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Q6. A steel shaft is 650 mm long and 48 mm diameter. It transmits a power of 20 kW at a speed of 120 rev/min. The shaft is to have a hole of 25 mm diameter bored axially from one end. The angle of twist between the ends of the shaft is not to exceed 1.5°. Calculate EACH of the following:
(a) The maximum depth to which the hole can be bored;

(b) The maximum torsional shear stress in the shaft.

Note: Modulus of Rigidity = 80 GN/m².

Q6. A high voltage cable, 220 m long, consists of 24 strands of 3 mm diameter aluminium wire and eight strands of 4 mm diameter steel wire. It is subject to a tensile force of 16 kN.

Calculate EACH of the following:

(a) The stress in EACH material;

(b) The extension of the cable.

Note: Modulus of Elasticity for Steel = 190 GN/m²

Modulus of Elasticity for Aluminium = 68 GN/m²

Q4. 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 0-100°C. The output signal range is to be 20-100 kN/m². The characteristic of the input bellows is 10 μm/°C, and the characteristic of the nozzle is 0.2 kN/m² per μm of flapper movement.

The gain of the device =  (% Change in output)/(% Change in input)

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 0.7;

(e) The output pressure at 90°C with a gain of 0.7 if the output pressure was 50 kN/m² at a temperature of 80°C.

Q2. A starter motor with 24 teeth engages with a flywheel rim having 384 teeth. The rotating parts of the starter motor have a mass of 12 kg with a radius of gyration of 0.1 m and the engine rotational mass is 700 kg with an effective radius of gyration of 0.5 m. The engine must be accelerated to 200 rev/min from rest in 6 seconds. Calculate EACH of the following:

(a) the angular acceleration of the starter motor;

(b) the average driving power required by the starter motor.

Q2. A hollow square section beam of external dimension 200 mm, and thickness 10 mm, is loaded as shown in Fig Q6. Calculate EACH of the following:

(a) The maximum stress due to shear in the beam;

(b) The point of contraflexure

Q2. A single plate clutch with both sides effective has an outside diameter of 400 mm and an inside diameter of 180 mm. The clutch is designed to transmit 20 kW at 720 rev/min when new. In this condition the coefficient of friction between the clutch contact surfaces can be assumed to be 0.6.

Once the clutch starts to wear and the surfaces become contaminated, the maximum power that the clutch can transmit will be reduced. The axial thrust on the clutch faces is provided by eight identical springs placed in parallel, each with a spring stiffness of 16 kN/m. Maximum wear of the clutch plates is limited to 0.6 mm at each contact surface. Calculate EACH of the following:

(a) The total spring load (W) required when the clutch is new;

(b) The minimum coefficient of friction of the worn clutch plates if 80% of the original maximum power can be transmitted.

Note: For constant pressure T =  (2μW(r₁³- r₂³)/(3(r₁²- r₂² )

For constant pressure T = μNW(r₁+ r₂ )/2

n = Number of surfaces in contact