U03 A2 Unit 4003 Engineering Science I | Fundamentals of Mechanical Engineering Systems 2026
U03 A2 – Fundamentals of Mechanical Engineering Unit 4003 Engineering Science I – Assignment 2
Fundamentals of Mechanical Engineering Systems
Qualification
Pearson BTEC Higher Nationals in Engineering
Unit number and title
4003 Engineering Science I (U03)
Unit code
J/651/0710
Assignment number and title
Assignment 2 – Fundamentals of Mechanical Engineering Systems
Unit level
4
Credits
15
Assignment Format and Submission Submit your assignment as one professionally presented PDF file through Totara. Do not upload separate files for individual tasks unless the assignment brief specifically requires them.
Required Document Structure Arrange your assignment in this order:
Cover page– include: Full name Course title Unit number and title Assignment number and title Submission date Academic year of the assignment brief used, for example 2026/2027 Contents page – show each section and its page number. AI declaration – declare any permitted use of artificial intelligence. Assignment evidence – organise your work under clear headings such as Task 1, Task 2 and Task 3. Reference list – provide a complete Harvard-style list of all sources used. Appendices – include supporting evidence, presentation slides and speaker notes where required. Important: The academic year must be clearly shown on the cover page and must match the assignment brief used for the submission.
Place calculations, tables, figures and screenshots within the relevant task wherever possible. Label them clearly and refer to them in your written response.
Use clear headings, page numbers and consistent formatting. Follow all word-count, file and evidence requirements stated in the assignment brief.
File Name Name your PDF:
Surname_FirstName_UnitNumber_AssignmentNumber.pdf
Example: Smith_Jane_4014_A1.pdf
Upload native files or video/presentation links only when specifically requested. Follow the AIAS level for each task and complete any required Approval Checkpoint.
Before submitting, confirm that:
Every task has been completed. The PDF opens correctly and contains all required evidence. The cover page shows the correct academic year. The academic year matches the assignment brief used. Vocational Scenario Congratulations! You have been employed by Universal Marine Solutions ltd. (UMS); a fictional company that designs and manufactures ship related structures, such as framing systems, hulls, and decks; and mechanical ships systems, such as propulsion systems, and cargo loading and unloading systems. Your job involves applying fundamental mechanical engineering principles for analysing various mechanical systems produced by UMS.
Task 1: Apply the fundamentals of mechanical engineering systems AI use for Task 1: This task is completed in a controlled environment designed to exclude AI. Knowledge, understanding, and skills are demonstrated and assessed independently.
- Your first task involves analysing one of the steel beams in a longitudinal framing system for a river ferry. The beam supports the engine room deck, and spans the distance between the fore end of the stern tube and the fore end of the engine.
Figure 1. Propeller shaft
Figure 1 was not included in the publicly available copies of this brief. The accompanying text states that the bearings act as pinned supports at 1 m and 4 m from the aft end of the propeller shaft, that the propeller hangs from the aft end, and that the stern tube does not support the propeller shaft.
a) Figure 1 illustrates the propeller shaft, which spans the distance between the aft end of the stern tube, and the fore end bearing (i.e., the bearing on the right). The propeller shaft is suspended above the deck by two bearings; you may assume the bearings act as pinned supports at 1m and 4m from the aft end of the propeller shaft, and that the whole system is in equilibrium. The stern tube does not support the propeller shaft. The propeller hangs from the aft end of the propeller shaft, and has a mass equal to your age in years in kg. For example, if are 32 years old, the propeller is 32kg. The propeller shaft is 200kg. Produce a free body diagram of the propeller shaft, including all the relevant forces, and calculate the reaction forces acting upwards through the bearings. Clearly state your age in years, and justify your chosen methods by showing each step and providing an explanation if necessary.
Figure 2. Engine room beam
Figure 2 was not included in the publicly available copies of this brief. Positions and lengths of the beam supports, gearbox and engine are given only in the figure. The text gives the following loads: each bearing is 60 kg; the gearbox exerts 3430 N/m and the engine exerts 3560 N/m on the beam; the beam itself is 300 kg.
b) Figure 2 illustrates the rest of the engine room, depicting the machinery resting on top of the engine room deck beam. Each bearing is 60kg; the gearbox exerts 3430N/m, and the engine exerts 3560N/m on the beam. Assume the propeller shaft is not fixed to the gearbox. The beam itself is 300kg, and the whole system is in equilibrium. Produce a free body diagram of the engine room deck beam, including all the relevant forces, and calculate the reaction forces acting upwards through the two supports underneath the beam. Justify your chosen methods by showing each step and providing an explanation if necessary.
(Tip: remember Newtons first law of motion, every action has an equal and opposite reaction).
- Your next task involves analysing a derrick used to move TEU containers on and off of a container ship, as depicted in figure 3. The process of moving cargo involves raising a container to a height above the weather deck, in pace with the process of filling the ballast tanks; keeping the ship balanced while the ships centre of buoyancy changes.
