Q1. Block B rests upon block A on an inclined plane and is tethered parallel to the incline and secured to a wall that is perpendicular to the same incline as shown in Fig Q1. Blocks A and B weigh 90 N and 30 N respectively and the coefficient of friction at all contact surfaces is one third.
Calculate EACH of the following:
(a) The minimum angle which will cause block A slide down the incline; (12)
(b) The tension in the tether holding block B at this angle of incline. (4)
Q2. A 500 kg mass is to be hauled up a 10o incline by a cable passing over a 200 mm diameter pulley to a second mass that is free to move vertically downwards. The coefficient of friction on the incline is 0.35 and the torque at the pulley bearings is a constant 40 Nm. Starting from rest, the 500 kg mass travels 8.5 m in 35 seconds.
(a) The magnitude of the required second mass; (10)
(b) The kinetic energy of the second mass after 35 seconds; (3)
(c) The rotational speed of the pulley in rpm. (3)
Q3. A projectile is fired at an angle of 27.5o above the horizontal ground from a cliff top 150 m high. The projectile hits a target 530 m away from the base of the cliff.
(a) The initial velocity of the projectile; (10)
(b) The magnitude and direction of the projectile’s impact velocity. (6)
Q4. A screw jack consists of single start, square form screw thread of 8 mm pitch and a mean diameter of 100 mm. The mean diameter of the bearing surface under the loading cap is 300 mm and the effort handle has an effective operating length of 600 mm from the axis of the screw thread. The coefficient of friction are 0.15 and 0.25 at the square thread and the bearing surface respectively.
(a) The minimum force required to raise a mass of 300 kg. (10)
(b) The minimum force required to lower the same mass. (6)
Q5. A sphere rolls up a plane inclined above the horizontal with an initial velocity of 10 m/s. Calculate EACH of the following:
(a) The maximum linear displacement of the sphere up the plane. (10)
(b) The time taken for the sphere to cover this distance up the plane. (6)
Note:
the moment of inertia for the sphere = 2/5 mr2
Q6. A 300 mm diameter solid steel shaft is shrink fitted with a 340 mm bronze linear. The composite shaft transmits a maximum torque of 136 kNm.
(a) The maximum shear stress in the steel shaft. (8)
(b) The minimum shear stress in the bronze bar. (4)
(c) The common angle of twist per unit length in degrees. (4)
Modulus of rigidity for steel = 90 MN/m2
Modulus of rigidity for bronze = 40 MN/m2
Q7. A solid steel bar 125 mm in diameter is encased in copper linear that is 10 mm thick. The component supports a compressive axial load of 250 kN evenly distributed over the full cross-sectional area. Calculate the final stress in the steel bar and copper linear if the temperature of the compound component is evenly increased by 120oC. (16)
Modulus of Elasticity for steel = 206 GN/m2
Modulus of Elasticity for copper = 125 GN/m2
Coefficient of linear expansion for steel = 11×10-6m/deg.C
Coefficient of linear expansion for copper = 17×10-6m/deg.C
Q8. A 600 mm internal diameter pipe is made of mild steel plate 20 mm thick. When running full of fresh water, the maximum stress due to bending is restricted to 80 MN/m2 . The pipe is to be simply supported at two points. Calculate the maximum permissible span. (16)
Density of steel = 7830 kg/m3.
Q9. A pressure operated valve has a diameter of 200 mm as shown in Fig Q9. A pressure of 55 kN/m2 fully opens the valve. The valve opens 50 mm against the loading of concentric springs. Spring ‘A’ has an initial compression of 40 mm. Spring ‘B’ has a stiffness of 11,400 N/m and its free length is 15 mm greater than the free length of the spring ‘A’.
(a) The stiffness of spring ‘A’ (8)
(b) The work done to open the valve. (8)
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