// Numbas version: finer_feedback_settings {"name": "USSKL6-30-1 Scientific Basis of Engineering Combined Written Assessment", "metadata": {"description": "

Simple Veriosn of Exam with randomised values

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Question Covering AC power and frquency response

Power & Frequency Response

", "advice": "

see spread sheet

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Q3ai_f_S": {"name": "Q3ai_f_S", "group": "Q3a", "definition": "random(100 .. 150#10)", "description": "

Frequency (f_s)

", "templateType": "randrange", "can_override": false}, "Q3ai_V_PP": {"name": "Q3ai_V_PP", "group": "Q3a", "definition": "random(5 .. 9#1)", "description": "

V_P-P

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DC Offset

", "templateType": "randrange", "can_override": false}, "Q3ai_R_L": {"name": "Q3ai_R_L", "group": "Q3a", "definition": "random(50 .. 150#10)", "description": "

Load Resistor R_L

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Frequency (f_s)

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V_P-P

", "templateType": "randrange", "can_override": false}, "Q3aii_R_L": {"name": "Q3aii_R_L", "group": "Q3a", "definition": "random(2000 .. 2000#1)", "description": "

R_L

", "templateType": "randrange", "can_override": false}, "Q3aii_t_rise": {"name": "Q3aii_t_rise", "group": "Q3a", "definition": "siground(dec(1/(Q3aii_t_rise_modifier*q3aii_f_s)),4)", "description": "", "templateType": "anything", "can_override": false}, "Q3aii_t_rise_modifier": {"name": "Q3aii_t_rise_modifier", "group": "Q3a", "definition": "random(3 .. 4#1)", "description": "

Modifier of t_rise

", "templateType": "randrange", "can_override": false}, "Q3aii_V_DC": {"name": "Q3aii_V_DC", "group": "Q3a", "definition": "random(1 .. 1#1)", "description": "

DC Offset

", "templateType": "randrange", "can_override": false}, "Q3b_R1": {"name": "Q3b_R1", "group": "Q3b", "definition": "random(3000 .. 3600#100)", "description": "", "templateType": "randrange", "can_override": false}, "Q3b_R2": {"name": "Q3b_R2", "group": "Q3b", "definition": "random(2000 .. 2000#1000)", "description": "", "templateType": "randrange", "can_override": false}, "Q3b_R3": {"name": "Q3b_R3", "group": "Q3b", "definition": "random(1800 .. 2000#500)", "description": "", "templateType": "randrange", "can_override": false}, "Q3b_R4": {"name": "Q3b_R4", "group": "Q3b", "definition": "random(10000 .. 20000#2000)", "description": "", "templateType": "randrange", "can_override": false}, "Q3b_VS": {"name": "Q3b_VS", "group": "Q3b", "definition": "random(12 .. 12#1)", "description": "", "templateType": "randrange", "can_override": false}, "Q3c_R_L": {"name": "Q3c_R_L", "group": "Q3d", "definition": "random(1 .. 3#1)", "description": "

Load Resistance (kΩ)

", "templateType": "randrange", "can_override": false}, "Q3c_C1": {"name": "Q3c_C1", "group": "Q3d", "definition": "random(1 .. 3#1)", "description": "

Smoothing Capacitor (uF)

", "templateType": "randrange", "can_override": false}, "Q3c_V_S": {"name": "Q3c_V_S", "group": "Q3d", "definition": "random(20 .. 23#1)", "description": "

Supply Voltage (V_S)

", "templateType": "randrange", "can_override": true}, "Q3c_Z_BDV": {"name": "Q3c_Z_BDV", "group": "Q3d", "definition": "siground(dec(q3c_v_s*(3/20)),2)", "description": "

Zener Diode Reverse Breakdown Voltage (V)

", "templateType": "anything", "can_override": false}, "Q3d_C1": {"name": "Q3d_C1", "group": "Q4d", "definition": "random(10 .. 12#0.1)", "description": "

