ebd1a unit4 ass.2 2011-2012.ausama.border&qes

7/30/2019 EBD1A Unit4 Ass.2 2011-2012.Ausama.border&Qes.

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Sharjah Institute of TechnologyAssessment 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:Ausama I.Hassan

Date Issued: /2/2012Completion

Date:20/2/2012 Submitted on: / /

QualificationBTEC LEVEL 3 Extended Diploma in Electrical and Electronic Engineering -Group A (EBD1A)

Unit No.: 4 Unit Title:Mathematics for Engineering

Technicians

Outcome No. : 2 Outcome Title:Be able to use trigonometric methods andstandard formulae to determine areas.

Assignment No.: 2

Assessment Title:Trigonometric Methods and StandardFormulaePart

:1 of

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

Refer

ence

To achieve the criteria the evidence must show that the

student is able to:

Tick if

met

Page

numbers

P4Solve circular and triangular measurement problems involving theuse of radian, sine, cosine and tangent functions.

P5Sketch each of the three trigonometric functions over a completecycle.

P6Produce answers to two practical engineering problems involvingthe sine and cosine rules.

P7Use standard formulae to find surface areas and volumes ofregular solids for three different examples respectively.

Declaration

I 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:Waleed IVs Signature Date

Criteria Achieved

P4 P5 P6 P7


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Front Sheet


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BTEC LEVEL 3 Extended Diploma in Electrical and Electronic Engineering

Unit 4: Mathematics for Engineering Technicians

In your work as a telecommunication technician, you may have to deal with a variety of calculations

and manipulations that need a knowledge of

Task 1: [ P4 ]1.

Figure (1 )

In figure (1), the two circular sectors have the following measurements:

rad.121==

cmr .51 =

cmr .102 =

Find :

A.),(,sec..

,,;.

21

21

AAtoreachofarea

sslengthsArc

B. Measures of 21 .. sands in cm.

C. If the radius sweeps the circle (in both circles) and comes back to its initial

position in

time (T, seconds), write down the angular speed ( )srad /,

(as a functionof (T).


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Then write down the equations for the number of revolutions per seconds

( )frequencyf, , first as a function of (T) then of )( for both circles?

Calculate the values for (T = 0.1 seconds)

D. For each circle, write down the equation of the projection ( )ix of the rotating

pointer,

starting from its initial horizontal position as a function of amplitude ( )ir

,angular speed

and time ( )t .

E.

1. In figure (2), write down the formulae of AandAA tan,.cos,sin in terms of

(a) and

(b) only.

2. Calculate the values of these functions of (A) when :

mbma 4,3 ==

Figure (2 )
http://upload.wikimedia.org/wikipedia/commons/6/6f/Rtriangle.svg


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From the top of a vertical cliff 40 m high, the angle of depression of anobject that is level with the base of the cliff is 34. If ( x) is thedistance of the object from the base of the cliff, calculate its value inmeters.

Example: Calculate the angle of elevation of the line of sight of a person whose eye is 1.7 m

above the ground, and is looking at the top of a tree which is 27.5 m away on level ground and

18.6 m high.

Task 2: [ P5 ]

1.


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Figure (3 )

Scotch Yoke is a device as shown in figure (3). An electrically driven wheel rotates

anticlockwise. On the wheel is a pin at radius (R).

The pin slides in the slot but the yoke can only move up and down in the guide.

Write down an equation for (x) as a function of ( ) for a given ( R=1 unit length )

Plot ( )1

x as a function of ( ) for a given ( R=1 unit length ) for one complete cycle.

2.


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Figure (4 )

Consider, again, the Scotch Yoke but in its new arrangement with the yoke restricted to

horizontal movement this time as shown in figure (4).

Again the wheel rotates anticlockwise. On the wheel is a pin at radius (R).

The pin slides in the slot but the yoke can only move horizontally left and right in the guide.

Write down an equation for (x) as a function of ( ) for a given ( R=1 unit length )

Plot ( )2

x as a function of ( ) for a given ( R=1 unit length ) for one complete cycle.

3. By writing2

1

x

xy = plot y as a function of ( ) for one complete cycle.

Task 3: [ P6 ]


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Figure (5 )

1. Consider two forces of magnitudes 11 Newtons and 8 Newtons

acting on

an electrically charged particle by other two charged particles,with an

angle o30 between them (see figure (5)). Use the Sine and CosineRules to

find the magnitude and direction of the resultant force?

2. Considering the same two forces of magnitudes 11 Newtons and

8 Newtons

acting on the particle, what should the angle between them be in

order

that the magnitude of the resultant force is

A. 19 Newtons?

B. 2 Newtons?


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Task 4: [ P7 ]

I. With the increasing frequency of hurricanes and other severe

weather

phenomena, installation of properlysized pyramidal electric

transducers in

hurricane prone heavily populated areas could become more than justvehicles

ofpowergeneration: they could have additional benefitsby savingboth lives and

property. Thus suggesting that the pyramid such as The Great Pyramid

of Giza

may scale up volumetrically as an antenna/electric transducer.

The Great Pyramid of Giza with its dimensions in proper length units isshown

in Figure (6 ):

1. Write down a formula for the volume V of the pyramid in terms ofits

square base of length (L ) and height (H).

2. Write down a formula for the surface area ( )SA of the pyramid

terms of L

and H.

3. Calculate the values of sAandV ,,


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Figure (6 )

II. A right-angled Cone antenna has a circular base of radius R ,

cone height H and slanted height L as shown in figure (7 ).

1. Write down a formula for the volume V of the Cone in terms of R

and H.

2. Write down a formula for the surface area ( )SA of the Cone in

terms of

L and R.3. Calculate the values of sAandV ,,

If mH 2=

mR 5.0=

III. A rectangular permanent magnet block has a length B, width

W and thickness T with a hole diameter D as shown in figure (8

).


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1. Write down the formula for the volume V of the block in terms of

W, B, T

and D.

2. Write down the formula for the surface area ( )SA of the block in

terms of W, B, T and D.

3. Calculate the values of sAandV ,, when :

mmD 50=

mmB 100=

mmW 60=

mmT 20=

Figure (7 ).

Assessment Feedback Form


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(This feedback sheet must be completed by the ASSESSOR where appropriate

Students Name:

Unit No.: 4Assessment Title:Trigonometric Methods andStandard Formulae

Grading Criteria Achieved:

Unit Title: Mathematics for Engineering Technicians

Outcome No.: 2

Outcome Title:Be able to use trigonometric methods andstandard formulae to determine areas.

Assignment No.: 2

Part: 1o

f1

Criteria

ReferenceAssessment Criteria

Achieve

dEvidence Comments/feedback

P1Solve circular and triangular measurementproblems involving the use of radian, sine, cosineand tangent functions.

Yes/NoTask1:

P2Sketch each of the three trigonometric functionsover a complete cycle. Yes/No

Task2:

P3Produce answers to two practical engineeringproblems involving the sine and cosine rules. Yes/No

Task3:

M2Use standard formulae to find surface areas andvolumes of regular solids for three differentexamples respectively.

Yes/No

Assessors General Comments:

Assessors Name: Ausama I.Hassan Signature: Date:

Students Comments:

Students Name: Signature: Date

Student's Work has been Internally Verified

IVs Name: Waleed IVs Signature Date

Feedback Sheet

Criteria Achieved

P4 P5 P6 P7


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ebd1a unit4 ass.2 2011-2012.ausama.border&qes

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