s SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER EXAMINATIONS 202/203 XE2 ENGINEERING CONCEPTS (Test) Time allowed: TWO hours Answer: Attempt FOUR questions only, a maximum of TWO questions from each SECTION. The total number of questions is SIX. Items permitted: Any approved calculator Items supplied: Appendix A & B - Formula sheets Appendix C - Answer sheet for Q3 (c) and Q3 (d) Marks for whole and part questions are indicated in brackets ( ) [XE2] 202/203 Page of 6 Printing date: 5/0/203
Section A Attempt only TWO questions in this section Question (a) Three resistors, R = 400 Ω, R 2 = 400 Ω and R 3 = 600 Ω are connected as shown in Figure Q. below. A d.c. supply, V s = 20 V, is to be used. V R d.c. supply V s R 2 R 3 V 2 Figure Q. (i) Calculate the total current drawn from the voltage source and the voltage drop across each resistor. (4 marks) (ii) Calculate the power dissipated in each resistor, giving the answer in mw. (6 marks) (b) Consider the case when the d.c. supply is now replaced by a sinusoidal a.c. supply, 20 V rms at a frequency of 20 khz signal. Sketch the signal for one cycle only, taking care to indicate the period and the peak-to-peak value of the waveform. Calculate the power dissipated in R 3. Your answer will also include a sketch of the waveform of the voltage signal across R 3 for only one cycle of the applied waveform. You should indicate the amplitude as well as the period of the waveform on the diagram. (5 marks) Question is continued on the next page [XE2] 202/203 Page 2 of 6 Printing date: 5/0/203
Question continued (c) Consider the case when the above a.c. supply is now replaced by a square wave signal source at a frequency of 200 Hz. The maximum level of the square wave signal is 5 V and the minimum is 0 V. Replace R 2 and R 3 with a single capacitor, C. Assume that the new values of the components are as follows: R = 500 Ω and C = µf Draw the new circuit diagram. Sketch the waveform for the applied waveform, V s, taking care to indicate the values and units for the horizontal and vertical axes. On the same diagram, sketch the waveform of the signal across the capacitor, V c, with reference to V s. Your answer will include an indication of the values of the amplitude and time at intervals of the time constant. You need only sketch one cycle of the applied square waveform in both cases. You are expected to show all working. (0 marks) [XE2] 202/203 Page 3 of 6 Printing date: 5/0/203
Question 2 R 2 R - + V V 2 Figure Q2. (a) An input voltage, V, of 3 V is applied to the circuit shown in Figure Q2. above. Calculate the output voltage, V 2, if R = 600 Ω and R 2 = 800 Ω. Your answer will include a full rationale (i.e. all working and explanations where appropriate). Assume that a power supply of +/- 0 V is used for the above op-amp circuit. (4 marks) (b) The above input is now replaced by a 5 khz, V rms sinusoidal signal source. Sketch the waveform of the output signal, showing clearly the period and amplitude of the signal, indicating the values on the horizontal and vertical axes. Compare the output signal with the input signal, indicating clearly any differences or similarities. Comment if there is any evidence of clipping at the output. Marks will be given for evidence shown of all calculations. (6 marks) Question 2 is continued on the next page [XE2] 202/203 Page 4 of 6 Printing date: 5/0/203
Question 2 continued (c) A simple op-amp amplifier is required for a temperature sensor which is to be used to measure temperature in the range 0 C to 40 C. At 0 C the output of the temperature sensor is 00 mv, whilst at 40 C, it is 400 mv. You are required to design an amplifier so that the output is approximately 3 V when the temperature sensor gives a reading at 30 C. The following are the only components that are available: a +/- 2 V power supply, a 74 device and one of each of the following standard resistors: kω, 2.2 kω, 3.3 kω, 3.9 kω, 4.7 kω, 5.9 kω and 0 kω. Your answer will include a circuit diagram, full working for the choice of the resistors and op-amp configuration and the final gain of your circuit based on the values of the resistors chosen. (0 marks) (d) Your colleague wants to use the amplifier you designed in (c) above to test her pressure sensor. However, the output of her pressure sensor gives a maximum of V and a minimum of 0.2 V. Advise your colleague as to what the output of your amplifier would be if she were to use your circuit without any modifications. (5 marks) [XE2] 202/203 Page 5 of 6 Printing date: 5/0/203
