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Cork Institute of Technology
Higher Certificate in Engineering in Mechanical Engineering – Award
(National Certificate in Engineering in Mechanical Engineering - Award)
(NFQ – Level 6)
Summer 2005
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 Mr. R. Simpson
Section A – Mechanics of Machines
Q1. (a) State the mathematical relationship between the Angular Impulse of a Torque, and the change in Angular Momentum produced by the impulse. (5 marks)
(b) A shaft, which is rotating freely at 750 rpm, is connected by the operation of a clutch, to a shaft which is initially at rest. The moment of inertia of the rotating shaft is 65 kg-m^2 , and that of the shaft at rest is 30 kg-m^2. (i) Assuming no external torque acts on the system, calculate the common speed of the two shafts after the clutch stops slipping. (6 marks) (ii) Calculate the angular impulse between the two shafts due to the operation of the clutch. (5 marks) (iii) Calculate the time during which the clutch is slipping before the two shafts reach their common speed, if the maximum torque rating of the clutch is 750 N-m. (4 marks)
Q2. As a check on the basketball before the start of a game, the referee drops the ball from an overhead position, 2.1 m above the floor, onto the floor. The ball rebounds vertically to a height 1.1 m above the floor. (a) What type of collision, or impact, would the impact of the ball on the floor be classified as, and explain what changes, if any, in momentum, and energy occur in such a collision. (6 marks) (b) (i) Calculate the velocity of the ball just before, and just after, it strikes the floor. (4 marks) (ii) Calculate the ‘coefficient of restitution’, ‘e’ of the ball on the floor. (5 marks) (iii) Calculate the percentage of the original energy lost during the impact, and explain briefly, the form into which this ‘lost’ energy might have been converted. (5 marks)
Q3. (a) Define the Law of the Simple Machine. (4 marks) (b) A test on a machine gave the following results: Load kN 10 20 30 40 50 60 70 Effort kN 2.2 4.19 6.21 8.2 10.2 12.18 14. (i) Determine the Law of this machine. (5 marks) (ii) If the Velocity Ratio of this machine = 8, draw the load-friction effort graph. (5 marks) (iii) Calculate the Limiting Efficiency of this machine. (3 marks) (iv) Calculate the effort required to overcome friction at a load of 45 kN, and indicate the equivalent value on the load-friction effort graph. (3 marks)
Q4. (a) Define carefully, with the aid of a sketch: (i) Centripetal and (ii) Centrifugal forces arising from the rotation of a body about an axis, indicating clearly the difference between them. (8 marks) (b) A rotor, of mass 4 tonnes, is mounted on a horizontal shaft which is supported by two equally spaced bearings. If the centre of gravity of the rotor is 1.5 mm out of alignment from the axis of rotation, calculate the maximum and minimum load on each bearing when the speed of the shaft is 750 rpm. (12 marks)
Section B
Q7. (a) An axial tensile load of 120 kN, is applied to a 28 mm diameter steel bar. The extension of a 250 mm gauge length of the bar under this load is found to be 0.23 mm. Calculate the Modulus of Elasticity of the material of the bar. (5 marks) (b) The bar is to be bored axially to produce a cylinder, with the same outside diameter of 28 mm, to reduce weight. If the maximum allowable stress in the material is limited to 235 MN/m^2 , with the load remaining at 120 kN, calculate the maximum possible inside diameter of the cylinder. (7 marks) (c) Calculate the change in diameter of: (i) the bar in case (a) above, under the 120 kN load (ii) the cylinder in case (b) above, under the limiting stress of 235 MN/m^2. (8 marks) Assume Poisson’s Ratio υ = 0.3, and take the value of E calculated in (a) above.
Q8. (a) State the equation of the Simple Theory of Torsion and clearly define each of the symbols used. (6 marks (b) The driveshaft of a machine is required to transmit a torque of 0.7 kN-m. The shaft is solid, and stepped, consisting of two sections, the length of the smaller diameter section being 0.5 m, and that of the larger diameter section being 0.75 m long. If the maximum permissible shear strength of the shaft material is 55 MN/m^2 , and the maximum twist in the shaft is not to exceed 1.5 degrees, calculate the diameter of each of the two sections of the shaft. Assume G, the Modulus of Rigidity of the shaft material equals 75 GN/m^2. (14 marks)