Figure 3. Derrick
Figure 3 was not included in the publicly available copies of this brief. The text states that the container starts at rest, accelerates to 1.5 m/s by the time it reaches the height of the weather deck, then decelerates to 0 m/s after reaching 6 m above the weather deck. The starting height relative to the weather deck is given only in the figure.
a) The container illustrated in figure 3 begins at rest, but accelerates to 1.5m/s by the time it reaches the height of the weather deck, then decelerates to 0m/s after reaching 6m above the weather deck. The mass of the container is equal to (your age in years x 100)kg. For example, if you are 32 years old, the container is 3200kg. Produce two fully annotated kinematic free body diagrams that include all unknown values related to the forces at play; the first depicting the acceleration of the container towards the weather deck, and the second depicting the deceleration of the container up to 6m above the weather deck.
b) Determine the force required to act through the derricks cable to raise the container to the height of the weather deck, then the force required to raise the container from the height of the weather deck to the maximum possible height. Justify your chosen methods by showing each step and providing an explanation if necessary.
- The distance between the top of the weather deck, and the waterline is called the freeboard, and the distance from the waterline to the bottom of the keel is called the draft. It is important to be aware the draft of a ship at lightweight (when a ship is completely unloaded), to determine the maximum safe deadweight of the ship (the total mass of the ship’s cargo, ballast water, fuel, and crew and passengers).
Figure 4. Floating ship hull
Figure 4 was not included in the publicly available copies of this brief. The text states that the hull may be treated as a rectangular cuboid floating in seawater, and that the minimum permitted freeboard is 1.4 m. The hull dimensions needed to calculate draft and deadweight are given only in the figure.
a) Determine the draft of the ship hull illustrated in figure 4, given that it is floating in seawater. You may assume the hull is a rectangular cuboid. Justify your chosen method by showing each step and providing an explanation if necessary.
b) Calculate the maximum deadweight of the ship, given that the minimum permitted freeboard distance for this ship is 1.4m. Justify your chosen method by showing each step and providing an explanation if necessary.
- Seawater is pumped into a ship for multiple reasons, among which is to exchange heat with the engine coolant fluid in a heat exchanger. Coolant fluid is first heated by the engine through a pipe that expands in size to accommodate smaller tubes filled with seawater; exchanging thermal energy with the coolant, forming a heat exchanger. Figure 5 illustrates the flow of engine coolant entering a heat exchanger.
Figure 5. Heat exchanger
Figure 5 was not included in the publicly available copies of this brief. Pipe diameters and lengths needed for the pressure-drop calculation are given only in the figure. The text gives Q = 25 MW, coolant density ρ = 975 kg/m³, specific heat capacity cp = 4180 J/kg·K, a temperature change of 33 °C, and a required pressure of 1 kPa in the heat exchanger.
a) Determine the volumetric flow rate of the coolant through the heat exchanger necessary to achieve a change in temperature of 33 °C. Assume the volume of the sea water pipes are negligible.
Q = Heat removed by sea water = 25 MW ρ = Density of the coolant = 975 kg/m3 V = Volumetric flow rate cp = Specific heat capacity of the coolant = 4180 J/kg·K ΔT = Change in temperature Justify your chosen method by showing each step and providing an explanation if necessary.
b) A pump is used to control the pressure of the coolant passing through the engine. Given that the pressure of the coolant passing through the heat exchanger needs to be 1kPa to achieve your calculated value of volumetric flowrate, calculate what the pressure of the coolant should be before it enters the heat exchanger to account for the pressure drop. Justify your chosen method by showing each step and providing an explanation if necessary.
- UMS has built a prototype of a new marine diesel engine, and you need to fully analyse the thermodynamic processes occurring in one of the cylinders. The properties of air inside each cylinder changes four times via a cycle of four thermodynamic processes:
State 1 to 2: Isentropic compression (i.e., the cylinder compresses the air) State 2 to 3: Isobaric heating (i.e., ignition) State 3 to 4: Isentropic expansion (i.e., the power stroke of the engine) State 4 to 1: Isochoric cooling (i.e., exhaustion of hot air) The following properties of the air in the cylinder are known:
P1 = 100 kPa (i.e., pressure of the air at state 1) T1 = 300 K P2 = 500 kPa T3 = 1200 K You may assume the air in the cylinder is an ideal gas with the following specific heats:
cp = 1005 J kg−1 K−1 cv = 718 J kg−1 K−1 a) Calculate the ratio of specific heats. Justify your chosen method by showing each step and providing an explanation if necessary.
b) Calculate the values of pressure and temperature of each of the four states, and present the determined values in a table. Justify your chosen methods by showing each step and providing an explanation if necessary.
c) If 60g of air is drawn into the engine cylinder, determine:
i. How much work is done during the isobaric heating process. ii. How much heat is transferred during the isochoric cooling process. Justify your chosen methods by showing each step and providing an explanation if necessary.
Learning Outcomes and Assessment Criteria The tables below reproduce the Pearson criteria covered by this assignment. Use them to check the evidence across your whole submission.
LO2: Apply the fundamentals of mechanical engineering systems Criterion
Published requirement
P3
Determine the support reactions of a beam carrying a combination of a concentrated load and a uniformly distributed load.
P4
Apply Archimedes and Bernoulli’s principles in contextual engineering applications.
P5
Determine the ideal gas properties during a process.
M2
Determine unknown forces by applying d’Alembert’s principle to a free-body diagram.
D2
Analyse thermodynamic systems with ideal gas by using the first law of thermodynamics