Question 3 (a) Show with the aid of diagrams and truth tables the differencse between the operation of a 2-input Exclusive-OR gate and a 2-input OR gate. State any assumptions made. (5 marks) (b) A square wave of frequency khz with a maximum voltage of 5 V and a minimum voltage of 0 V is fed to input Y as shown in Figure Q3. below. Logic Input X Input Y Output Z Figure Q3. Show, with justification and appropriate diagrams, what the waveform of output Z will look like for each of the following cases: (i) A logic is fed to input X of a 2-input NAND gate as shown in Figure Q3. above. (4 marks) (ii) A logic 0 is now fed to input X of a 2-input NAND gate as shown in Figure Q3. above. (4 marks) (c) The signal (labelled as INPUT) in Figure Q3.2 (in the next page) is fed to the clock input and the signal labelled T is fed to the T-input of a T-type Flip-Flop. Sketch the waveform at the output of the T-type Flip-Flop, Q T, on the answer sheet giving reasons for your answer. Assume that Q T is initially logic 0 as indicated in Figure Q3.2 below and that the T-type Flip-Flop triggers on the falling edge of the clock pulse. (6 marks) Question 3 is continued on the next page [XE2] 202/203 Page 6 of 6 Printing date: 5/0/203
Question 3 continued INPUT 2 3 4 5 6 7 8 9 0 T 0 Q T 0 Figure Q3.2 for Question 3 (c) (d) Sketch the output waveform, Q D, on the answer sheet if the signal (labelled as INPUT) as illustrated in Figure Q3.3 is fed to the D-input of a D-type Flip-Flop. Assume that Q D is initially logic 0 as indicated in the Figure Q3.3 below and that the D-type Flip-Flop triggers on the rising edge of the clock pulse. (6 marks) Clock INPUT 2 3 4 5 6 7 8 9 0 0 Q D 0 Figure Q3.3 for Question 3 (d) You are advised to use the answer sheet provided in Appendix 3 on page 6 for parts (c) and (d) of this question. Please ensure that your student registration number is completed in the top right hand corner BEFORE you use the sheet. On completion, attach the sheet to your answer book. [XE2] 202/203 Page 7 of 6 Printing date: 5/0/203
Section B Question 4 Attempt only TWO questions in this section (a) Describe briefly what is meant by each of the following: (i) The moment of a force. (ii) The concept of static equilibrium. (iii) The difference between a determinate and an indeterminate system in statics. (iv) A free-body diagram (in simple terms). (8 marks) (b) Figure Q4. shows a schematic of a hydraulic tilting platform system. A force F is exerted on piston A, which in turn actuates piston B through the displacement of an incompressible hydraulic fluid contained in the cylinders and pipe-work between A and B. The value of the effective diameters of pistons A and B are d A = 0.3 m and d B = 0. m respectively. Piston B mechanically links to the tilting platform C with a point surface joint, allowing only one transmissible effort along the vertical axis of piston B. The axis of piston B is located.2 m away from the platform hinge H (cylindrical joint) as shown in Figure Q4.. On platform C sits a crate D of mass m = 0 kg at a distance from the platform hinge of 0.8 m and subjected to friction with platform C following a coefficient of friction of value f = 0.5. (Note: the calculated answers to the questions below are independent of each other. Please use the values provided for each individual question.) Assume that g = 9.8 m/s 2. (i) Calculate the magnitude of reaction forces R, R 2 and R 3 of the mechanical supports of platform C in the position shown in Figure Q4.. Consider the system shown in Figure Q4. to be in static equilibrium and the mass of platform C to be negligible. (4 marks) Question 4 is continued on the next page [XE2] 202/203 Page 8 of 6 Printing date: 5/0/203