Capacitance C1

", "templateType": "randrange", "can_override": false}, "Q3d_L1": {"name": "Q3d_L1", "group": "Q4d", "definition": "random(170 .. 190#10)", "description": "

Inductance

", "templateType": "randrange", "can_override": false}, "Q3d_R_L": {"name": "Q3d_R_L", "group": "Q4d", "definition": "random(1 .. 5#4)", "description": "", "templateType": "randrange", "can_override": false}, "Q3d_V_S": {"name": "Q3d_V_S", "group": "Q4d", "definition": "random(1 .. 10#9)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Unnamed group", "variables": []}, {"name": "Q3b", "variables": ["Q3b_R1", "Q3b_R2", "Q3b_R3", "Q3b_R4", "Q3b_VS"]}, {"name": "Q3a", "variables": ["Q3ai_f_S", "Q3ai_R_L", "Q3ai_V_DC", "Q3ai_V_PP", "q3aii_f_s", "Q3aii_R_L", "Q3aii_t_rise", "Q3aii_t_rise_modifier", "Q3aii_V_DC", "q3aii_v_pp"]}, {"name": "Q3d", "variables": ["Q3c_R_L", "Q3c_C1", "Q3c_V_S", "Q3c_Z_BDV"]}, {"name": "Q4d", "variables": ["Q3d_C1", "Q3d_V_S", "Q3d_L1", "Q3d_R_L"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Part a) Signal Waveforms

Draw or derive the voltage and current wave forms for the following:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Waveform

Varibles

Circuit

i. Sinusoidal

R_L: {Q3ai_R_L} Ω

Frequency (f_s): {Q3ai_F_S} Hz

V_P-P:{Q3ai_V_PP} V

DC Offset (V_DC): {Q3ai_V_DC} V

$\"Simple$

ii. Triangular

R_L: {Q3aii_R_L/1000} kΩ

Frequency (f_s): {Q3aii_F_S} Hz

V_P-P:{Q3aii_V_PP} V

DC Offset (V_DC): {Q3aii_V_DC} V

t_Rise: {Q3aii_t_rise*1000} ms

$\"Simple$

SPICE Circuit suitable for analysis: SbE CC1 Q3a (multisim.com)

[4Marks]

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Part b) Power Calculation

The figure shows a resistor network connected to a Triangular Waveform source and the equations that can be used to convert between Star and Delta impedance configurations:

$\"Resistor$

Circuit Varibles: V_S(peak) = {Q3b_VS}V, f = {100}Hz t_rise = {2}ms Hz, R₁= {siground(dec(Q3b_R1/1000),2)}kΩ, R₂= {siground(dec(Q3b_R2/1000),2)}kΩ, R₃= {siground(dec(Q3b_R3/1000),2)}kΩ, R₄= {siground(dec(Q3b_R4/1000),2)}kΩ

For the values given, calculate or determine the RMS power dissipated in the whole circuit and resistor R₁.

SPICE Circuit Suitable for Analysis: *SbE CC1 Q3b (multisim.com)

[6Marks]

Part c) Power Supply

The figure shows a circuit designed for Voltage Reduction, Rectification and Regulation of an AC power source.

Circuit Variables: V_S = {Q3c_V_S}V_RMS; C₁ = {Q3c_C1}mF; R₁={1}Ω; R_L = {Q3c_R_L}kΩ; T₁: Turns on Primary Winding, N_P = 20 and Secondary N_S = 9; Diodes D₁ & D₂, Forward Bias Voltage = 860mV; Diode Z₁, Reverse Breakdown Voltage = {Q3c_Z_BDV}V.

For the component values given, explain how the circuit operates. Ensure that you:

\n
- Draw or derive the wave forms expected/observed at each of the stages (A, B C & D).
- Explain why the wave form changes as it does and what role the components have and why they might have been chosen.
- Calculate or derive the power consumed by the load.
\n

SPICE Circuit Suitable for Analysis: SbE CC1 EL Q3c (multisim.com)

[8 Marks]

Part d) Frequency Response

The circuit shown has a capacitor and inductor in parallel which has been designed to be in resonance at a known frequency. The signal is measured across the load (R_L).

