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Q1. A light cord passing over a light, smooth pulley has masses of 2 kg and 4 kg respectively attached to its ends. The pulley has a diameter of 300 mm. The 4 kg mass is held 3 m above ground level, with tension in the cord, and then released. Calculate EACH of the following:

(a) The time taken for the 4 kg mass to reach ground level;

(b) The time the cord remains slack after the 4 kg mass reaches ground level if the 4 kg mass does not bounce.

Q3. A winch motor drives a pinion with 320 teeth. Friction at the motor bearings is constant at 20 Nm. The pinion then meshes with a gear wheel having 640 teeth which drives a shaft of 120 mm diameter. This shaft is supported in bearings having a coefficient of friction of 0.12 and drives a winch drum of diameter 340 mm. Calculate EACH of the following:

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

(b) The input power required by the motor when raising the mass of 2 tonnes at a steady speed of 0.3 m/s if the motor efficiency is 90%.

Q2. An extending ladder has two sections, each of length 4 m and mass 20 kg. It stands on rough, horizontal ground and leans against a smooth wall at an angle of 30º to the wall. The coefficient of friction between the ladder and the ground is 0.2. A person of mass 80 kg is working half way (2 m) up the lower section.

(a) Sketch the arrangement showing all forces present.

(b) Calculate the minimum overlap of the two sections if the ladder is not to slide away from the wall.

Q2. A free-fall lifeboat is released from rest on an incline of 30º to the horizontal. The lifeboat takes 2.4 seconds to travel 10 m along the incline, at which point it starts to free-fall under the effect of gravity alone. Calculate EACH of the following:

(a) The acceleration of the lifeboat as it travels down the incline;

(b) The velocity at which the lifeboat leaves the incline;

(c) The horizontal distance the lifeboat will travel after leaving the incline when the vertical distance to the water at this point is 40 m;

(d) The velocity and angle at which the lifeboat enters the water.

Q1. A hammer of mass 1.5 kg moves vertically downwards with a velocity of 10 m/s to drive a steel pin of mass 40 grams into a horizontal floor to a depth of 28 mm.

Calculate EACH of the following:

(a) The common velocity of the hammer and pin immediately after impact;

(b) The percentage reduction of energy at impact;

(c) The average resisting force offered by the floor.

Q4. A cable consists of one steel wire 4 mm diameter and eight brass wires each 2 mm diameter. The stress in the brass wires is not to exceed 60 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

Q9. The stepped steel shaft shown in Fig Q7 is to transmit a torque. The larger diameter section of the shaft is to have a hole drilled in it to a depth of 100 mm. Calculate EACH of the following:

(a) The diameter of the drilled hole ‘d’ that would make the maximum stress in the hollow part of the shaft equal to the maximum stress in the 34 mm diameter section;

(b) The length of the 34 mm section if the total angle of twist for the shaft is to be 0.02 rad when a torque of 400 Nm is applied.

Note: Modulus of Rigidity for shaft material = 80 GN/m²