Task 1

The standard (305x102x28) 'I' section beam is loaded as shown below and has a modulus of elasticity of 205 GPa.
a. Determine all the forces acting on the beam (Take g = 9.81 m/s²). Draw bending moment and shear force diagrams, to scale.
c. Determine all local maxima and minima bending moments.
d. Determine the minimum radius of curvature on the beam.
e. Determine the mean shear stress in the beam.

L01: AC 1.1, Determine distribution of shear force, bending moment and stress due to bending in simply supported beams.

AC 1.2, Select standard rolled steel sections for beams and columns to satisfy given specifications. Ml, Identify and apply strategies to find appropriate solutions: An effective approach to study and research has been applied. M3, Present and communicate appropriate findings: The appropriate structure and approach has been used.)

Task 2

A standard column 356x368x202 is subjected to an on centre load of 1.5 MN applied evenly over the entire Column of length 4 m.

Determine:
a. The compressive stress in the column.
b. How far the load can be moved off centre before the outside edge goes into tension in either direction.
c. The distance from the neutral axis to the edge in tension and the edge in compression for a load offset distance of 0.125 m in the x-direction.
d. The slenderness ratio for the column in both directions.

(LO1: AC 1.2, Select standard rolled steel sections for beams and columns to satisfy given specifications. M1, Identify and apply strategies to find appropriate solutions: Complex problems with more than one variable have been explored; An effective approach to study and research has been applied. D1, Use critical reflection to evaluate own work and justify valid conclusions: The validity of results has been evaluated using defined criteria.)

Task 3

a. A shaft of diameter 50 mm and 5 m long is required to transmit a power of 30 KW at 1500 rpm. If G = 90 GPa find:-
i. The angle of twist in the shaft
ii. The maximum shear stress in the shaft (to ensure this is less than 50 MPa)

b. The shaft is to be replaced by a hollow shaft with an inside diameter of 35 mm. If the above conditions are to be met find:-
i. The new outside diameter to keep the angle of twist the same.
ii. The maximum shear stress in the shaft (again to ensure it is less than 50 MPa).
iii. The percentage decrease in mass of the shaft.

(L01: AC 1.3, Determine the distribution of shear stress and the angular deflection due to torsion in circular shafts. M3, Present and communicate appropriate findings: There is a coherent, logical development of principles/ concepts for the intended audience.)

Task 4

A. A rocket lifts off from a launch pad on Earth (g = 9.81 m/s²) and has a mass of 10000 kg (for the following assume the mass of the rocket remains unchanged and air resistance is negligible).
i. If the rocket motors produce 200 kN of thrust determine the acceleration of the rocket away from the Earth.
ii. If the motors are shut down after 2 minutes, what speed is the vehicle traveling at?
iii. How long will the rocket take to come to a stop before falling back to Earth?

B. A car of mass 1500 kg starts from rest and is subject to a force of 4500 N.
i. Assuming no road resistance, determine:
1. The acceleration of the vehicle.
2. The speed of the vehicle after 20 seconds.
ii. Repeat the above calculations assuming a road resistance of 1250 N.
iii. For the case with road resistance of 1250 N after the 20 seconds the brakes are
applied and the vehicle is brought to rest with a deceleration of 2 m/s2.
1. What braking force needs to be applied to achieve this deceleration?
2. How long will the car take to stop?
3. How far will the car travel in the braking phase?

(L01: AC 2.1, Determine the behaviour of dynamic mechanical systems in which uniform acceleration is present. M2, Select/design and apply appropriate methods/ techniques: Relevant theories and techniques have been applied.)

Task 5

A. A spring is initially compressed by 50 mm when a steel ball of mass 2 kg is released from just being in contact with the uncompressed spring. Determine:
i. The spring stiffness (k) of the spring.
ii. The amount the spring would be compressed if the mass was dropped from 200 mm above the spring.

B. A truck of mass 2000 kg has 4 solid wheels each of mass 125 kg and 0.8 m diameter. The truck is released from the top of a slope and descends through 5 m. Assuming the system is frictionless, determine:
i. The total kinetic energy of the truck at the bottom of the slope.
ii. The velocity of the truck at the bottom of the slope.
iii. The angular velocity of the wheels at the bottom of the slope.
iv. The linear and angular components of the kinetic energy.
(L01: AC 2.2, Determine the effects of energy transfer in mechanical systems. D3, Demonstrate convergent/lateral/creative thinking: Problems have been solved.)

Task 6

A. A pendulum of length 500 mm has a mass of 0.5 kg on the end and an initial displacement, d, of 100 mm from the rest position. Assuming no resistance in the system, determine:
i. The frequency of oscillation of the pendulum on release of the mass.
ii. The time to reach a displacement of d = 0 on the first swing.
iii. The speed of the mass at this point.

B. A spring with stiffness, k = 2500 N/m, has a mass of 0.25 kg suspended from it. The amplitude
of oscillations of the mass is 15 mm. If the mass starts at t = 0 s at the maximum downward displacement, determine:
i. The frequency and periodic time of the oscillations.
ii. The displacement of the mass at t = 0.07 s.
iii. The velocity of the mass at this point.
iv. The acceleration of the mass at this point.

(L01: AC 2.3, Determine the behaviour of oscillating mechanical systems. D2, Take responsibility for managing and organising activities: The importance of interdependence has been recognised and achieved.)