Circuit Varibles: V_S = {Q3d_V_S}V_(RMS), R_L = {Q3d_R_L} kΩC₁ = {Q3d_C1}μF L₁= {Q3d_L1} mH

Using calculation or simulation, evaluate the performance of the circuit in a frequency range from 1Hz to 10kHz. Ensure that you:

Explain what is meant by the term resonance and what role does it play in the circuit.
Calculate or determine the frequency that the circuit will be in resonance.
Plot and discuss the voltage relationship across the capacitor/inductor and the voltage across the load (R_L).
Discuss what application this type of circuit is useful for.

SPICE Circuit Suitable for Analysis: *SbE CC1 Q3d (multisim.com)

[12 Marks]

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Question covering DC and Step response circuits

Steady State & Step Response

", "advice": "

See Spread Sheet

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"Q2b_R3": {"name": "Q2b_R3", "group": "Ungrouped variables", "definition": "q2b_rs1", "description": "

", "templateType": "anything", "can_override": false}, "Q2b_Resistivity": {"name": "Q2b_Resistivity", "group": "Ungrouped variables", "definition": "random(640 .. 640#10)", "description": "

Resistivity of Silicon (Ωm)

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Supply Voltage V

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Resistance of R₁ in MΩ

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Cross Sectional Area mm²

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length pf gauge mm

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Length of sample after load is applied (mm)

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Cross Sectional Area of Guage when load is applied mm²

", "templateType": "anything", "can_override": false}, "Q2b_RS1": {"name": "Q2b_RS1", "group": "Ungrouped variables", "definition": "siground(dec((Q2b_Resistivity*(Q2b_l1/1000))/(Q2b_a1/1000000)),4)\n", "description": "", "templateType": "anything", "can_override": false}, "Q2b_RS2": {"name": "Q2b_RS2", "group": "Ungrouped variables", "definition": "siground(dec((Q2b_Resistivity*(Q2b_l2/1000))/(Q2b_a2/1000000)),4)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Q2b_Resistivity", "Q2b_VS", "Q2b_R1", "Q2b_R2", "Q2b_R3", "Q2b_A1", "Q2b_l1", "Q2b_Volume_of_Sample", "Q2b_l2", "Q2b_A2", "Q2b_RS1", "Q2b_RS2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Part a. Circuit Symbols

For each of the symbols shown in the table, state the name and function of the device:

$\"Circuit$

[4 Marks]

Part b. Wheatstone Bridge Calculation

A Wheatstone Bridge is used to measure the change of resistance before & while a load is applied to a gauge block made of silicon material with resistivity ρ = {Q2b_Resistivity}Ωm.

$\"Wheatstone$

Circuit Varibles: V_S = {Q2b_VS} V, R₁ = {siground({Q2b_R1}/1000000,2)} MΩ, R2 = {siground({Q2b_R2}/1000000,2)} MΩ, R3 = {siground({Q2b_R3}/1000000,2)} MΩ

The dimensions of the gauge before the load is applied are: Cross Sectional Area, A₁ = {Q2b_A1} mm², length, l₁ = {Q2b_l1} mm.

The dimensions of the gauge when the load is applied are: Cross Sectional Area, A₂ = {Q2b_A2} mm², length, l₂ = {Q2b_l2} mm.

Calculate the resistance (R_S1) of the gauge before the load is applied.
Calculate/determine the reading of V_OUT for R_S1
Calculate the resistance (R_S2) of the gauge when the load is applied.
Calculate/determine the reading of V_OUT for R_S2

SPICE circuit suitable for analysis: SbE CC1 Q1b (multisim.com)

[6 Marks]

Part c. Step Response

The circuit shows a Resistor and Capacitor Network as well as the charge/discharge plots of the Capacitor when the switch is closed and opened.

