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Cork Institute of Technology
Higher Certificate in Engineering in Mechanical Engineering – Award
(NFQ Level 6)
Summer 2007
Mechanical Technology - Mechanics
(Time: 3 Hours)
Instructions Answer Five questions; Two questions from Section A, Two from Section B, and any One other question. Use separate answer books for each Section. All questions carry equal marks.
Examiners: Mr. J. M. Brady Mr. J. Connolly Dr. P. Delassus
Section A – Mechanics of Machines
Q1. (a) Explain carefully the meaning of the ‘Work-Energy Equation’ (5 Marks)
(b) A van, of mass 1.5 tonnes accelerates from a speed of 25km/hr to a speed of 50km/hr over a horizontal distance of 70m. Using the ‘Work-Energy Equation, calculate: (i) the average tractive force required to achieve the acceleration (8 Marks) (ii) the average braking force required to bring the van to rest from a speed of 50km/hr over 25m. (7 Marks)
Q2. (a) State the mathematical relationship between the Angular Impulse of a Torque, and the change in Angular Momentum produced by the Impulse. ( marks) (b) A cast-iron pulley is 220mm wide, and 30mm thick, with a mean diameter of 2.0m. Considering the pulley as a thin ring, calculate: (i) The Moment of Inertia of the pulley ( marks) (ii) The Torque required to produce a pulley speed of 6 rev/sec in 20 seconds, from rest. ( marks) (iii) The time taken for the same torque to accelerate the pulley speed from 6 rev/sec to 10 rev/sec, using the Angular Impulse-Angular Momentum
relationship. ( marks) Note: Density of cast-iron = 7500 kg/m 3 Q3. In a test carried out on the screw-jack lifting system on the table of a large forming press, the following results were recorded: to lift a Load of 1.25 tonnes, an Effort of 0.6 kN was required and to lift a Load of 2.1 tonnes, an Effort of 0.95 kN was required. The Velocity Ratio of the screw-jack system was 35, and assuming that both test results fall on a straight line, (a) derive the Law of this Machine; ( marks) (b) calculate the Efficiency of the machine at the Load value of 1.25 tonnes; ( marks) (c) calculate the Effort required to lift a load of 2.5 tonnes. ( marks)
Q4. A boat, weighing 3.0 tonnes is to be hauled by a winch, at a speed of 10 m/min, along a horizontal slipway into a shed to have an inboard engine, weighing 1.0 tonne fitted. (a) If the winch exerts a pull of 10 kN during the operation, calculate the coefficient of friction between boat and slipway. (5 marks) (b) If the same winch is used to pull the boat, with installed engine, out of the shed across the slipway, at the same speed, calculate the pull it must now exert. (5 marks) (c) If the speed required to pull the boat out of the shed was reduced to 8 m/min, what pull is now required? (d) Calculate the power rating of the winch, required to haul the boat out of the shed, with installed engine, at a speed of 10 m/min. (7 marks)
Section B – Mechanics of Materials
Q5. A steel bar of 40 mm diameter and 1600 mm long is subjected to a tensile test, in which an axial load of 150.2 kN is applied to the bar. The bar extension under this load is measured as 0.86 mm, and the reduction in diameter is measured as 0.0072 mm. (a) Calculate:
Q7 (a) State the equation of the Simple Theory of Bending, and define carefully each of the symbols used. ( marks) (b) The stresses set up in the top and bottom surfaces of a uniform I-section beam are 55 MN/m^2 compressive in the top surface, and 55 MN/m^2 tensile in the bottom surface. The beam is 180 mm wide by 320 mm deep, with flange and web thicknesses each 25 mm. (i) Calculate the Second Moment of Area of the beam cross-section, about it’s Neutral Axis. (Note: I (^) NA for a rectangle = BD
3 ) ( marks) (ii) Calculate the magnitude of the Bending Moment causing the stresses in the beam described above. ( marks) (iii) Is the Bending Moment positive, or negative, causing a sagging or hogging beam? ( marks)
Q8 (a) Explain the term ‘compound bar’ ( marks) (b) Explain: (i) the Equilibrium Equation and (ii) the Compatibility Equation as they are applied to compound bars. ( marks) (c) The suspension system for a set of lighting fittings consists of a series of compound bars, each formed from four brass wires of 2.5 mm dia, and one central steel wire of 1.5 mm dia. Assuming that all of the wires are of equal length, and that each ‘compound bar’ assembly carries a load of 500 N, calculate: (i) the stress in each of the wires. ( marks) (ii) the ‘equivalent’ or ‘combined’ modulus for the compound bar. (4 marks) (iii) the total extension of the bar, if it is initially 0.75 m long. ( marks) Take E for brass = 100 GN/m 2 and E for steel = 200 GN/m^2
