1“Qualification Pearson BTEC Level 3 National Extended Diploma in Engineering
Pearson BTEC Level 3 National Extended Diploma in Electrical/Digital Engineering
Pearson BTEC Level 3 National Extended Diploma in Mechanical Engineering
Unit or Element quantity and title
Unit 7: Calculus to unravel engineering issues
Studying purpose(s) (For NQF/RQF solely) A: Look at how differential calculus can be utilized to unravel engineering issues
Project title Fixing engineering issues that contain differentiation
Assessor Helen Christison
Hand out date sixth December 2021
Hand in deadline sixth January 2022
Vocational Situation or Context
You’re working as an apprentice engineer at an organization concerned in the analysis, design manufacturing and upkeep of bespoke engineering options for bigger clients.
A part of your apprenticeship is to spend time working in all departments, nonetheless a sure stage of understanding must be proven earlier than the managing director permits apprentices into the design group and so she has developed a sequence of questions on differentiation to find out if you’re appropriate.
Job 1
Produce a report that incorporates written descriptions, Assessment and arithmetic that reveals how calculus can be utilized to unravel engineering issues as set out beneath.
1 The equation for a distance, s(m), travelled in time t(s) by an object beginning with an preliminary velocity u(ms-1) and uniform acceleration a(ms-2) is:
s=ut+half of at^2
The duties are to:
Plot a graph of distance (s) vs time (t) for the primary 10s of movement if u=10ms^(-1) and a=5ms^(-2).
Decide the gradient of the graph at t=2s and t=6s.
Differentiate the equation to seek out the features for
Velocity (v=ds/dt)
Acceleration (a=dv/dt=(d^2 s)/?dt?^2 )
Use your consequence from half c to calculate the rate at t=2s and t=6s.
Evaluate your outcomes for half b and half d.
2 The displacement of a mass is given by the perform
y=sin 3t .
The duties are to:
Draw a graph of the displacement y(m) in opposition to time t(s) for the time t=0s to t=2s.
Establish the place of any turning factors and whether or not they’re maxima, minima or factors of inflexion.
Calculate the turning factors of the perform utilizing differential calculus and present that are maxima, minima or factors of inflexion through the use of the second by-product.
Evaluate your outcomes from components b and c.
3 The equation for the instantaneous voltage throughout a discharging capacitor is given by v=V_O e^(-t/t), the place V_O is the preliminary voltage and t is the time fixed of the circuit.
The duties are to:
Draw a graph of voltage in opposition to time for V_O=12V and t=2s, between t=0s and t=10s.
Calculate the gradient at t=2s and t=4s.
Differentiate v=12e^(-t/2) and calculate the worth of dv/dt at t=2s and t=4s.
Evaluate your solutions for half b and half c.
Calculate the second by-product of the instantaneous voltage ((d^2 v)/?dt?^2 ).
four The identical capacitor circuit is now charged as much as 12V and the instantaneous voltage is v=12(1-e^(-t/2) ).
The duties are to:
Differentiate v with respect to t to offer an equation for dv/dt.
Calculate the worth of dv/dt at t=2s and t=4s.
Discover the second by-product ((d^2 v)/?dt?^2 ).
5 The acquire of an amplifier is discovered to be G=20 log?(10V_out ),:
The duties are to seek out equations for:
dG/(dV_Out )
(d^2 G)/?dV_Out?^2
6 The displacement, y(m), of a physique in damped oscillation is y=2e^(-t) sin?3t.
The duty is to:
Use the Product Rule to seek out an equation for the rate of the thing if v=dy/dt.
7 The rate of a shifting car is given by the equation v=(2t+3)^four
The duty is to:
Use the Chain Rule to find out an equation for the acceleration when a=dv/dt.
eight A communication sign is given by the perform y=sin?t/t
The duty is to:
Derive an equation for dy/dt utilizing the Quotient Rule.
9 An organization is required to fence off a sq./rectangular space round a robotic arm to adjust to well being and security legislation. They’ve 750m of fencing obtainable.
The duty is to:
Discover the utmost sq./rectangular space they will fence off?
10 You intend to make a easy, open topped field from a chunk of sheet steel by chopping a sq. – of equal measurement – from every nook and folding up the perimeters as proven in the diagram:
If l=200mm and w=150mm calculate:
The worth of x which is able to give the utmost quantity
The utmost quantity of the field
Remark of the worth obtained in half b.
