Mechanical Engineering Exam Questions and Answers

Question 1: Stress Analysis

Answer all ten questions in this part.
This part is worth 40 percent of the total marks in this examination. Plan to spend no more than 40 percent of your time answering this part.
A 40 mm wide and 5 mm thick titanium alloy plate with a 7 mm edge crack is subjected to a tensile load of 50 kN as shown in figure 1 (a).

Figure 1 Figures for Question 1 (a) Plate with an edge crack (b) Y-calibration for a finite-width edge-cracked plate loaded in tension
a) What is the value of the stress intensity factor at the crack tip, assuming that the crack can be treated as a sharp edge crack? Give your answer to 2 s.f. (3 marks)
b) Will the plate fracture under the applied load? Briefly explain your reasoning. (1 mark)

A 0.75 m long solid circular section shaft with a radius of 30 mm transmits a torque of 150 Nm and is manufactured from steel with a shear modulus of 100 GPa. Give your answers to 2 s.f.
a) What is the maximum shear stress in the shaft due to the applied torque? (2 marks)
b) What is the angle of twist over the length of the shaft? (2 marks)
a) State two potential safety hazards associated with pressure vessels. (2 marks)
b) Explain the meaning of safety factor in the context of pressure vessel design. (1 mark)
c) A pressure vessel is to be manufactured from a material with an ultimate stress of 450 MPa. If the vessel is to be designed with a safety factor of 1.5, what is the maximum allowable stress that should be used for the design calculations? (1 mark)

The horizontal displacement of an aeroplane coming in to land, as it comes to rest, is given by 1 3 256 Sketch a graph of the velocity against time from t = 0 s as the plane lands until it comes to rest, showing the calculations for 2 key points on the graph.

Question 5 
Consider a perfectly elastic collision between two balls where initial velocity of both balls is set to be equal in magnitude but in opposite directions. The mass of one ball is much larger than the other ball. Clearly show your working to find the relationship between the resulting final velocities of the balls after a perfectly elastic collision. You may run the collision simulation tool in Study Week 9 to verify your answer but it is not essential. (4 marks)

Question 2: Torque and Shear Modulus

Question 6 
A 50 kg sliding mass is mounted on a flywheel of diameter 2.6 m that is rotating at a constant angular velocity of 0.5 rad s−1. The sliding mass is moving away from centre of the flywheel with a constant radial velocity of 0.5 m s−1. The sliding mass has no tangential velocity relative to the flywheel.
a) Calculate the magnitudes of the centripetal and tangential components of acceleration for the mass when it reaches the perimeter of the wheel. (2 marks)
b) Working to two significant figures, use your answer to part (a) of the question and calculate the magnitude of the force acting on the mass. You may run the simulation tool of a rotating flywheel in study session 10.2 to visualise the motion of the mass but it is not essential. (2 marks)

Question 7
Figure 2 (a) shows a plastic plumbing fitting from an industrial water system carrying chlorinated water at high temperature.
The fitting has broken, revealing the fracture surface shown in figure 2 (b). Name the type of failure that has occurred here and list three environmental factors that have contributed to the failure. (4 marks)

Question 8 
a) Estimate values for
i) the fatigue limit of ductile cast iron
ii) the endurance limit for a million cycles for 70Cu-30Zn brass (2 marks)
b) State and explain which material would survive longest if subjected to a periodic force of maximum amplitude 150 MPa, assuming failure is due only to fatigue. (2 marks)

Question 9
The Albert memorial, a historic monument in London, has a construction based on cast iron sections clad with lead. Damage to the lead cladding over time exposed parts of the cast iron core, leading to extensive corrosion. A major renovation was carried out in the 1990s.
a) Explain how the combination of iron and lead, exposed to a damp environment, fulfils the conditions for the establishment of an electrochemical cell. (2 marks)
b) Explain which metal would corrode and write a half equation to illustrate the process. (2 marks)

Question 10
Aluminium oxide, or alumina, is a widely used ceramic material. Table 1 shows values of average failure stress, σ, and Weibull modulus, m, for two samples of alumina with the same dimensions, produced using different processing methods. 
a) The two samples have identical chemical composition. Suggest how their microstructure may differ to produce the two very different values of average failure stress.
b) Explain briefly the significance of the different values of the Weibull modulus, m. (4 marks) 

PART B 
Answer all four questions in this part.
This part is worth 60 percent of the total marks in this examination. Plan to spend no more than 60 percent of your time answering this part. 

Question 11
Figure 4 shows the stress state for a point A on the skin of an aircraft wing and figure 5 shows a graph of angle (θ) against normal stress (σθ) and shear stress (τθ) for the stress element at point A.