Circuit Varibles: V_S = {5} V, V_B = {2.5} V t_ON={50} ms, t_OFF={200} ms C₁ ={10} μF , R₁ = {10} kΩ, R₂ = {2} kΩ

Explain what is happening in the circuit. What is the relationship between the voltage across and current through the Capacitor.

SPICE circuit suitable for analysis: SbE CC1 Q2c (multisim.com)

[8 Marks]

Part d. Circuit Analysis

The circuit shown is for a simple ‘No Volt Release’ circuit configuration which is used as a safety feature on electrical equipment:

$\"No$

Analyse the operation of this circuit for the intended purpose. Ensure that you:

Explain how the circuit functions including the function of the individual components.
Identify any limitations of the circuit.
Suggest improvements and/or augmentations to enhance the function.

SPICE circuit suitable for analysis: EveryCircuit - No Volt Release

[12 Marks]

Part b. Wheatstone Bridge Calculation

A Wheatstone Bridge is used to measure the change of resistance before & while a load is applied to a gauge block made of silicon material with resistivity ρ = {Q2b_Resistivity}Ωm.

$\"Wheatstone$

Circuit Varibles: V_S = {Q2b_VS} V, R₁ = {siground({Q2b_R1}/1000000,2)} MΩ, R2 = {siground({Q2b_R2}/1000000,2)} MΩ, R3 = {siground({Q2b_R3}/1000000,2)} MΩ

The dimensions of the gauge before the load is applied are: Cross Sectional Area, A₁ = {Q2b_A1} mm², length, l₁ = {Q2b_l1} mm.

The dimensions of the gauge when the load is applied are: Cross Sectional Area, A₂ = {Q2b_A2} mm², length, l₂ = {Q2b_l2} mm.

Calculate the resistance (R_S1) of the gauge before the load is applied.
Calculate/determine the reading of V_OUT for R_S1
Calculate the resistance (R_S2) of the gauge when the load is applied.
Calculate/determine the reading of V_OUT for R_S2

SPICE circuit suitable for analysis: SbE CC1 Q1b (multisim.com)

[6 Marks]

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Question covering Solenoids, Motors and Semiconductors

Electromechanical Application & Control

", "advice": "

See Spreadsheet

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Solenoid Inductace (L₁)

", "templateType": "randrange", "can_override": true}, "Q4b_R1": {"name": "Q4b_R1", "group": "EL Q4b", "definition": "random(1 .. 2#0.2)", "description": "

Solenoid Resistance (Ω)

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The length (l ) of the solenoid in mm

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the gap (g) between the solenoid and the armature in mm

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Force (F) generated by the solenoid in N

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PWM Duty Cycle

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Part a) Semiconductor Circuit Symbols

For each of the symbols shown in the table, state the name of the device and the function:

$\"Semiconductor$

[4 Marks]

Part b) Solenoid Calculation

The figure shows a solenoid electromagnet circuit compromising the inductance of the coil and the series resistance. It is being energised by a battery. The switch has been closed for {100*Q4b_L1*Q4b_R1}s.

$\"Solenoid$

The measured Inductance (L) of the solenoid is {siground(dec(Q4b_L1*1000),4)}mH and the Resistance is {Q4b_R1}Ω. The length (l ) of the solenoid is {Q4b_Solenoid_length}mm and the gap (g) between the solenoid and the armature is {Q4b_Armature_Gap}mm.

What is the current flowing in the inductor to generate a force of {Q4b_F_gen}N?
For this current, what is the magnitude of the supply voltage V_S?

[6Marks]

SPICE circuit suitable for analysis: SbE CC1 EL Q4b (multisim.com)

Part c) DC Motor Driver

The figure shows a circuit used to drive a Permanent Magnet DC Motor.

