Q1) In a four-ram hydraulic steering gear the diameter of ram is 100 mm and the distance between the centre line of the rams and rudder stock is 815 mm. The maximum rudder angle is 35° and the by-pass valves lift at a pressure of 7.6 MN/m2. The tilter arms are of parallel circular section and maximum stress in the arms occurs at the junction to rudder stock which is 610 mm from the rudder stock center.
Calculate EACH of the following:
(a) The rudder stock diameter for maximum torsional stress of 75 MN/m2; (10)
(b) Diameter of tilter arm for maximum bending stress of 105 MN/m2. (6)
Q2) A uniform ladder of 45 kg mass and 5.6 m length rests at an angle of 30 ° above the horizonal with one end on ground. A pipe 0.6 m from the opposite end of the ladder provides the other support as shown in Fig. Q2. The coefficient of friction at the ground and the roller are 0.3 and 0.2 respectively.
Attempt EACH of the following:
(a) Sketch a clearly labelled force diagram for this system; (6)
(b) Calculate the maximum distance from the base of the ladder that a 20 kg mass can be supported before the ladder starts to slip. (10)
Q3) A 100 tonne locomotive is coupled to a 200-tonne train by a drawbar. It pulls the train up a 1 in 200 (sine) incline at a constant velocity of 20 km/hr against a tractive resistance of 50 N/tonne. During the ascent the draw bar fails.
(a) Power developed by the locomotive prior to the drawbar failure; (8)
(b) Minimum gap between the train and locomotive 10 seconds after the drawbar failure if the power developed by the locomotive remains constant. (8)
Q4) A drive pinion and gear wheel system provide a speed reduction ratio of 3 to 1. The 45 kg pinion has a 150 mm radius of gyration whilst the 420 kg gear wheel has a 440 mm radius of gyration. Under no load the pinion attains its rotational speed of 900 rpm in 150 revolutions from rest.
Calculate EACH of the following
(a) Time taken to attain maximum speed. (2)
(b) Total torque in pinion shaft to accelerate the gearing system; (10)
(c) Total kinetic energy in the system at maximum speed. (4)
Q5) A cam operated valve moves vertically with simple hormonic motion. The cam shaft speed is 600 rev/min and the valve is opened and closed during 160° of cam rotation. The valve travel is 100 mm and its mass is 1.8 kg. The valve opends downwards against a spring.
(a) Maximum velocity of the valve; (8)
(b) Instantaneous velocity of the valve when its displacement is 40 mm from the end of its downward travel. (2) (c) Minimum spring constant required at full opening to ensure that the valve remains in contact with the cam profile. (6)
Q6) A shearing machine has a flywheel of mass 1220 kg with a 0.58 m radius of gyration. During a 150 mm cutting stroke the speed falls from 200 to 180 rpm. The work done during cutting is equivalent to kinetic energy of the flywheel.
(a) Torque required to attain a speed of 200 rpm in 60 seconds from rest; (6)
(b) Average cutting force of the shearing machine; (8)
(c) Angular impulse transmitted to the flywheel during cutting. (2)
Q7) A 14 kg wheel and shaft runs in horizontal bearings. The shaft is 50 mm in diameter and has a cord wound around it with a hook at its free end. A 0.3 kg mass hanging from the hook is just sufficient to overcome friction, whilst a 2 kg mass fall 1.05 m in 8 seconds from rest.
(a) Radius of gyration for the wheel and shaft; (12)
(b) Torque transmitted to the wheel and shaft by the 2 kg mass. (4)
Q8) A close coiled helical spring consists of 24 coils of tubular steel. The mean diameter of the coils is 75 mm, external diameter of the tube is 12.5 mm and its thickness is 2.5 mm. The shear stress in the material is linited to 70 N/mm2.
Calculate EACH of the following :
(a) Maximum axial load the spring can carry; (10)
(b) Deflection under this load. (6)
Modulus of rigidity for spring material = 90 GN/m2.
Q9) A cylindrical gas bottle is pressurized to 80 bars. The internal diameter of the bottle is 125 mm with wall thickness of 5 mm.
(a) Tensile stress on an oblique plane at 30° to the longitudinal axis of the bottle; (6)
(b)Shear stress on the same oblique plane; (4)
(c) Magnitude and direction of the resultant stress on the same oblique plane. (6)
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