Q1. In the simply supported framework, shown in Fig Q1, the pin-jointed members are each 3 m in length.
(a) Calculate the reaction forces at either end of the framework. (2)
(b) Determine the magnitude and nature of the force in each of the members. (14)
Q2. A steel wedge is 450 mm long, 55 mm thick at the butt end, 5 mm thick at the sharp end with an equal taper on both sides. It is driven horizontally between an engine bedplate and the stools with a force of 4.5 kN, shown in Fig Q2. The coefficient of friction is 0.15. Calculate EACH of the following:
(a) the equivalent mass lifted by the wedge; (10)
(b) the force required to remove the wedge. (6)
Q3. A projectile is fired vertically upwards with an initial velocity of 305 m/s. The effect of air resistance is a constant force equal to one-seventh of the gravitational force experienced by the projectile.
Calculate EACH of the following:
(a) the time taken to reach the maximum height; (6)
(b) the maximum height attained by the projectile; (4)
(c) the time the projectile takes to fall from maximum height to its starting position. (6)
Q4. A screw jack is to be used to raise a casting of mass 1500 kg. The single start screw thread has a pitch of 2.5 mm. A force of 45 N is applied at right angles to a turning bar at a fixed radius of 600 mm to produce a constant rotational speed.
(a) the velocity ratio of the screw jack; (3)
(b) the efficiency of the screw jack lifting this casting; (5)
(c) the output work done per revolution; (3)
(d) the constant rotational speed, expressed in rpm, if the casting is lifted 150 mm in 12 seconds. (5)
Q5. A simple pendulum consists of a mass of 0.23 kg on the end of a wire of fixed length. The pendulum moves with simple harmonic motion with an angular amplitude of 7.5° completing 60 oscillations in 75 seconds.
(a) the maximum linear acceleration of the mass; (2)
(b) the length of the pendulum; (5)
(c) the maximum linear velocity of the mass; (4)
(d) the maximum tension in the wire. (5)
Q6. Three masses A, B and C are to rotate on a common plane with the same angular velocity. Their masses and radii from the centre of rotation are: 7 kg at 375 mm radius, 10 kg at 315 mm and 12.5 kg at 225 mm respectively.
Calculate the angles between each of the masses so that the system is balanced. (16)
Q7. A position of moving with simple hormonic motion passes points A and B, 400 mm apart with the same speed.
If it takes 2 seconds to travel from A to B, and a further 3 seconds to reach point B when reciprocating, calculate EACH of the following:
(a) the periodic time. (6)
(b) the amplitude. (8)
(c) the maximum acceleration. (2)
Q8. A weight of 8. 5 kN falls a 5 mm vertical distance onto a steel bar as shown in Fig Q8. The bar has a length 200 mm and a cross sectional area of 2500 mm2.
(a) the stress induced within the bar; (6)
(b) the stress if the same load is applied gradually; (8)
(c) the stress if the same load is applied suddenly without impact. (2)
Note: Modulus of Elasticity for steel = 200 GN/ m2.
Q9. A solid steel bar, 75 mm diameter is fitted inside a 1O mm thick brass liner that has an internal diameter of 75 mm. The compound component is machined to a single length and positioned such that both ends are rigidly fixed. At ambient temperature there are no stresses in the steel or brass. During operation the temperature of the component is raised by 65°C.
(a) the direct stress in the steel bar induced by the temperature change; (14)
(b) the direct stress in the brass liner induced by the temperature change; (2)
Note:
Modulus of Elasticity for steel= 200 GN/m2
Coefficient of linear expansion for steel = 11 x 10-6/°C
Modulus of Elasticity for brass= 90 GN/m2
Coefficient of linear expansion for brass= 18.4 x 10-6/°C
Username or email address *Required
Password *Required
Note: Entering wrong username in the login form will ban your IP address immediately. Entering wrong password multiple times will also ban your IP address temporarily.
Log in
Lost your password? Remember me
No account yet?
