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Q3. Two close coiled helical springs are used in parallel for an engine valve assembly. The springs have the following dimensions:

During the fitting of the valve to the springs, the outer spring is compressed 8 mm more than the inner spring. The final force on the spring assembly is 700 N. Calculate EACH of the following:

(a) The compression of the inner spring when the valve is closed;

(b) The maximum shear stress in each spring when the valve is opened vertically downwards by 30 mm.

Note: Modulus of Rigidity of Spring Material = 70 GN/m²

Q2. Three masses are attached to a disc and rotate in the same plane. Mass A is 5.5 kg at 0.8 m radius, mass B is 6.2 kg at 1.2 m radius and mass C is 3.8 kg at 0.8 m radius. Masses B and C are at 140° and 210° respectively, clockwise from mass A. Determine EACH of the following:

(a) The magnitude and direction of the out of balance force when the disc rotates at 60 rev/min;

(b) The radius and angular position at which a 5-kg mass should be placed in order to balance the system.

Q1. A box of mass 400 kg is pulled at constant speed up a ramp inclined at 20º above the horizontal by the application of a horizontal force of 2750 N. Calculate EACH of the following:

(a) the coefficient of friction between the box and the ramp;

(b) the minimum force that could be used to move the box, and its line of action.

Q10. A cast iron cylinder cover is secured by twelve steel bolts, each of 18 mm diameter. The effective cross sectional area of the cylinder cover is 0.15 m². On assembly, the bolts are tightened up so that the tensile stress in each bolt is 20 MN/m². The resulting stress in the cylinder cover is evenly distributed across its effective area.

Calculate the temperature rise at which the stress in the bolts will be zero.

Note: For Cast Iron modulus of Elasticity = 100 GN/m²

For Steel modulus of Elasticity = 200 GN/m²

For Cast Iron coefficient of linear expansion = 11 x 10^-6 per °C

For Steel coefficient of linear expansion = 12 x 10^-6 per °C

Q1. A simple pendulum consists of a mass of 0.3 kg on the end of a wire. The pendulum performs 60 oscillations in 120 seconds, the angular amplitude of each being 8 degrees and can be assumed to move with simple harmonic motion. Calculate EACH of the following:

(a) the maximum linear acceleration of the mass;

(b) the length of the pendulum;

(c) the maximum velocity of the mass;

(d) the maximum tension in the wire.

Q3. An “I “section beam is loaded as shown in Fig Q6. Calculate EACH of the following:

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

(b) The maximum bending moment on the beam;

(c) The point of contraflexure.

Q2. A hollow steel shaft transmits a torque of 30 kNm. The outside diameter is 1.5 times the inse diameter and the angle of twist is one degree over a length equal to 18 times the outside diameter.

Calculate EACH of the following:

(a) The inside diameter of the shaft;

(b) The maximum shear stress in the shaft;

(c) The diameter of a solid shaft of the same material which could transmit the same torque without exceeding the maximum shear stress calculated in Q7(b).

Note: For steel, Modulus of Rigidity = 80 GN/m²