math
Assignment 2 – Modelling Engineering Situations Using Trigonometry and Calculus
ASSESSMENT FEEDBACK
Note: the Notional Score is for formative feedback purposes only. 5 is allocated as sufficient for meeting the criteria, less than 5 is an indication of extra work required, more than 5 is an indication extra work included.
PASS grade must be achieved:
Outcomes Learner has demonstrated the ability to: Source of evidence Tutors comments Notional Score (10)
Outcome 2
Be able to analyse and model engineering situations and solve problems using trigonometric methods
LO2.1: use trigonometric functions to solve engineering problems
Task 1
LO2.2: use sinusoidal functions and radian measure to solve engineering problems
Task 2
LO2.3: use trigonometric and hyperbolic identities to solve trigonometric equations and to simplify trigonometric expressions
Task 3
Outcomes Learner has demonstrated the ability to: Source of evidence Tutors comments Notional Score (10)
Outcome 3
Be able to analyse and model engineering situations and solve problems using calculus
LO3.1: differentiate algebraic and trigonometric functions using the product, quotient and function of function rules
Task 4
LO3.2: determine higher order derivatives for algebraic, logarithmic, inverse trigonometric and inverse hyperbolic functions
Task 5
LO3.3: integrate functions using rules, by parts, by substitution and partial fractions
Task 6
LO3.4: analyse engineering situations and solve engineering problems using calculus
Task 7
MERIT grade descriptors that may be achieved for this assignment:
Merit Grade Descriptors Indicative Characteristics Source of evidence Tutors comments Notional Score (10)
M1
Identify and apply strategies to find appropriate solutions
The significance of small percentage errors in the measured variables on the overall value has been discussed and justified
Task 7 question 13
M2
Select/design and apply appropriate methods/techniques
In two or more questions, answers have been confirmed by an alternative method.
All Tasks that the individual has indicated
M3b
Present and communicate appropriate findings
Throughout the report, the solutions are coherently presented using technical language appropriately and in a professional manner
All Tasks
General Information
All submissions to be electronic in MS Word format with a minimum of 20 typed words. All answers must be clearly identified as to which task and question they refer to. All work must be submitted through Learnzone.
Task 1 – Learning Outcome 2.1
Use trigonometric functions to solve engineering problems
The diagram shows a roof truss with one axis of symmetry.
Find the sizes of the angles marked with the letters p, q, r, and s.
If DE = 1m find:
The span, AB of the truss
The height of C above the level of AB.
In the force system shown, the maximum tension either of the lifting ropes can withstand is 205kN. Can the 230kN load be lifted safely? Justify your answer by making appropriate calculations.
Task 2 – Learning Outcome 2.2
Use sinusoidal functions and radian measure to solve engineering problems
An oscillating mechanism has a maximum displacement of 3.2m and frequency of 50Hz. At the displacement is 150cm. Express displacement in the general form A sin .
A vehicle is travelling at 180 km/hr and has wheels of 55 cm diameter.
Determine the number of revolutions made by the wheels over 15 km.
Determine the angular velocity of the wheels in both rad/s and rev/s assuming the speed remains constant.
Task 3 – Learning Outcomes 3.3
Use trigonometric and hyperbolic identities to solve trigonometric equations and to simplify trigonometric expressions
Simplify
(use the exponential representation)
Prove
Task 4 – Learning Outcome 3.1
Differentiate algebraic and trigonometric functions using the product, quotient and function of a function rules
Differentiate the following functions with respect to the variable x:
(x^3+1)(x^2+2)
tan??(5x-4)?
x^3 sin?5x
Task 5 – Learning Outcome 3.2
Determine higher order derivatives for algebraic, logarithmic, inverse trigonometric and inverse hyperbolic functions
Sketch the graph and find the maximum and minimum values of the equation:
y=2x^3+3x^2-12x+4
When a shaft rotates with angular velocity ? the displacement y at a distance x from one end due to centrifugal force is given by the equation:
Show that the equation is satisfied by:
y=Ae^nx+Be^(-nx)+C cos?nx+D sin?nx
Where A, B, C, and D are constants.
Task 6 – Learning Outcome 3.3
Integrate functions using the rules, by parts, by substitution and partial fractions
Integrate the following functions using the appropriate method chosen from the list below:
basic rules
by parts
by substitution
using reduction formulae
by using partial fractions
(6x^8-4x^11 )dx
(x^2 ln?x )dx
x^4 e^2x dx
Task 7 – Learning Outcome 3.4
Analyse engineering situations and solve engineering problems using calculus
A body of weight W on the point of slipping down a plane inclined at angle ? to the horizontal is shown below. The component of weight down the slope is Wsin? and that normal to the slope is Wcos?. The friction force F acts up the plane to oppose the motion. Find the coefficient of friction in terms of the angle ?.
A circular door is hinged so that it turns about a tangent. If its diameter is 1.0m find its second moment of area and radius of gyration about the hinge.
The volume V of a liquid of viscosity coefficient delivered after time t when passed through a tube of length l and diameter d by a pressure p is given by
V =
If the errors in V, p and l are 1%, 2% and 3% respectively, determine the error in .
End of assessment brief
Created: 2013-01-18 00:29
Deadline: 2013-01-18 21:38
Time Left: 19h 12m
Level: —
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