TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
Post on 14-Apr-2018
215 Views
Preview:
Transcript
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
1/12
Sharjah Institute of Technology
Assessment Activity Front Sheet
(This front sheet must be completed by the STUDENT where appropriate and included with the work submitted for assessment)
Students Name: Assessors Name:
Date Issued:Completion
Date:Submitted on: / /
Qualification BTEC National Diploma in Communications Technology -Year 2
Unit No.: 28 Unit Title: Further Mathematics for TechniciansOutcome No. : 4 Outcome Title:
Be able to apply calculus.
Assignment No. : 4Assessment Title: Calculus Techniques and Applications
Part: 1 Of 1
In this assessment you will have opportunities to provide evidence against the following criteria.
Indicate the page numbers where the evidence can be found.
Criteria
Refere
nce
To achieve the criteria the evidence must show that
the student is able to:Tick if
met
Page
numbers
P9Find the differential coefficient for three differentfunctions to demonstrate the use of function of afunction and the product and quotient rules.
P10Use integral calculus to solve two simple engineering
problems involving the definite and indefinite integral.
M3Use differential calculus to find themaximum/minimum for an engineering problem.
D2 Use numerical integration and integral calculus toanalyse the results of a complex engineering problem.
DeclarationI certify that this assignment is my own work, written in my own words. Any other persons work
included in my assignment is referenced / acknowledged.
Students Name: Students Signature: Date:
Internal Verifiers approval to use with students
IVs Name: IVs Signature: Date:
Criteria Achieved
P9 P10 M3 D2
Front Sheet
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
2/12
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
3/12
Assignment 3 Trigonometric Expressions and Techniques
Scenario
In your work as a Communications technician , you may have todeal with a
variety of calculations and manipulations that need a knowledgeof differential
and integral calculus. As part of your course you are required toprove your
abilities to do such calculations and manipulations through solvingthe following
tasks.
-
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
4/12
Task 1: [ Pass P9 ]
A.An object moves along the x-axis so that its position at any time, )0( t ,
is given by
( )ttts += 2cos)(
Find the velocity of the object as a function oft.
B.
A ring-shaped conductor with radius R (as shown in the figure above)carries a total charge
(Q) uniformly distributed around it. The electric field at a point P that lies
on the axis of the
ring at a distance x from its center is given by:
( ) 23
224
1
Rx
QxE
o
x
+=
Find the expression for the rate of change of ( xE ) with respect to ( x ),
with the other values being constant.
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
5/12
C.
In electrostatics, the electric field, ( yE ), at a point P due a line charge isrelated to the
perpendicular distance, ( y ), by the following equation:
( )
+= 21
221 4)4
2( yLyL
Eo
y
Where, oL ,, are constants.
Find the expression for the rate of change of ( yE ) with respect to ( y
).
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
6/12
Task 2: [ Pass P10 ]
A.
The angular velocity ( ) is the time rate of change of the angulardisplacement ( )
of a rotating object. See the figure above. In testing the shaft of anelectric motor, its
angular velocity is given by:
25016 tt +=
Where (t) is the time of rotation (in seconds).
Find the angular displacement( )
through which the shaft goes in10 seconds.
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
7/12
B.
A proton is fired at an initial velocity of 150 m/s at an angle of o60 abovethe horizontal
into a uniform electric field as shown in the figure above. Theacceleration (a) due to this
field is, therefore, in the negative y-direction and uniform with a value of24
/1092.1 sm
(the negative sign is chosen so that all quantities directed up are positiveand all quantities
directed down are negative.)
Find the expressions for the y-component of the velocity )( yv and the y-component of
the displacement )( ys for the proton as a function of time (t).
Hint:
dtdva
y
y = , and dtdstv
y=)(
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
8/12
0)0(
,60cos150)0(
=
=
y
y
s
v
Task 3: [ Merit M3 ]
The magnetic reluctance , ( )R , ofan iron core with a rectangular crosssection is inversely
proportional to the product of its width (w) and its depth (d). (See figureabove.)
Find the dimensions of the iron core with the minimum magneticreluctance that can be
cut from an iron piece with a circular cross section which has a diameter(D =10 2 cm ).
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
9/12
Task 4: [ Distinct D2 ]
A small mass of metal attached to a spring which is stretched toundergo simple
harmonic motion described by the following equation:
ttv sin3)( =
Where,
=)(tv velocity of mass as a function of time, t. (m/s)
= angular velocity of oscillation. (rad/s)
If the period of oscillation, T, is equal to 2 seconds, find the
displacement of the
mass after ( 1 ) second using:
1. Simpsons Rule; use n = 10
2. Trapezoidal Rule; use n = 10
3. Integral calculus method.
Then find the percentage error of each ofSimpsons Rule and
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
10/12
Trapezoidal Rule
with respect to the accurate Integral calculus method and
conclude which one is
more accurate.
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
11/12
Feedback Sheet
Assessment Feedback Form(This feedback sheet must be completed by the ASSESSOR where appropriate)
Students Name:
Unit No.: 28
Assessment Title:
Calculus Techniques andApplications
Unit Title: Further Mathematics for Technicians
Outcome No.: 4
Outcome Title:Be able to apply calculus.
Assignment No.: 4
Part: 1 of 1
Criteria
referenceAssessment Criteria Achieved Evidence Comments/feedback
P9
Find the differential coefficient for threedifferent functions to demonstrate the use offunction of a function and the product andquotient rules.
Yes/NoTask1
Calculations
P10Use integral calculus to solve two simpleengineering problems involving the definite
and indefinite integral.Yes/No
Task2calculations
M3Use differential calculus to find themaximum/minimum for an engineeringproblem.
Yes/NoTask3
calculations
D2 Use numerical integration and integralcalculus to analyse the results of a complexengineering problem.
Yes/NoTask4
calculations
Assessors General Comments:
Assessors Name: Ausama Ibrahim Hassan Signature: Date:
Students Comments:
Students Name: Signature: Date:
Student's Work has been Internally Verified
IVs Name: Waleed IVs Signature: Date:
Criteria Achieved
P9 P10 M3 D2
7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1
12/12
top related