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BA British Applied College CU Umm Al Quwain BTEC Assignment Brief Qualification Unit or Component number and title Learning alm(s) (For NQF/RQF only) Assignment title Assessor Hand out date Hand in deadline Internal Verifler IV Date P Pearson BTEC LEVEL 3 Subsidiary Diploma in Engineering Unit 1 Mechanical Principles A Examine how algebraic and trigonometric mathematical methods can be used tosolve engineering problems B Examine how static engineering systems can be used to solve engineering problems C Examine how dynamic engineering systems can be used to solve engineering problems D Exame how fluid engineering systems can be used to solve engineering problems. Mechanical Principles Dr. Sivakumar Ramalingam 21/02/2022 Learning Aim A & B 23/03/2022 Learning Aim C & D 10/05/2022 Dr. Haran Pragalath D.C. 20/02/2022

Instructions to Learners Read the Set Assignment carefully. You will be asked to carry out specific written activities and calculations, using the information provided. You will need to have access to: . a non-programmable calculator that does not have the facility for symbolic algebraic manipulation or allow the storage and retrieval of mathematical formulae . the Information Booklet of Formulae and Constants for Unit 1 . standard drawing equipment (a pencil, a ruler, a rubber, a pair of compasses anda protractor). At all times you must work independently and must not share your work with other learners. You must complete an authentication sheet and submit this along with your work. You should show all of your working when completing calculations. Where required, all answers must be rounded to two decimal places unlessotherwise stated. You must state units of measure where possible. Outcomes for submission 4 You will need to submit one task booklet on completion of the supervised assessment period. Drawings and graphs must be completed in pencil. You must submit your own, independent work as detailed in the Set Assignment. Youmust complete an authentication sheet and submit this along with your task booklet. 1. The student should include a Statement of Authenticity to be signed by students when submitting evidence for assessment in Student Declaration Form 2. Using the values of variables in the tasks given in table-1 for each student number, you must present your individual calculations in step-by-step manner with full use of units and standared form 3. Students can approach the tutor for formative assessment on 16-03-2022 for Learning Alm A & B. and 03-05-2022 for Learning Aim C & D. Set Assignment Information Mechanical engineers need to carry out calculations to check that components and mechanisms perform as required and meet specifications. These calculations apply static, dynamic and fluid principles and rely on the correct application of algebraic and trigonometric rules and processes to determine answers.

ACTIVITY 1 1 An engineer has plotted the results of a first investigation on a graph. A second investigation is represented by the formula: y=x-2 (a) Plot the results of the second investigation on the same graph. x -2 0 2 4 6 8 First investigation results A 6 2 (b) State the coordinates (x, y) where the two lines from each investigation cross (c) Calculate the gradient of the line for the first investigation. (d) Determine the equation of the straight line for the first investigation. 2 The diagram shows a cover plate that has a diameter of 75mm. A sector of a circle

hole has been cut through the plate: go Diagram not to scale and all dimensions in millimetres (a) Convert 8" into radians. (b) Calculate the area of the sector of a circle hole. (c) Calculate the area of the cover plate after the sector of a circle hole has been cut out. (d) Three 4mm diameter holes will be drilled through the cover plate to allow it to be attached to a piece of machinery. The plate is 2mm thick. Calculate the total volume of material that will be removed when drilling the three holes. 3 The diagram shows a drill drift that is made from 4mm thick carbon steel. F 26 185 - Diagram not to scale and all dimensions in mm (e) Calculate the volume of the drill drift. The cost of manufacturing the drill drift is calculated using the following formula: C=4+m²t+nt Where C is the cost of the drill drift(s) (in dollars), m is the number of machining operations that need to be completed, t is the time taken to machine one drill drift inminutes, and n is the number of drill drifts being produced. (f) Rearrange the formula to make the subject. (g) Calculate the time taken to machine one drill drift (n) when:

