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Q4. A Hartnell governor has two flyweights each of mass 0.5 kg. The flyweight arm length is 60 mm and the sleeve arm length is 25 mm. At a governor speed of 1600 rev/min and rising, the radius of the flyweights is 30 mm. A speed increase of 2% causes the central sleeve to move by 1.2 mm. Friction in the governor is equivalent to a force of 40 N at the sleeve. Calculate the spring stiffness.

Q7. A crane lifting wire of 22 mm diameter is found to extend by 1.2 mm per meter length when subjected to a tensile load of 70 kN.

The crane wire is attached to a spare piston ready for lifting. Whilst the crane wire is still slack the piston becomes dislodged from its storage mounting and falls a distance of 30 mm before taking up the slack in the crane wire. The crane wire is 3.8 m long and the instantaneous extension due to the falling piston is 2.8 mm. Calculate EACH of the following:

(a) The modulus of elasticity for the crane wire material;

(b) The mass of the piston.

Q1. A winch motor drives a pinion with 320 teeth, and friction at the motor bearings is constant at 18 Nm. The pinion then meshes with a gear wheel having 960 teeth which drives a shaft of 140 mm diameter. This shaft is supported in bearings having a coefficient of friction of 0.1 and drives a winch drum of diameter 380 mm. Calculate EACH of the following:

(a) The driving torque required by the motor when raising a mass of 2 tonnes at steady speed;

(b) The input power required by the motor when raising the load in Q3 (a) at a steady speed of 0.2 m/s if the motor efficiency is 88%.

Q3. The piston of a reciprocating engine has a mass of 800 kg. The engine has a stroke of 2.4 m and a bore of 950 mm. At an engine speed of 90 rev/min the cylinder pressure just after TDC is 110 bar. The piston rod has a diameter of 340 mm. The piston may be assumed to move with simple harmonic motion. Calculate EACH of the following:

(a) The velocity of the piston when 0.8 m from TDC;

(b) The maximum acceleration of the piston;

(c) The nature and magnitude of the stress in the piston rod just after TDC.

Q3. A basic flapper/nozzle device is shown in Fig Q4. The pneumatic signal for the input bellows unit is proportional to the measured temperature within the range 0 – 500℃. The output signal range is to be 20 - 100 kN/m².

The characteristic of the input bellows is 3 mm/ºC, and the characteristic of the nozzle is 0.1 kN/m² per mm of flapper movement. The gain of the device = % change in output

Calculate EACH of the following:

(a) The flapper movement at the nozzle for 100% input change;

(b) The resulting change in output;

(c) The gain of the device;

(d) The new setting of x, the distance from the pivot to the nozzle, to achieve a gain of magnitude 0.7;

(e) The output pressure at 450°C with a gain of magnitude 0.7 if the output pressure was 50 kN/m² at a temperature of 430°C.

Q8. A compound shaft consists of a 25 mm thick bronze sleeve fitted over a 375 mm diameter steel shaft. The compound shaft transmits 2.9 MW at 92 rev/min. Calculate EACH of the following:

(a) The torque transmitted by the bronze sleeve;

(b) The torque transmitted by the steel shaft;

(c) The maximum shear stress in the bronze sleeve;

(d) The maximum shear stress in the steel shaft.

Note: Modulus of Rigidity of the steel = 80 GN/m²

Modulus of Rigidity of the bronze = 45 GN/m²

Q3. A cable consists of one steel wire 6 mm diameter and eight brass wires each 3 mm diameter. The stress in the brass wires is not to exceed 50 MN/m². Calculate EACH of the following:

(a) The maximum load the cable can carry;

(b) The equivalent modulus of elasticity for the cable.

Note: Modulus of Elasticity for Steel = 210 GN/m²

Modulus of Elasticity for Brass = 80 GN/m²

Q4. A steel beam of symmetrical I section is shown in Fig Q9. The beam has a mass of 30 kg per meter run and is 9 m long. The beam is simply supported at each end and the maximum bending stress is not to exceed 140 MN/m² at any point. Calculate EACH of the following:

(a) The maximum uniformly distributed load that can be carried;

(b) The minimum radius of curvature when this maximum uniformly distributed load is carried.

Note: Modulus of elasticity for steel = 210 GN/m²