Q1) A Pin-jointed frame is loaded as shown in fig Q1.
Determine the magnitude and nature of the force in EACH of the four members. (16)
Q2) When released blocks A and B slide freely down the incline as shown in fig Q2. Block A is 15 kg with a 0.25 coefficient of friction acting between its contact surface and the plane. Block B is 55 kg with a 0.1 coefficient of friction acting between its contact surface and the plane.
Calculate the magnitude of the contact force between the blocks. (16)
Q4) A 500 kg mass is to be raised vertically by a screw jack. The single start thread is square with a 12 mm pitch and a 50 mm mean diameter. The coefficient of friction is 0.15.
Calculate EACH of the following:
a) the effort required to raise the load at the end of a 300 mm lever; (12)
b) the efficiency of the screw jack when raising the load. (4)
Q5) A winch motor drives a pinion with 320 teeth. The friction at the motor bearings is a constant 20 Nm. The pinion meshes with a gear wheel that has 640 teeth which drives a 120 mm diameter shaft. The shaft is supported in bearings with a coefficient of friction of 0.12 and drives a winch drum with an effective diameter of 340 mm. The winch drum raises a mass of 2 tonnes at a constant vertical velocity of 0.3 m/s as shown in fig Q5.
a) the driving torque required by the motor; (12)
b) the input power if the motor is 86% efficient. (4)
Q6) A slider crank mechanism drives a block between two parallel, horizontal guides as shown in fig Q6. The block has a stroke of 120 mm and oscillates in simple harmonic motion with a frequency of 1.667 Hz. The mass of the block is 2 kg and the coefficient of friction at the contact surfaces of the guide is 0.12. When the connecting rod is 15o above the line of stroke, the block is 40 mm away from its mid-stroke position.
a) the kinetic energy of the block; (6)
b) the force in the operating. (10)
Q7) A simply supported beam is loaded as shown in Fig Q7.
Calculate the position of any points of contra-flexure. (16)
Q8) A diesel engine exhaust valve is controlled by two concentric springs. The outer spring is made from 20 mm diameter wire with 10 active coils, a free length of 360 mm and a mean diameter of 254 mm. The inner spring is made from 16 mm diameter wire with 12 active coils, a free length of 380 mm and a mean diameter of 178 mm. When the exhaust valve is shut, the length of both springs is 320 mm.
The travel of the valve from shut to open is 38 mm.
a) the work done to fully open the exhaust valve; (10)
b) the increase in strain energy to fully open the exhaust valve. (6)
Note:
Modulus of Rigidity for both springs =80 GN/m2.
Q9) A 16 mm diameter steel cable running over a pulley is used to vertically lower a mass of 2 tonnes at a constant velocity of 0.2 m/s. The pulley suddenly jams when the length of the cable is 10 m.
a) the stress in cable due to the sudden stop; (14)
b) the extension of the cable due to the sudden stop. (2)
Note: Modulus of Elasticity for steel = 208 GN/m2.
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