$\"DC$

Circuit Variables:

V_CC=12V; V_PWM=5V, 1kz, {25}% Duty Cycle; R₁ = 1kΩ; Motor Armature Resistance R_A = 1kΩ; Motor Inductance L_A = 100μH; Diode Reverse Breakdown Voltage = 1kV.

Explain the operation of the circuit. Ensure that you:

Explain the link between the V_PWM and the operation of the MOSFET.
Explain the purpose and operation of the protection diode.

SPICE circuit suitable for analysis: SbE CC1 EL Q4c - Multisim Live

[8 Marks]

Part d) Servo Vs Stepper Motor

Simplified models of Servo Motor Control and a Stepper Motor Control are shown in shown in the figures below:

$\"Stepper$

One of these technologies provides precision position control and the other provides precision motion control. Compare the two technologies highlighting the advantages and disadvantages of each and for each suggest a suitable medical application that they would be best suited for.

Ensure that you give a brief description of how each motor control type functions.

[12 Marks]

Friction & Centripital Motion

Friction & Centripetal Motion

An ambulance is making a turn along a road with a camber (θ = {MeQ7_Camber_theta}°) having a radius of curvature, r= {MeQ7_turn_radius}m. The mass of the ambulance is {MeQ7_Ambulance_Mass}kg. The coefficient of static friction between the tyres and the road (μ) is {MeQ7_CoFriction}. The angle that the ambulance subtends while making the turn (β) is {MeQ7_Turn_Beta}°.

$\"Ambulance$

The ambulance is at the maximum safe speed so no slipping occurs.

", "advice": "

see spreadsheet

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"MeQ7_Camber_theta": {"name": "MeQ7_Camber_theta", "group": "Ungrouped variables", "definition": "random(4 .. 7#1)", "description": "

Road camber (θ)

", "templateType": "randrange", "can_override": false}, "MeQ7_turn_radius": {"name": "MeQ7_turn_radius", "group": "Ungrouped variables", "definition": "random(90 .. 120#10)", "description": "

radius of curvature, r, (m)

", "templateType": "randrange", "can_override": false}, "MeQ7_Ambulance_Mass": {"name": "MeQ7_Ambulance_Mass", "group": "Ungrouped variables", "definition": "random(1000 .. 1200#30)", "description": "

The mass of the ambulance (kg)

", "templateType": "randrange", "can_override": false}, "MeQ7_CoFriction": {"name": "MeQ7_CoFriction", "group": "Ungrouped variables", "definition": "random(0.1 .. 0.3#0.1)", "description": "

The coefficient of static friction between the tyres and the road.

", "templateType": "randrange", "can_override": false}, "MeQ7_Turn_Beta": {"name": "MeQ7_Turn_Beta", "group": "Ungrouped variables", "definition": "random(45 .. 60#5)", "description": "

The angle that the ambulance subtends while making the turn

", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["MeQ7_Camber_theta", "MeQ7_turn_radius", "MeQ7_Ambulance_Mass", "MeQ7_CoFriction", "MeQ7_Turn_Beta"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Part a) Use the vertical components of the forces acting on the ambulance to calculate the total normal reaction force (N_C)

[3marks]

Part b) Resolve the horizontal forces acting on the Ambulance and write an expression that makes the normal reaction force the subject of the equation (i.e N_C = ….).

[3marks]

Part c) Calculate the maximum safe speed in km/h so no slipping occurs?

[3marks]

Part d) How long does it take to complete the turn?

[3marks]

Part e) What kinetic energy will the ambulance have at the end of the turn?

[3marks]

Ensure you include a free body diagram in your workings.