Question 4 continued (ii) Determine the displacement of piston B resulting from the movement of piston A along the positive x axis by a distance of 50 mm according to the coordinate system shown in Figure Q4.. (Consider the fluid contained in pistons A and B and connecting pipe to be incompressible and that no leaks occur in the operation of this system). (4 marks) (iii) Calculate the magnitude of force F required on piston A to produce an actuation force on piston B of 50 N. Consider the system to be in static equilibrium and in the position as shown in Figure Q4.. (4 marks) (iv) Calculate the minimum extension of piston B required from the position shown in Figure Q4. so that the crate is about to start sliding along platform C. Consider a coefficient of friction between the crate and platform of value f = 0.5. Please also note that the axis of the piston push rod remains vertical as the platform tilts and at a fixed distance of.2 m away from the platform hinge as shown in Figure Q4.. (5 marks) Platform C, f = 0.5 R Crate D, m = 0 kg R 3 R 2 y x + Piston A, d A = 0.3 m.2 m 0.8 m H F Piston B, d B = 0.3 m Figure Q4. [XE2] 202/203 Page 9 of 6 Printing date: 5/0/203
Question 5 (a) Explain the concepts in adhesives technology of the following: (i) Cohesion (ii) Adhesion (iii) Wetting Briefly describe two examples of an application for adhesives. (8 marks) (b) Figure Q5. shows a "pinball machine" type spring-loaded plunger A of mass m A = 0.3 kg capable of hitting, when the handle of the plunger is pulled and released, a block B (initially at rest) of mass m B = 0.2 kg along a frictionless surface C then up a ramp D inclined by 5 degrees to the horizontal with a friction coefficient f = 0.4. At rest, block B is located in relation to plunger A in such a way that the spring of plunger A needs to extend by 5 mm from its rest position shown in Figure Q5. in order to hit block B and propel it along surface C. Consider the sliding action of plunger A to operate without friction and the value of the spring constant to be 200 N/m. (Note: The calculated answers to the questions below are independent of each other. Please use the values provided for each individual question.) (i) The handle of plunger A is pulled so that the spring is compressed from its rest position by a distance of 50 mm, and then released. Calculate the kinetic energy of the plunger when hitting block B. (5 marks) (ii) Plunger A hits block B at an initial velocity of 0 m/s. Given that the value of the coefficient of restitution for the impact between plunger A and block B is e = 0.6, calculate the magnitude of the velocity of plunger A and block B after impact. (6 marks) (iii) Using the work and energy theorem, calculate the maximum distance, s, reached on ramp D by block B, considering an initial linear velocity of B alongside s at the bottom of the ramp of 4 m/s. Also consider that block B has a value of gravitational potential energy at the bottom of the ramp of zero. (6 marks) Question 5 is continued on the next page [XE2] 202/203 Page 0 of 6 Printing date: 5/0/203
Question 5 continued Plunger A, m A = 0.3 kg Spring shown in its rest position, k = 200 N/m Box B in initial resting position, m B = 0.2 kg Sliding surface C, no friction s Sliding surface D, with friction, f = 0.4 5 deg 5 mm Position of B when starting to slide up ramp D Figure Q5. [XE2] 202/203 Page of 6 Printing date: 5/0/203
