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    Employability Skills: Brush up Your Engineering
    Employability Skills: Brush up Your Engineering
    Employability Skills: Brush up Your Engineering
    Ebook818 pages4 hours

    Employability Skills: Brush up Your Engineering

    By Clive W. Humphris

    ()

    Read preview

    About this ebook

    An enhanced eBook published in full colour. Now including extensive interactive content enabling exploration by inserting any values that would occur in a real situation whereby the graphics are redrawn to reflect those changes.

    Calculations can be also tested against any standard subject textbook to compare the results.

    Interactive Technology when used in the classroom can motivate passive students by encouraging their active participation where STEM subjects are ideally suited to Mobile Interactive Technology.

    Students are more likely to be comfortable with technology they understand i.e. their phone and can interact with, often preferring 'Learning-by-Doing' over traditional pencil and paper methods.

    Full colour graphics that are redrawn for every input change will make the learning experience more enjoyable and effective as it encourages experimentation of real world situations as almost any practical values are accepted.

    Students who struggle to be fully engaged in normal classroom activity can often achieve the unexpected once sat in front of a digital screen where they can learn without the embarrassment of full class exposure.

    Mobile Interactive Technology can bring any STEM textbook to life by inserting printed values from the book into their mobile device and comparing the results.

    Colourful visual presentation assists the learning process as students will more likely remember, thereby increasing their personal confidence as they believe they are learning more as a result. Knowing the content is on their phone encourages them to dip-in in a spare moment more than open a traditional textbook.

    Conclusion: Students will spend more time engaged with the Mobile Interactive Technology than with a traditional textbook.

    For each topic group students can test their understanding by considering an open question whereby their ease of answering will provide an indication of personal progress.

    LanguageEnglish
    PublisherClive W. Humphris
    Release dateOct 9, 2012
    ISBN9781301731466
    Employability Skills: Brush up Your Engineering
    Author

    Clive W. Humphris

    Clive W. Humphris M0DXJ: Ex Technology Teacher. Software Developer, Author and Director of eptsoft limited. Married with two children and four grandchildren.Apprentice Instrument Maker at Marconi’s with Senor Technical Management roles in Radio Rentals and Alcatel Business Systems before starting eptsoft providing educational software to schools colleges and universities worldwide since 1992.Interests outside of developing digital products for eptsoft, include Running, Walking and Reading.

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      Book preview

      Employability Skills - Clive W. Humphris

      EmpEng600

      Table of Contents

      Employability Skills: Brush Up Your Engineering

      by Clive W. Humphris 

      Portable Learning, Reference and Revision Tools.

      Copyright by eptsoft limited 2018

      All rights reserved.

      Acknowledgement

      Our thanks and appreciation goes to John D. Ransley MIEE from Whitbourne in Worcestershire for all his help and expert guidance in developing this eBook and app content.

      Introduction

      Employability Skills titles include interactive eBook content on your mobile device where you can insert your own values directly, view calculations and update graphics that reflect those changes! See the Table of Contents to explore. 

      Calculations can be also tested against any standard subject textbook to compare the results.

      Technical employees thereby have a collection of common formulae to hand that can be used as a quick and easy reference for their workplace.

      Interactive Technology can motivate study and is ideally suited to tablets and phones where the reader is looking for an easy way to brush up their existing skills in a quiet moment without having to resort to heavy reference and textbooks.

      Full colour graphics that are redrawn for every input change will make the refresh experience more enjoyable and effective as it encourages experimentation of real world situations where almost any practical values are accepted.

      Mobile Interactive Technology can also bring any other technical textbook to life by inserting printed values from the book into their mobile device and comparing the results.

      For each topic group readers can TEST THEIR UNDERSTANDING by considering an open question whereby their ease of answering will provide an indication of personal progress.

      8 9 2012-01-02T11:29:00Z 2012-03-21T09:30:00Z 3 709 4045 eptsoft 33 8 4967 9.3821

      AREA: Parallelogram Area.

      Interactive Content!

      A parallelogram is a four sided polygon whose opposite sides are parallel. Also shown are examples of parallelograms that are known by other names, nevertheless they still have the properties that give them a parallelogram shape.

      The length of the perimeter is total length of the sides of the figure. The sides are often named base and slant height. Therefore the perimeter length is equal to the (base length + slant height) × 2.

      A parallelogram area can be calculated simply by multiplying the base by the height. Where the height is determined by the angle a. or can be found by applying Pythagorean theorem to the slant height.

      The area of the triangles outside the parallelogram can be ignored.

      8 9 2012-01-02T11:29:00Z 2012-03-21T09:30:00Z 3 709 4045 eptsoft 33 8 4967 9.3821

      AREA: Trapezium Area.

      A trapezium (trapezoid) is a slightly more complex shape, where all the side lengths and angles can be different or unequal. However, two of the sides will always be parallel. The area is found by adding the length of the top to that of the base and either multiplying by 0.5 or dividing by two.

      The area calculation then considers the shape as a rectangle. The angles are unimportant unless you wish to calculate the length of an unknown side which is then found by applying the trigonometric ratios.

