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Q1. In a set of sheer legs both front legs are 8 meters long and are fixed 5 meters apart on a horizontal base. The back stay of this concurrent non-coplanar force system is 15 meters long and is fixed on the same base at 8 meters measured linearly from the centre of the front legs shown in Fig Q1. The mass suspended by the system is 25 tonnes.

(a) Determine the magnitude and nature of the force in EACH of the following;

(i) the back stay. (8)

(ii) each front leg. (6)

(b) Define the term concurrent non-coplanar force system. (2)

Q2. A body of mass 100 kg is to be pulled along a horizontal plane, where the coefficient of friction between the contact surfaces has a constant value of 0.4 If a force is applied to the body at an angle of 45^o above the horizontal plane:

(a) sketch the force diagram indicating the interacting forces and the relevant angles. (4)

(b) calculate EACH of the following:

(i) the magnitude of the force that will slide the body at constant speed. (6)

(ii) the magnitude and direction of the minimum force that will move the body. (6)

Q4. A single-start worm rotates a 50-tooth worm-wheel in a simple lifting machine. The system is driven by an effort wheel that is 250 mm in diameter.

(a) If the effort required lifting a mass of 700 kg is 125 N with an overall efficiency of 35%, calculate EACH of the following.

(i) the mechanical advantage of the lifting machine. (2)

(ii) the velocity ratio of the lifting machine. (2)

(iii) the diameter of the load wheel. (4)

(iv) the time taken to raise the load 1. 5 m if the effort wheel rotates at a constant speed of 50 rpm. (4)

(b) Sketch the arrangement. (4)

Q5. A piston reciprocates with simple harmonic motion when driven by an engine with a constant speed of 120 rpm. When the piston is 0.75m from mid-stroke position it has an instantaneous velocity equivalent to 0.6 maximum velocity

Calculate EACH of the following:

(a) the stroke of the engine. (8)

(b) the velocity of the piston when it is 0.7 m from top dead Centre. (4)

(c) the maximum acceleration of the piston. (4)

Q6. A loaded truck of mass 5 tonnes is travelling on rails at 7 m/s and collides with an unloaded truck of mass 2 tonnes travelling at 3 m/s in the same direction. After collision the trucks move as a single body:

(a) Define the terms elastic and inelastic collisions. (2)

(b) Calculate EACH of the following:

(i) the velocity of the combined mass. (6)

(ii) the change in kinetic energy. (4)

(iii) the distance travelled by the trucks after the collision against a constant resistive force of 1400 N. (4)

Q7. A solid rectangular beam carries a uniformly distributed load of 10 kN/m over its entire span of 6 m which is simply supported at both ends, as shown in Fig Q7. The beam has a breadth 100 mm and a maximum bending stress of 70 MN/m².

Calculate EACH of the following:

(a) the magnitude and position of the maximum bending moment. (2)

(b) the minimum depth of the beam. (8)

(c) the minimum dimensions of a replacement solid square beam under these loading conditions. (6)

Q8. A close coiled helical spring with mean coil diameter 40 mm is made from 5 mm diameter wire. The stress in the wire must not exceed 250 N/mm² at the maximum spring deflection of 20 mm.

Calculate EACH of the following:

(a) the number of coils in the spring. (8)

(b) the load which causes maximum deflection. (6)

(c) the energy stored within the spring at maximum deflection. (2)

Note: Modulus of Rigidity for wire= 88 kN/mm^2.

Q9. A composite component consists of steel rod, which is 250 mm long with diameter of 35 mm, which is firmly attached to an aluminium rod 625 mm in length as shown in Fig Q9. When the component has tensile load of 32 kN applied to it the extension of the steel and aluminium section are identical.

Calculate EACH of the following:

(a) The diameter of the aluminium rod. (8)

(b) The stress in each section of the component. (4)

(c) The total extension of the component. (4)

Note:

Modules of elasticity for steel = 200 GN/m².

Modules of elasticity for aluminium = GN/m².