors lift which is widely used in the motor
industry for jacking up cars. The four members AD, BC, CF and DE are all of the
same length 1.3 m. Members AD and BC are not directly linked whereas members
CF and DE are connected by a pin at point 0. The lift is power operated through a
hydraulic ram GH. Assuming that the weight of the car being jacked up is 15 kN
and the weights of the lift table and the four members AD, BC, CF and DE are all negligible. (i) Draw a free body diagram for the lift table and hence. determine the forces at
A and B. (7 marks) (ii) From the geometry of the lift, determine 9 and (t). _ (5 marks) (iii) Draw a free body diagram for member AD and hence determine the force in
the hydraulic ram. (6 marks) (iv) Determine the pressure in the hydraulic ram which has an internal diameter of
100 mm. (3 marks) Figure A1 (P.T.O.) Foundations of Engineering Mechanics (ENGGlOlO) Page 3 A2. (a) Figure A2(a) shows a member which is subjected to an axial loading P. Consider a
plane with its normal at an angle 0 from the axial direction. Show that the normal
stress 0 and shear stress I on this oblique plane can be expressed as o = —P—c0520
A0 1: = —P—sin0 c050 Ao where A0 is the crosssectional area at 0 = 0°. Determine the maximum and minimum values of c and 1: and hence draw the graphs of o and 1 against 0 from 0
= 0° to 360°. (8 marks) Figure A2(a) (b) A wooden member with a 70 mm x 110 mm rectangular cross section will be
fabricated with an inclined glue joint. If the allowable stresses for the glue are
‘ 5.0 MPa in tension and 2.9 MPa in shear, determine (i) the optimum angle 0 for the glue joint; (3 marks)
(ii) the maximum safe load P for the wooden member; and (2 marks) (iii) using the graphs in (a), explain why your solutions to (i) and (ii) above are
valid for 0° S 0 < 45° but not for 45° S 0 S 90°. (4 marks) [Qn. A2 is cont’d on Page 4] (P.T.O.) Foundations of Engineering Mechanics (ENGGlOlO) Page 4 [Qn. A2 is cont’d] (c) Figure A2(b) depicts an assembly consisting of a steel bolt and an aluminium collar. The pitch of the single threaded bolt is 3 mm and its crosssectional area is
600 mmz. The cross—sectional area of the collar is 900 m2. The nut is brought to a
snug position and then given an additional 1/8 of a turn. Determine the stresses in
the aluminium collar and the steel bolt. Given the Young’s moduli of elasticity of
steel and aluminium are ES = 200 GPa and EA] = 70 GPa respectively. (8 marks) 50mm Hr....'.....‘
lll llllllllllll Steel Bolt l
I runny" Aluminium Collar Figure A2(b) (13.10.) Foundations .of Engineering Mechanics (ENGGlOlO) Page 5 A3. Figure A3(a) and (b) shows the bar ACE is ﬁxed at both ends and loaded by a torque T0
at point C. The material of the bar is the same throughout segments AC and CB. The
diameter, the polar moment of inestia and the length of each of the two segments AC and CB are as shown in the ﬁgure. Obtain formulas for :
(a) the reactive torques T A and T3 at the ends; I (10 marks) (b) the maximum shear stresses ‘EAc and ICE in each segment of the bar; and (8 marks) (c) the angle of rotation (bc at the cross section where the load To is applied. (7 marks) Foundations of Engineering Mechanics (ENGGl 010) Page 6 SECTION B B1. (a) A test track for motor vehicles is purposely designed to have its road surface
inclined sideway at bends so that a tested vehicle can run at higher speeds through
these bends. Figure Bl(a) shows a motor vehicle running at a bend of radius R with its road surface inclined at 9. Radius of bend = R <————————— Note : The direction of
movement of the
motor vehicle is
into the paper. Figure B l (a) (i) Draw a free body diagram for the motor vehicle to show all the forces acting
on it. . (3 marks) (ii) If the coefﬁcient of static ﬁiction between the tyres of the motor vehicle and
the road surface is us, determine the maximum speed that the motor vehicle
can be driven through the bend without skidding. Express your answer in terms of R, 6 and us. (6 marks) (b) A sky diver and his parachute weigh 890 N. He is falling vertically at 30.5 m/s
when his parachute opens. With the parachute in its open mode, the magnitude of the drag force (in Newton) is 0.50 2, where u is the speed of the sky diver. (i) What is the magnitude of the sky diver’s acceleration at the instant the
parachute opens? (3 marks) (ii) What is the magnitude of his velocity when he has descended 6.1 m from the
point where his parachute opens? (6 marks) (c) Figure Bl(b) shows a 2m bar sliding on the plane surfaces. Point B is moving to
the right at 3 m/s. What is the velocity of the midpoint G of the bar? (7 marks) [Qn. B1 is cont’d on Page 7] (13.10.) Foundations of Engineering Mechanics (ENGGlOlO) Page 7 [Qn. B1 is cont’d] Figure B 1 (b) (P.T.O.) Foundations of Engineering Mechanics (ENGGlOlO) Page 8 B2. 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 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) (c) 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) Note : Take density of water = 1,000 kg/m3, acceleration due to gravity = 9.81 m/sz. Figure B2 (P.T.O.) Foundations of Engineering Mechanics (BNGGlOlO) Page 9 B3. Figure B3 shows a pipe bend. The diameter of the pipe bend is 300 mm at inlet and
150 mm at outlet and the ﬂow is turned through 60° in a vertical plane. The axis at inlet
is horizontal and the centre of the outlet section is 1.5 m above the centre of the inlet
section. The total volume of ﬂuid contained in the bend is 0.085 m3. Water is ﬂowing
through the bend at 0.2 m3/s when the inlet pressure is 140 kPa. Friction may be ignored. (a) Use continuity to ﬁnd the water velocities at the inlet and the outlet. (4 marks)
(b) Use the Bernoulli equation to ﬁnd the pressure at the outlet. (8 marks)
(c) Calculate the components of the impact force on water. (8 marks) ((1) Hence determine the magnitude and direction of the net force exerted on the bend.
(5 marks) / '\ Diameter, d2 = 150 mm 1.5 m Diameter, (11 = 300 mm
Pressure, P1 = 140 kPa ——>
Flow, Q = 0.2 m3/s Figure B3  END OF PAPER  ...
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