[5 Marks]

"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "Me - Random", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "MeQ2 - Friction on an Incline Plane - Randomised Variables Only", "extensions": [], "custom_part_types": [], "resources": [["question-resources/UWESbeMeCC1_-_Q2_Friction_on_a_Slope.jpg", "/srv/numbas/media/question-resources/UWESbeMeCC1_-_Q2_Friction_on_a_Slope.jpg"], ["question-resources/UWESbeMeCC1_-_Q2_Crate_A_FBD.png", "/srv/numbas/media/question-resources/UWESbeMeCC1_-_Q2_Crate_A_FBD.png"], ["question-resources/UWESbeMeCC1_-_Q2_Crate_A_B_FBD.png", "/srv/numbas/media/question-resources/UWESbeMeCC1_-_Q2_Crate_A_B_FBD.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Robert Bauld", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19446/"}], "tags": [], "metadata": {"description": "

2 bodies on an incline plane

Friction on an Incline Plane

Two blocks, A & B, rest on a slope at an angle of incline θ.

$\"2$

The mass and coefficents of friction between the crates and the plane are:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

	mass (kg)	Coefficient of Friction (μ)
Crate A	{mass_crate_A}	{co_eff_A}
Crate B	{mass_crate_B}	{co_eff_B}

", "advice": "

Worked answers to follow exam

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Acc_Grav": {"name": "Acc_Grav", "group": "Ungrouped variables", "definition": "9.81", "description": "

Gravitational Constant

", "templateType": "number", "can_override": false}, "mass_crate_A": {"name": "mass_crate_A", "group": "Ungrouped variables", "definition": "random(30 .. 40#1)", "description": "", "templateType": "randrange", "can_override": false}, "mass_crate_B": {"name": "mass_crate_B", "group": "Ungrouped variables", "definition": "random(19 .. 25#1)", "description": "

Mass of Crate B (kg)

", "templateType": "randrange", "can_override": false}, "co_eff_A": {"name": "co_eff_A", "group": "Ungrouped variables", "definition": "random(0.15 .. 0.2#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "Co_eff_B": {"name": "Co_eff_B", "group": "Ungrouped variables", "definition": "random(0.25 .. 0.32#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "Theta_A": {"name": "Theta_A", "group": "Ungrouped variables", "definition": "degrees(arctan(co_eff_a))", "description": "", "templateType": "anything", "can_override": false}, "Theta_B": {"name": "Theta_B", "group": "Ungrouped variables", "definition": "degrees(arctan(co_eff_b))", "description": "", "templateType": "anything", "can_override": false}, "Weight_Crate_A": {"name": "Weight_Crate_A", "group": "Ungrouped variables", "definition": "mass_crate_a*acc_grav", "description": "

", "templateType": "anything", "can_override": false}, "Weight_Crate_B": {"name": "Weight_Crate_B", "group": "Ungrouped variables", "definition": "mass_crate_b*acc_grav", "description": "

", "templateType": "anything", "can_override": false}, "fric_A": {"name": "fric_A", "group": "Ungrouped variables", "definition": "weight_crate_a*co_eff_a", "description": "", "templateType": "anything", "can_override": false}, "fric_b": {"name": "fric_b", "group": "Ungrouped variables", "definition": "co_eff_b*weight_crate_b", "description": "", "templateType": "anything", "can_override": false}, "Theta_AB": {"name": "Theta_AB", "group": "Ungrouped variables", "definition": "degrees(Arctan((fric_a+fric_b)/(weight_crate_a+weight_crate_b)))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Acc_Grav", "mass_crate_A", "mass_crate_B", "co_eff_A", "Co_eff_B", "Theta_A", "Theta_B", "Weight_Crate_A", "Weight_Crate_B", "fric_A", "fric_b", "Theta_AB"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Part a) Calculate (to within 1 decimal place) the angle θ when Crate A begins to slide.

[7 Marks]

Part b) Calculate (to within 1 decimal place) the angle θ when Crate B begins to slide.

[2 Marks]

Part c) If the 2 masses are connected at points C & D by a cable.

Calculate the angle (to within 1 decimal place) the two joined crates begin to slide.

[6 Marks]

Ensure you include a free body diagram in your workings.

