Q1. A 100 N cylinder with a radius of 600 mm is supported between crosspieces which make an angle of as shown in Fig. Q1. The crosspieces are pinned at point C and tied by a cord between points D and E.
Calculate the tension in the cord DE. (16)
Q2. A 30 kg is tethered to a 15 kg block on a plane inclined at above the horizontal as shown in Fig.Q2. The coefficient of friction between the 30 kg block and the plane is 0.25. The coefficient of friction between the 15 kg block and the plane is 0.375.
Calculate the tension in the cord. (16)
Q3. A ship leaves port travelling North West at 12 knots. A second ship leaves the same port 3 hours later travelling West of South at 15 knots. Determine how long after the second ship leaves port that the ships will be 100 nautical miles apart. (16)
Q5. A coal truck with a total mass of 5 tonnes has four 300 kg wheels that are each of 0.6 m in diameter with a 0.4 m radius of gyration. It is initially travelling at 3 m/s as it begins to descend a 3o incline that is 250 m in length. Tractive resistance to motion is 60 N/ tonne. Calculate EACH of the following:
a) The energy lost descending the incline; (2)
b) The speed of the truck at the bottom of the incline. (14)
Q6. Three masses A, B and C are fixed to a balanced disc at radii 120 mm, 100 mm and 80 mm respectively as shown in Fig. Q6.
A has mass 1 kg, B has mass 0.5 kg and C has mass 0.7 kg. A fourth mass D is required to statically balance the system. Calculate EACH of the following:
a) The magnitude of the balancing mass to be fitted at a radius of 60 mm; (12)
b) The angular position of the balancing mass in relation to mass A. (4)
Q7. A reciprocating engine runs at 110 rpm with a stroke of 1.6 m and a connecting rod 2.4 m in length. It imparts simple harmonic motion to a 250 mm diameter piston. When the crank pin is 32o beyond top dead centre the pressure on the piston is 0.8 MN/m2.
Calculate EACH of the following:
a) The instantaneous velocity of the piston. (6)
(b) The instantaneous torque at the crank pin. (8)
(c) The instantaneous acceleration of the piston. (2)
Q8. A solid intermediate shaft is to be fitted to a 16 MW engine operating at 110 rpm. The shaft is in sections with flanged couplings with 12 bolt holes on a pitch circle diameter that is 1.5 times greater than the shaft diameter. The limiting shear stress for the shaft is 180 MN/m2 and 160 MN/m2 for the bolts respectively.
(a) The shaft diameter for a safety coefficient (factor of safety) of two; (8)
(b) The diameter of the bolts for a safety coefficient (factor of safety) of two. (8)
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