Q1. (a) Define EACH of the following terms:
(i) Stable equilibrium. (2)
(ii) unstable equilibrium. (2)
(iii) Neutral equilibrium. (2)
(b) A solid aluminium hemisphere 250 mm diameter rests its curved surface on a rough plane inclined at an angle of 15o to the horizontal. Calculate the force F needed on the edge of the hemisphere, as shown in Fig Q1, to maintain the axis of the hemisphere in the vertical position. (10)
Note:
The density of Aluminum=2800 kg/m3
The volume of the sphere can be calculated from (4πr2)/3.
Q2. A block of mass 4 kg rests on a horizontal plane and a second block of mass 6 kg rests on a plane incline at 25° to the horizontal. The blocks are connected together by a light inextensible wire passing under pulley as shows in Fig Q2.
The blocks are further connected by a light inextensible wire and pulley to a deadweight W which is sufficient to move the system with a constant velocity. The coefficient of friction between both blocks and the planes is 0.2 and the friction in the pulleys is negligible.
(a) Sketch the system showing all the forces acting for steady motion. (6)
(b) Calculate the magnitude of the mass required at the deadweight W. (10)
Q3. A projectile is fired vertically upwards from ground level with an initial velocity of 22 m/s. Two seconds later a second projectile is fired vertically upwards, from the same point, with an initial velocity of 15 m/s.
Calculate EACH of the following:
(a) the height above ground level at which they will meet. (12)
(b) the magnitude and direction of the velocity of the first projectile at the instant of meeting.
Q4. A loaded truck with a total mass of 6 tonne has four wheels each of mass 250 kg, diameter 400 mm and radius of gyration 300 mm. The truck Is travelling at 2 m/s when it starts to descend an incline of 3°. The incline is 150 m long and resistance to motion is constant at 450 N.
(a) the energy lost in descending the incline. (2)
(b) the speed of the truck at the bottom of the incline. (14)
Q5. A single plate friction clutch with both sides effective having an outside diameter of 400 mm and an inside diameter of 160 mm, is designed to transmit 10 kW at 500 rev/min when new. In this condition the coefficient of friction between the contact surfaces can be taken to be 0.62. There are eight clutch springs each having a stiffness of 8 kN/m. The maximum wear of the clutch friction plate is limited to 1.5 mm of each contact surface.
During service, clutch plate wear takes place, the surfaces become contaminated and the power reduces.
(a) the total spring load required when the clutch is in the new condition; (8)
(b) the minimum coefficient of friction of the worn clutch if 75% of the original power can still be transmitted at the same speed. (8)
For constant pressure T = 2/3μnW ((r13 – r13)) / ((r12 - r22 ))
For constant wear T = μnW/2 (r1+r2)
n = Number of pair of surfaces in contact
Q6. An electric motor drives a pump through the compound gear train as shown In Fig Q6. The power required by the pump is 70 kW at a speed of 125 rev/min. The velocity ratio of the entire gear system is 24. The transmission efficiency is 90 per cent and the pitch of the teeth is the same for all gear wheels.
(a) the number of teeth on gears A and B. (7)
(b) the output torque from the motor. (7)
(c) the speed of gear B. (2)
Q7. A concentric vertical column consists of two column each 100 mm high as shown in Fig Q7. The inner column is brass of cross section area 122 mm2 and the outer hollow column is steel of cross section area 50 mm2. The column supports an axial load of 20 kN.
(a) the stress in each material; (12)
(b) tile change in length of the column. (4)
The modulus of Elasticity for steel=208 GN/m2
The Modulus of Elasticity for brass=97 GN/m2
Q8) A winding drum is driven through 85% efficient 1:1 gearing by a solid square section shaft with a length of side x. The shaft rotates at 150 rpm whilst lifting a 20-tonne mass at a constant velocity of 0.25m/s and the angle of twist within the shaft is 1o for its overall length of 30x.
Calculate the minimum dimension for length of side x. (16)
Modulus of rigidity for the shaft material = 80 GN/m2
Polar 2nd moment of area for solid square cross section = x4/6
Q9. A valve spindle of total length 250 mm is 20 mm diameter for 100 mm of its length and 30 mm diameter for the remainder.
The valve spindle is at a temperature of 120"C and at this temperature, it is free of stress. The spindle cools to 20"C but is only able to contract by 0.25 mm lengthwise.
Calculate the maximum stress in the spindle. (16)
The Modulus of Elasticity for the spindle material= 200 GN/m2
Coefficient of linear expansion for spindle material = 12×106 per ℃.
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