C=$'Y' and m=3 4 The diagram shows a plate that has been cut from a sheet of aluminium. 240 B 38 90 Diagram not to scale and all dimensions in mm unless otherwise stated. (a) Calculate the length of side DC. (b) Calculate the distance between point B and point E. The plate is cut out using a Computer Numerical Control (CNC) machine that startsfrom point A and works clockwise around the plate before returning to point A. (c) Calculate the total length of cut completed by the CNC machine. ACTIVITY 2 1 The diagram shows a racing car of mass 750 kg decelerating at a constant rate on a straight and level track. A 300 m V₂ 50 m/s m/s Diagram not to scale (a) Calculate the rate of deceleration of the racing car. (b) Calculate the time taken for the car to decelerate to V; m/s. The racing car then travels along another straight plece of track at a velocity of V₂ m/s. As it passes point A the engine stops and the car begins to freewheel up the incline of the track. Assume there is no friction or wind resistance. 56 115 ELE

original track level h X Point at which the car comes to rest Diagram not to scale (c) Calculate the height (h) above the original track level where the car will come to rest. The engine is then restarted and the racing car travels on a curved length of trackthat has a radius of 12m at a constant tangential velocity of V₂ m/s. (d) Calculate the centripetal acceleration of the racing car on the curved lengthof track. (e) Explain one way that friction would affect the racing car as it travels around the curved section of the track. 2 The diagram shows a gradually tapering pipe. The pipe runs full with an unknown incompressible fluid. The inlet flow velocity of the fluid is V. m/s. end elevation (cross section) Inlet end elevation (cross section) Outlet Direction of flow Inlet area=0.4 m² side elevation Outlet area=0.6 m² Diagram not to scale (a) Calculate the volumetric flow rate of the unknown fluid at the inlet. (b) Calculate the outlet velocity of the unknown fluid.. 2.5 m³ of the fluid has a mass of 890kg. (c) Calculate the mass flow rate of the unknown fluid in the gradually tapering pipe. 3 The diagram shows a simply supported beam. Assume the beam has no mass and is in static equilibrium.

0.5m 5 KN UDL-W kN/m 0.5 m 1.5 m 0.5 m Diagram not to scale (a) Calculate the equivalent concentrated load produced by the uniformly distributedload (UDL). (b) Calculate the vertical reaction force at point A. A concentrated load of 20kN is added that acts downwards, at point C. To keep the beam in static equilibrium, an additional concentrated load (D) of unknown magnitude is also added to the beam. UDL= W kN/m 5 KN 20 KN 10.5 m/0.5 m 1.5m 0.5 m Diagram not to scale. (c) Ignore the additional concentrated load D Calculate the turning moment at point B due to the additional concentrated loadat point C, the UDL and the 5kN concentrated load. (d) Calculate the magnitude of the additional concentrated load (D) to keep the beam in static equilibrium. 4 The diagram shows one of four connectors used to attach a carriage to a fairground ride. Each connector contains a tie bar that supports an equal amount of load.

63==3) -Circular Pin F Diagram not to scale The carriage has a mass of m kg including two passengers. (a) Calculate the load F in one of the tie bars. Each tie bar has an original length of 370mm. When the load of carriage is applied, each tie bar extends by 3x10-³ mm. (b) Calculate the direct strain in one tie bar. State your answer to 3 significant figures (3 SF). The circular pin has a radius of 5x10-³ m. (c) Calculate the shear stress in the circular pin. (d) Explain how the modulus of rigidity (G) of the material used for the circular pinaffects its performance under loading.

Table 1: List of variables and values assigned to each student. S.No. Name PA89151 ABDALLA 4 MOHAMED ABDALLA IBRAHIM 0 X C=Y V₂ V₁ (o) (mm) ($) (m/s) (m/s) 40 40 8 6.5 5.75 UDL = W (kN/m) 13 m (kg) 280

Assessment criteria Pass Merit Learning aim A: Examine how algebraic and trigonometric mathematical methods can be used to solve engineering problems A.P1 Solve given routine problems using algebraic methods. A.M1 Solve routine problems accurately and non-routine problems using both algebraic and trigonometric methods. A.P2 Solve given routine problems using trigonometric methods. Learning aim B: Examine how static engineering systems can be used to solve engineering problems B.P3 Solve routine problems that involve static systems. B.M2 Solve routine problems accurately and non-routine problems that involve both static systems and loaded components. B.P4 Solve routine problems that involve loaded components. Learning aim C: Examine how dynamic engineering systems can be used to solve engineering problems C.P5 Solve routine problems that involve kinetic and dynamic parameters. C.M3 Solve routine problems accurately and non-routine problems that involve dynamic systems. C.P6 Solve routine problems that involve angular parameters. Learning aim D: Examine how fluid engineering systems can be used to solve engineering problems D.P7 Solve routine problems that involve fluid systems. D.M4 Solve routine problems accurately and D.P8 Solve routine problems that involve non-routine problems that involve fluid systems. immersed bodies. Distinction A.D1 Solve routine and non-routine problems accurately, using algebraic and trigonometric methods. BCD.D2 Solve routine and non-routine problems accurately using mechanical engineering methods.