Q1. The mass centre of a solid 25 cm diameter cylinder weighing 500 N is initially rolling without slipping at 10 m/s up a slope inclined at an angle of 20° above the horizontal.
Calculate the time it will take to reach its highest point of travel. (16)
Q2. A 220 mm long steel bolt has a 30 mm diameter for 150 mm of its length and a 2 5 mm diameter for the remainder of its length. The bolt is tightened so that there is a total extension of 0.4 mm.
Calculate EACH of the following:
(a) the tensile force within the bolt. (6)
(b) the strain energy stored within the bolt. (10)
Note: Modulus of Elasticity for the spring boll material = 190 GN/m2
Q3. A cam operated valve moves vertically with simple harmonic motion. The camshaft speed is 740 rpm and the valve is opened and closed during 140° of cam rotation. The valve travel is 90 mm, its mass is 1.7 kg and the valve opens vertically downwards against a spring.
(a) The minimum spring constant required at full opening to ensure that the valve remains in contact with the cam profile. (10)
(b) The percentage difference in valve velocity between maximum and a 20 mm displacement from the mid-travel position. (6)
Q4. A four-stroke single cylinder engine produces 260 Kw at 600 RPM with a 15% energy fluctuation of the work done per cycle. A flywheel is to be fitted to stabilise the speed for power generation so that the frequency is 60 ± 0.15 Hz.
Calculate the diameter of a solid flywheel that is 300 mm thick. (16)
Note: Density of the flywheel material= 7800 kg/m3
Q5. A 2.5 tonne pile driver fails vertically onto a 500 kg pile driving it 325 mm into horizontal ground against an average resistance force of 285 Kn.
(a) the vertical height the pile driver falls. (10)
(b) the percentage of energy lost during impact. (6)
Q6. A 450 mm internal diameter pipe is made of mild steel plate 25mm thick. When running full with diesel fuel oil the maximum stress due to bending is restricted to 80 MN/m2 The pipe is to be simply supported at its TWO end points.
Calculate the maximum permissible length of pipe.
Note: Density of diesel Fuel oil = 860 kg/m3
Density of mild steel= 7860 kg/m3
Q7. A winch motor drives a pinion with 120 teeth. The friction at the motor bearing is a constant 20 Nm. The pinion meshes with a gear wheel that has 360 teeth which drives 120 mm diameter shaft. The horizontal shaft supports a winch drum with an effective diameter of 420 mm and the assembly is balanced in bearings with a coefficient of friction of 0.12 as shown in Fig Q7.
The winch drum raises a mass of 2.25 tonnes at a constant vertical velocity of 0.3 m/s. (16)
Calculate the minimum input power for an 86% efficient motor.
Q8. A sphere rolls without slipping up a smooth plane inclined 25° above the horizontal with an initial velocity of B mis.
(a) the maximum linear displacement of the sphere up the plane. (10)
(b) the time taken for the sphere to roll 5 m back down the plane from this point. (6)
Note: Moment of Inertia for o sphere=2/5mr2
Q9. A 25 kg wheel and shaft runs in horizontal bearings. The shaft is 60 mm in diameter and has a cord wound around it with a hook at its free end. A mass of 0. 7 kg hanging f ram the hook is just sufficient to overcome friction whilst a 4.5 kg mass falls 1.8 min 10 seconds from rest.
Calculate the minimum torque transmitted to the wheel and shaft by the falling 4.5 kg mass. (16)
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