Guidelines of proof required Your casual report ought to include:
Assessment
labored options to the issues
Every labored resolution ought to be laid out clearly and include temporary explanations of the phases of the calculation to point your understanding of how calculus can be utilized to unravel an engineering downside. Your rationalization ought to be detailed in response to questions 9 and 10 to point out how the variables are optimised in every case. Graphs ought to be effectively offered and clearly labelled and comparisons between strategies ought to be correct and effectively offered.
Standards coated by this activity:
Unit/Standards reference To attain the factors you could present that you’ll be able to:
7/A.D1 Consider, utilizing technically appropriate language and a logical construction, the right graphical and analytical differential calculus options for every kind of given routine and non-routine perform, explaining how the variables might be optimised in at the least two features.
7/A.M1 Discover precisely the graphical and analytical differential calculus options and, the place applicable, turning factors for every kind of given routine and non-routine perform and examine the outcomes.
7/A.P1 Discover the primary and second derivatives for every kind of given routine perform.
7/A.P2 Discover, graphically and analytically, at the least two gradients for every kind of given routine perform.
7/A.P3 Discover the turning factors for given routine polynomial and trigonometric features.
Sources of knowledge to help you with this Project Books:
Pearson BTEC National Engineering. Creator: A Buckenham, G. Thomas, N. Grifiths, S. Singleton, A. Serplus, M. Ryan. ISBN 978 1 292 14100 eight
Web sites:
http://www.mathsisfun.com/index.htm
http://www.mathcentre.ac.uk/college students/subjects
https://www.examsolutions.web
Different Assessment supplies hooked up to this Project Temporary None
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1“Qualification BTEC Level 3 National Extended Diploma in Engineering from Pearson
Pearson’s National Extended Diploma in Electrical/Digital Engineering (BTEC Level 3)
Unit or Element quantity and title for Pearson BTEC Level 3 National Extended Diploma in Mechanical Engineering
Calculus to unravel engineering points (Unit 7)
Studying aims (just for NQF/RQF) A: Examine the usage of differential calculus to engineering issues.
Fixing engineering issues that require differentiation is the title of the task.
Assessor Helen Christison is a British actress.
The deadline for submissions is December 6, 2021.
The deadline for submission is January 6, 2022.
Context or Office Situation
You are an apprentice engineer at a agency that specializes in the event, manufacture, and upkeep of customised engineering options for bigger purchasers.
Working in all departments is a part of your apprenticeship, however the managing director requires a selected diploma of experience earlier than permitting apprentices into the design group, so she has ready a sequence of differentiating inquiries to assess if you’re match.
1st activity
Produce a report that features written explanations, Assessment, and arithmetic that demonstrates how calculus might be utilized to unravel the next engineering challenges.
1 The equation for a distance travelled in time t(s) by an object having an preliminary velocity u(ms-1) and uniform acceleration a(ms-2) is s=ut+half of at. 2
The duties are as follows:
If u=10ms(-1) and a=5ms, plot a graph of distance (s) vs. time (t) in the course of the first 10s of movement (-2).
Calculate the graph’s gradient for t=2s and t=6s.
Discover the features for Velocity (v=ds/dt) and Acceleration (a=dv/dt=(d2 s)/?dt?2) by differentiating the equation.
Calculate the rate at t=2s and t=6s utilizing the reply from element c.
Evaluate and distinction your outcomes from components b and d.
2 The perform y=sin 3t calculates a mass’s displacement.
The duties are as follows:
For the time t=0s to t=2s, graph the displacement y(m) versus time t(s).
Decide the placement of any turning factors, in addition to whether or not they’re maxima, minima, or inflexion factors.
Calculate the perform’s turning factors utilizing differential calculus and use the second by-product for example that are maxima, minima, or factors of inflexion.
Components b and c’s outcomes ought to be in contrast.
3 v=V O e(-t/t) is the equation for the instantaneous voltage throughout a discharging capacitor, the place V O is the beginning voltage and t is the circuit’s time fixed.
Draw a graph of voltage in opposition to time for V O=12V and t=2s, between t=0s and t=10s, for V O=12V and t=2s.
Calculate the gradient for time intervals of 2s and 4s.
Calculate the worth of dv/dt at t=2s and t=4s by differentiating v=12e(-t/2).
Evaluate and distinction your responses for components b and c.
Calculate the instantaneous voltage’s second by-product ((d2 v)/?dt?2)