[5 Marks]

"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "MeQ4 - Kinematics - Randomised Variables Only", "extensions": [], "custom_part_types": [], "resources": [["question-resources/UWESbeMeCC1_Q4_-_Kinematics.png", "/srv/numbas/media/question-resources/UWESbeMeCC1_Q4_-_Kinematics.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Robert Bauld", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19446/"}], "tags": [], "metadata": {"description": "

Rocket Launched to zenith

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Kinematics

At t₀, a small rocket of mass {Rocket_Mass} kg is launched vertically from rest and it accelerates uniformly at {Rocket_Acc} ms^-2 for a period of {Time_1} s, at which point all of the fuel is used(t₁).

The rocket then continues to travel freely in the vertical direction until it eventually reaches its maximum altitude (t₂), after which it falls to earth and impacts the ground at exactly the same height it was launched (t₃).

$\"rocket$

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Acc_Grav": {"name": "Acc_Grav", "group": "Ungrouped variables", "definition": "9.81", "description": "

Acceleration due to gravity.

", "templateType": "number", "can_override": false}, "Rocket_Acc": {"name": "Rocket_Acc", "group": "Ungrouped variables", "definition": "random(20 .. 25#1)", "description": "", "templateType": "randrange", "can_override": false}, "Rocket_Mass": {"name": "Rocket_Mass", "group": "Ungrouped variables", "definition": "random(40 .. 60#5)", "description": "", "templateType": "randrange", "can_override": false}, "Time_1": {"name": "Time_1", "group": "Ungrouped variables", "definition": "random(10 .. 15#1)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Acc_Grav", "Rocket_Acc", "Rocket_Mass", "Time_1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Part a) Calculate the rocket’s velocity at the instant (t₁) when all of the fuel is used.

[2 Marks]

Part b) Calculate the altitude (m) at the instant (t₁) when all of the fuel is used.

[2Marks]

Part c) The time it takes to reach the maximum altitude.

[4Marks]

Part d) The maximum altitude reached.

[4 Marks]

Part e) Its velocity at the instant (t₃) just prior to impact with the ground.

[3 Marks]

Ensure you indicate the relative kinematic values of the rocket on a diagram in your workings.

[5 Marks]

"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "MeQ5 - Centre of Gravity - Randomised Variables Only", "extensions": [], "custom_part_types": [], "resources": [["question-resources/UWESbeMeCC1_Q5_-_Centre_of_Gravity.png", "/srv/numbas/media/question-resources/UWESbeMeCC1_Q5_-_Centre_of_Gravity.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Robert Bauld", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19446/"}], "tags": [], "metadata": {"description": "

Determinig the CoG of a composite part

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Centre of Gravity

A component consists of 3 horizontal concentric solid cylinders, A, B & C fixed together as shown in the diagram.

$\"Component$

The dimensions and material properties are:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n Cylinder \n	\n Material \n	\n Density ρ (kgm^-3) \n	\n Diameter (mm) \n	\n Length (mm) \n
\n A \n	\n Aluminium Alloy \n	\n ρ_A \n	\n {Den_a} \n	\n d_A \n	\n {Dia_a} \n	\n l_A \n	\n {Len_a} \n
\n B \n	\n Copper Alloy \n	\n ρ_B \n	\n {Den_b} \n	\n d_B \n	\n {Dia_b} \n	\n l_B \n	\n {Len_b} \n
\n C \n	\n Steel \n	\n ρ_C \n	\n {Den_c} \n	\n d_C \n	\n {Dia_c} \n	\n l_C \n	\n {Len_c} \n

", "advice": "

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Part a) Calculate the total volume of the component.

[4 Marks]

Part b) Calculate the total mass of the component.

[4 Marks]

Part c) Calculate the total weight of the component.

[2 Marks]

Part d) Calculate the coordinate of the Centre of Gravity along its length.

[5 Marks]

Ensure you show the position of the CoG on a diagram in your workings.

