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

Simple Veriosn of Exam with randomised values

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3 Forces Applied to an Eye bolt. Use force components to calculate the Reaction force.

Three wires cause three concurrent forces to act on an eye bolt.

$\"Eye$

\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

	Force	Angle from the x axis
	(N)	(°)
Force 1	{Force1_Mag}	{Force1_Ang}
Force 2	{Force2_Mag}	{Force2_Ang}
Force 3	{Force3_Mag}	{Force3_Ang}

For the reaction force provided by the eye bolt, use force components to determine:

", "advice": "

worked solutions avaiable after exam

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Magnitude of Force 1

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Angle of Pull for Force 1

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Part a) The magnitude.

[12 Marks]

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Part b) The direction. (Give answer to one decimal place).

[3 Marks]

Ensure you include a diagram in your workings.

[5 Marks]

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2 bodies 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}

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Worked answers to follow exam

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Gravitational Constant

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Mass of Crate B (kg)

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

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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]

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Drawing is not to scale

Forces are not shown

A cylindrical, steel tensile test specimen with the original dimensions {Spec_len}mm and {Spec_dia}mm diameter performs as follows in a tensile test:

At the limit of its elastic deformation the force exerted was {Elastic_Force} N.
At its elastic limit the specimen was found to have a length of {Spec_fin} mm.
The maximum force the material withstood was {Max_Force} N.

", "advice": "

Here is the worksheet for the Lab Session on Tensile Testing.

Here is a video expliaining Tensile Testing.

Acceleration due to Gravity ms^-2

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Original Length of Sample (mm)

", "templateType": "randrange", "can_override": false}, "Delta_len": {"name": "Delta_len", "group": "Ungrouped variables", "definition": "random(0.5 .. 1.5#0.05)", "description": "

Change in length of the sample (mm)

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Diameter of the sample in mm

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Force at limit of elastic deformation.

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The maximum force the material withstood (N).

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Cross Sectional Area of the Sample (mm^2)

", "templateType": "anything", "can_override": false}, "Yield_Str": {"name": "Yield_Str", "group": "Ungrouped variables", "definition": "Elastic_Force/Spec_xArea", "description": "

Calculated Yield Strength(MPa)

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Calculated Maximum Tensile Strength(MPa)

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Calculated Strain

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Youngs Modulus (GPa)

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The final length of the specimin in mm

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Diameter of the hook

", "templateType": "randrange", "can_override": true}, "Hook_safety": {"name": "Hook_safety", "group": "Ungrouped variables", "definition": "random(2 .. 5#1)", "description": "

Hook Safty factor

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Cross sectional area of the hook

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Maximum force that the hook can handle

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The maximum mass on the hook

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The safe load that can be applied to the hook.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Acc_Grav", "Spec_len", "Delta_len", "Spec_dia", "Elastic_Force", "Max_Force", "spec_fin", "Spec_xArea", "Yield_Str", "Ten_Str", "Max_Elas_Strain", "Yon_Mod", "Hook_dia", "Hook_safety", "Hook_xArea", "Hook_Max_F", "Hook_max_mass", "Hook_safe_load"], "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 tensile strength of the sample.

[4 Marks]

Part b) Calculate the Youngs modulus of the sample.

[6 marks]

Part c) The same steel is used to manufacture a hook with a minimum diameter d_H of {Hook_dia} mm and has a stated Factor of Safety (FoS) of {Hook_safety}.

Calculate the maximum mass that can suspended for the lifting hook without risk of deformation.

[5 Marks]

Ensure you give a complete explanation for your answers in your workings.

[5 Marks]

"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "UWESbeMeCC2 Q4 - 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": "

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).

$\"rocket$

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Acceleration due to gravity.

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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"}, {"name": "UWESbeMeCC2 Q5 - 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": "

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

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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]

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Friction and Accelration of a block with 2 forces applied

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Ver1.1

A block of mass {Block_Mass} kg rests on a rough horizontal surface, and is subjected to a pushing force of {Push_1} N acting downwards on the block on the left hand side at an angle of {Alpha} ° to the horizontal, and pulling force of {Pull_2} N acting upwards on the block on the right hand side at an angle of {Beta} ° to the horizontal and shown:

$\"Block$

Drawing is not to scale

Given that the block is on the verge of slipping, calculate:

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Part a) The normal reaction between the block and the surface.

[3 Marks]

Part b) The limiting frictional force (N).

[3 Marks]

Part c) The coefficient of friction.

[3 Marks]

Part d) If the block begins to slide and accelerates from rest to {4.6} ms^-1 in {2.18} seconds

Calculate the acceleration of the block .

[3Marks]

Part f) Calculate the kinetic energy (J) gained by the block.

[3Marks]

Ensure you include a free body diagram 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.
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For your submission, you will need to submit the pdf of this paper and a copies of your answer sheets.

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Refer to the guidance document for more detail on the Assessment.

Ver 1.3

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