Q1) TWO masses initially at rest are connected by a cable, running parallel to their respective surface, which is guided by a pulley as shown in Fig Q1. Mass A is 60kg, mass B is 80 kg, and the pulley is 15 kg, has a diameter of 1.6 m, a radius of gyration of 0.6 m and turns against a constant bearing friction of 20 Nm.
The coefficient of friction for mass A is 0.2 and the coefficient of friction for mass B is 0.25.
Calculate the angular acceleration of the pulley. (16)
Q3) A projectile is fried out to sea with initial velocity of 60 m/s at an angle of 30o above the horizontal from a cliff top 100 m above sea level.
Calculate EACH of the following:
(a) the linear displacement from launch site to impact; (14)
(b) the vertical velocity just before impact. (2)
Q4) The tension in a flat belt pulley system is 100 N when stationary. The wheel is 225 mm diameter and rotates at a constant speed of 1800 rpm whilst in operation with a 225o angle of lap. The power output is 1.8 kW.
Using the relationship:
F1/F2=eμθ
Where:
F1 - force in the tight side of the belt.
F2 - force in the slack side of the belt.
µ - the coefficient of friction.
Ѳ- the angle of lap in radians
Calculate the minimum coefficient of friction when no slipping occurs.
Q5) A winch drum has a mass of 800 kg and a radius of gyration of 600 mm. The winch has a single brake shoe acting on a brake drum of diameter 1.2 m. The coefficient of friction between the shoe and the drum is 0.8. Friction in the winch bearings is constant at 10Nm.
Calculate the EACH of the following:
(a) the normal force to be applied to brake shoe to slow the winch down from 320 rev/min to 100 rev/min in 30 seconds; (10)
(b) the work done by the brake during this process. (6)
Q6) A FOUR-stroke single cylinder engine produces 750 kW at 720 RPM with an energy fluctuation of 20% of the work done per cycle. A flywheel is to be fitted in order to stabilise the speed for power generation such that the frequency is 60 ± 0.2 Hz.
Calculate the diameter of a soild flywheel that is 350 mm thick. (16)
Note: Density of the flywheel material =7800 kg/m3.
Q7) Block A is connected to block B by a cable that runs on a pulley system comprised of TWO identical massless, frictionless pulleys as shown in Fig Q7.
Block A has a mass of 2.8 kg and is initially at rest whilst block B has a mass of 6 kg.
(a) the cable tension once the system is released; (14)
(b) the vertical displacement of block B for it to attain a velocity of 0.75 m/s. (2)
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)
Note:
Modulus of rigidity for the shaft material = 80 GN/m2.
Polar 2nd moment of area for solid square cross section = x4/6.
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