[5 Marks]

"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "MeQ8 - Kinetic & Potential Energy _ randomised variables only", "extensions": [], "custom_part_types": [], "resources": [["question-resources/ME_Q8.png", "/srv/numbas/media/question-resources/ME_Q8.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Robert Bauld", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19446/"}], "tags": [], "metadata": {"description": "

Trolley on a slope

Kinetic & Potential Energy

A trolley of total mass {MeQ8_Trolley_mass} kg is being manoeuvred down a ramp with a {MeQ8_Angle_of_Slope}^\u25e6 slope. During this motion, the trolley experiences a rolling resistance to its motion of {MeQ8_RollingResistance} N.

Whilst travelling at a velocity of {MeQ8_Trolley_v_Start} m/s, a braking force is applied, and the trolley is brought uniformly to rest in a distance (d) of {MeQ8_Distance_Travelled} m. During this period of constant deceleration, it may be assumed that the rolling resistance remains constant, acting to assist the braking force.

$\"Trolley$

During the period that the trolley is slowing down, calculate the following:

", "advice": "

see spreadsheet

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"MeQ8_Trolley_mass": {"name": "MeQ8_Trolley_mass", "group": "Ungrouped variables", "definition": "random(45 .. 55#1)", "description": "

Trolley total mass

", "templateType": "randrange", "can_override": false}, "MeQ8_Angle_of_Slope": {"name": "MeQ8_Angle_of_Slope", "group": "Ungrouped variables", "definition": "random(3 .. 6#1)", "description": "

ramp slope.

", "templateType": "randrange", "can_override": false}, "MeQ8_RollingResistance": {"name": "MeQ8_RollingResistance", "group": "Ungrouped variables", "definition": "random(20 .. 26#1)", "description": "

resistance to its motion

", "templateType": "randrange", "can_override": false}, "MeQ8_Trolley_v_Start": {"name": "MeQ8_Trolley_v_Start", "group": "Ungrouped variables", "definition": "random(0.5 .. 1.5#0.2)", "description": "

Trolley initial velocity

", "templateType": "randrange", "can_override": false}, "MeQ8_Distance_Travelled": {"name": "MeQ8_Distance_Travelled", "group": "Ungrouped variables", "definition": "random(7 .. 17#1)", "description": "

trolley is brought uniformly to rest in a distance (d)

", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["MeQ8_Trolley_mass", "MeQ8_Angle_of_Slope", "MeQ8_RollingResistance", "MeQ8_Trolley_v_Start", "MeQ8_Distance_Travelled"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Part a) The vertical height descended & change in potential energy.

[2 Marks]

Part b) Its decrease in kinetic energy.

[2 Marks]

Part c) The work done against the rolling resistance.

[2 Marks]

Part d) The energy absorbed by the brakes.

[3 Marks]

Part e) The average braking force.

[2 Marks]

Part f) The deceleration.

[2 Marks]

Part g) The resultant decelerating force which acts on the truck parallel to the slope.

[2 Marks]

Ensure you include diagrams in your workings.

[5 Marks]

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Instructions

Ensure you have typed your UWE Candidate No. into the Sheet ID.
If you have forgotten to type you UWE Candidate No. in, click the \"generate different sheets\" button and type the number into the \"start with ID box\"
Please tick the \"page break between questions\" radio button.
Click the \"print this sheet button\" to generate a pdf of the paper (with your UWE Candidate NO. on).
For your submission, you will need to submit the pdf of this paper and a copies of your answer sheets.

You have until 17:30 17 May 2024 to submit your Assessment.
Refer to the guidance document for more detail on the Assessment.

Candidates must answer 4 questions, 2 for Electronics and 2 for Mechanics:\n
- Question 1. This the standard Electronics question that you will need to answer.
- Question 2&3. These are the additional Electronics questions. You will need to answer only one, you may choose which one you answer.
- Question 4. This is the standard Mechanics Question that you will need to answer.
- Question 5,6,7&8. These are the additional Mechanics questions. You will need to answer only one, you may choose which one you answer.
\n

Ver 2.2

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