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Q4. A 2 m long uniform ladder of mass 15 kg rests against a smooth vertical wall. The ladder stands on an inclined plane, which rises at 10° away from the wall.

(a) Sketch the ladder arrangement showing all forces acting.

(b) Calculate the largest angle possible between the ladder and the wall for the ladder to be stable and not slide away from the wall.

Note: Coefficient of friction between the ladder and the inclined plane is 0.24

Q3. An engine room lift cage has a mass of 1 tonne. The hoist wire is wound around a motor driven drum, with the lift cage on one end and a balance mass of 0.8 tonne suspended from the other end. The drum is 1.4 m diameter with a mass of 250 kg and radius of gyration of 450 mm.

The maximum tension in the hoist wire is not to exceed 12 kN. Calculate EACH of the following:

(a) The maximum allowable acceleration of the lift cage when being raised;

(b) The driving torque required at the drum to achieve the acceleration found in part Q2(a);

(c) The motor output power when the lift is moving upwards with a constant velocity of 3 m/s.

Q5. A Hartnell governor has two rotating flyweights each of mass 0.8 kg. The pivot arms are vertical and the flyweights are at an orbital radius of 100 mm at a mean speed of 720 rev/min.

The length of the flyweight arms is 120 mm and the length of the sleeve arms is 80 mm. The spring stiffness is 30 kN/m and friction in the governor is equivalent to a force of 12 N at the sleeve if the governor speed increases or decreases. Calculate EACH of the following:

(a) The spring force when the governor is running at its mean speed, assuming friction is not present;

(b) The vertical movement of the sleeve for a speed decrease of 20 rev/min, including the effect of friction.

Q2. A piece of steel is tested in compression and when the compressive yield stress is applied to a test specimen of 100 mm length, the compression is measured to be 0.16 mm.

A strut is to be made from the same type of steel and it is to be a solid, square section column of 450 mm² cross-section and 2 m long. It will be fixed at both ends. Calculate EACH of the following:

(a) The Modulus of Elasticity for the steel being used;

(b) The critical load for the strut using Euler’s equation;

(c) The ratio of compressive yield stress to critical stress for the strut.

Note: Compressive Yield Stress for the steel = 320 MN/m² for a fixed end strut, F_C = 4π² EI / L₂

Q9. An intermediate propeller shaft is fitted to an engine of power output 16 MW running at 110 rev/min. The shaft is solid with a coupling flange at each end. Each flange has 12 bolts on a pitch circle diameter of 1.5 times the shaft diameter. The limiting shear stress is 180 MN/m² for the shaft material and 160 MN/m² for the bolt material. Calculate EACH of the following:

(a) The diameter of the bolts for a safety coefficient (factor of safety) of 2.

Q7. A steel bar is 1.1 m long and 60 mm diameter. An axial hole 38 mm diameter is to be drilled from one end to such a depth that the extension of the drilled part is twice the extension of the solid part when an axial tensile force is applied. Calculate EACH of the following:

(a) The required depth of the drilled hole;

(b) The strain energy in the bar when an axial tensile load of 20 kN is applied.

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