Question 6 (a) Describe briefly each of the following: (i) The concept of static friction and kinetic friction. (ii) The direction of a friction force in relation to the sliding or potential sliding direction of an object. (iii) The relationship between friction force and normal force (iv) A simple experiment to determine the static friction coefficient between an object and a surface (8 marks) (b) Figure Q6.2 shows a rotating flywheel featuring a spring loaded braking system. Flywheel A of radius 0.5m rotates about its centre O and has a mass moment of inertia of value I O = 2.5 kg.m 2. Brake shoe B is pressed on the outer radius of the flywheel with a variable normal force N which results in friction force F to be produced according to friction coefficient f = 0.3. The spring C of spring constant value k = 500 N/m is acting onto the brake shoe and can be preset into compression from its natural rest position d 0 by acting on the position of a sliding back plate with an adjustment screw as shown in Figure Q6.2. (Note: the calculated answers to the questions below are independent of each other. Please use the values provided for each individual question.). (i) Calculate the friction force F produced by the brake pad B onto flywheel A when spring C is compressed by s = 30mm from its natural rest position. Consider a friction coefficient of value f = 0.3. (5 marks) (ii) During operation, the magnitude of braking force F is varied according to time in a sequence shown on the plot in Figure Q6.2. Using the principle of impulse and momentum for the case of rotating motion, calculate the rotational speed in rad/s of the flywheel after the braking sequence has occurred at time t = 45s. Consider the initial rotational speed of the flywheel at time t = 0s to be 500 rpm. (6 marks) Question 6 is continued on the next page [XE2] 202/203 Page 2 of 6 Printing date: 5/0/203
Question 6 continued (iii) Using the work and energy theorem, calculate how many revolutions it would take for the flywheel to fully stop from an initial rotational speed of 50 rad/s when a constant braking friction force F of magnitude 20 N is applied to the flywheel. (6 marks) y x + ω Brake shoe B, f = 0.3 d 0 s Spring C, k = 500 N/m O N Adjustment Screw and push-plate r = 0.5 m F Flywheel A, I O = 2.5 kg.m 2 Figure Q6. F ( N ) 30 0 t ( s ) 0 0 5 30 45 Figure Q6.2 [XE2] 202/203 Page 3 of 6 Printing date: 5/0/203
APPENDIX : Formula Sheet for Section A Ohms Law, R = V/I Power, P = V I V rms = 0.707 V peak Resistors in series: R T = R + R 2 Resistors in parallel: /R T = /R + /R 2 Transients: Opamp V c = V ( -e -t/rc ) V c = V e -t/rc Closed-loop Gain for a non-inverting amplifier: V R R G 2 2 V R Closed-loop Gain for an inverting amplifier: V R G 2 2 V R Potential Divider V = R R +R 2 V T V T R V V 2 = R 2 R +R 2 V T R 2 V2 Current Divider I = R 2 R +R 2 I T IT I I 2 R R2 I 2 = R R +R 2 I T [XE2] 202/203 Page 4 of 6 Printing date: 5/0/203
APPENDIX 2: Formula Sheet for Section B Acceleration due to gravity, g = 9.8 m/s 2 Newton's second law: Force = rate of change of momentum Equations of linear motion with constant acceleration (u: initial velocity, v: final 2 2 2 s ut 2at v u 2as v u at s u v 2 velocity) t Equations of circular motion with constant acceleration ω 2 = ω + α.t, θ = /2(ω + ω 2 ).t, θ = ω.t + /2α.t 2, ω 2 2 = ω 2 + 2α.θ Linear motion: Work s 2 s Fds, Power = F.V, Impulse Circular motion: Torque/Moment: M = I.α = F.r, Work = 2 t Md, Impulse 2 Mdt, t centripetal acceleration = ω 2.r = v 2 /r, centripetal force = mω 2 r = m.v 2 /r, Angular momentum = I.ω, rotational kinetic energy = /2.I.ω 2, Rotational power = M.ω t 2 t Fdt Work-energy theorem: total energy at + external work between and 2 = total energy at 2 Principle of impulse and momentum: initial momentum at t + sum of all the impulses applied between t and t 2 = final momentum at t 2 Impact coefficient of restitution: ( V e ( V B A ) ) 2 ( V ( V A B ) ) 2 moments of inertia: solid disc, I = /2 m.r 2, hoop, I = mr 2 Hooke's Law: F = -kx, Elastic potential energy in a spring = /2.k.x 2, [XE2] 202/203 Page 5 of 6 Printing date: 5/0/203
Please ensure that you attach this sheet to your answer book. Student Registration number: Appendix 3 - Answer sheet for Question 3 (c) & (d) INPUT 2 3 4 5 6 7 8 9 0 T 0 Q T 0 Figure Q3.2 for Question 3 (c) Clock INPUT 2 3 4 5 6 7 8 9 0 0 Q D 0 Figure Q3.3 for Question 3 (d) Version 305.02 dsg [XE2] 202/203 Page 6 of 6 Printing date: 5/0/203