      The perimeter length of a trapezoid is the sum of all the side lengths.

      8 9 2012-01-02T11:29:00Z 2012-03-21T09:30:00Z 3 709 4045 eptsoft 33 8 4967 9.3821

      AREA: Triangle Area.

      A triangle is a polygon (a plane shape having three or more sides) with three sides.

      As some triangles have standard properties they can be given a descriptive name. The right-angle being the most common having one of its angles equal at 90°. The Isosceles triangle will always have two equal sides and two equal angles, where the equilateral has three equal sides and three equal angles. Others not shown are acute-angled where all the angles are less than 90°, Obtuse-angled with one angle greater than 90° and then the scalene triangle where none of the sides or angles are the same.

      The area of a triangle will always be exactly half of a square or rectangular shape with the same height and base dimensions. The angles are unimportant.

      Drawing the triangle inside a rectangle of the same dimensions shows the area of the combined triangles outside the main diagram will equal the triangle area. The perimeter of a triangle is the sum of the lengths of the three sides.

      8 9 2012-01-02T11:29:00Z 2012-03-21T09:30:00Z 3 709 4045 eptsoft 33 8 4967 9.3821

      AREA: Annulus Area.

      To find the surface area of an annulus or ring, which could be drawn for example to show the cross sectional area of a pipe, tube or a flexible copper cable.

      Calculate the area occupied by the outside diameter and subtract that for the hole or central conductor.

      8 9 2012-01-02T11:29:00Z 2012-03-21T09:30:00Z 3 709 4045 eptsoft 33 8 4967 9.3821

      AREA: Cylinder Surface Area.

      A cylinder is a solid with a curved surface and two circular bases. The height is the measurement between the base and top surfaces.

      To determine the area, first consider a cylinder as a tube with the same dimensions and make a cut up the side allowing the shape to be laid flat. You will have a square or rectangle.

      Calculate the surface area of this rectangle and add to it the area of one end, multiplied by two. You then have the total surface area of a cylinder.

      8 9 2012-01-02T11:29:00Z 2012-03-21T09:30:00Z 3 709 4045 eptsoft 33 8 4967 9.3821

      AREA: Pyramid Net and Surface Area.

      A net is a shape that when cut out and folded, will represent a solid object.

      To find the surface area it is necessary to calculate the individual area of one isosceles triangle (pyramid side) and multiply by four, this is then added to the base area.

      8 7 2012-01-02T14:29:00Z 2012-03-21T09:45:00Z 3 516 2946 eptsoft 24 5 3617 9.3821

      SURFACE AREA and SYMMETRY: Surface Area of a Cone.

      Interactive Content!

      A cone is a solid whose base is a circle and whose side tapers to a point, called the vertex or apex and whose height is a vertical line between the base and the apex. The slant height is the length of the side from base to the apex.

      If a cone is slit up the side and laid flat it will form the sector of a circle.

      To find the total surface area of a cone we first calculate the area of the sector and add this to the base area. To enable us to draw the sector shape we would then need to calculate its angle ø using the formulae shown.

      8 7 2012-01-02T14:29:00Z 2012-03-21T09:45:00Z 3 516 2946 eptsoft 24 5 3617 9.3821

      SURFACE AREA and SYMMETRY: Sphere Surface Area.

      A sphere is a solid with a curved surface whose points are all equidistant from the centre. An engineering example of a sphere is a ball bearing.

      The surface area of a sphere is found by applying the formula shown.

      Because of its shape it is difficult to produce a net of a sphere. This would enable a physical measurement the surface area to be taken. However, as with any complex shape one method would be to coat the surface area with some material and then measure how much of that coating it took to cover the object.

      8 7 2012-01-02T14:29:00Z 2012-03-21T09:45:00Z 3 516 2946 eptsoft 24 5 3617 9.3821

      SURFACE AREA and SYMMETRY: Lines of Symmetry.

      A line of symmetry is drawn at a position where one half of the object can be exactly mirrored in the other. It is possible to have more than one line of symmetry where a line can be drawn both horizontally, vertically, diagonally or any other angle on the object.

      Typical examples where this occurs would be for a circle or square.

      8 7 2012-01-02T14:29:00Z 2012-03-21T09:45:00Z 3 516 2946 eptsoft 24 5 3617 9.3821

      SURFACE AREA and SYMMETRY: Planes of Symmetry.

      The two halves, A and B of the object are symmetrical. The line at which they are cut or divided is the 'plane of symmetry'. A plane of symmetry occurs when a three-dimensional object can be cut and mirrored as an opposite half.

      Some objects can have many planes of symmetry depending upon how they are viewed.

      8 7 2012-01-02T14:29:00Z 2012-03-21T09:45:00Z 3 516 2946 eptsoft 24 5 3617 9.3821

      SURFACE AREA and SYMMETRY: Pyramid.

      The pyramid is an example of an object showing more than one line of symmetry. Each cut would produce two identical objects.

      How many faces has a pyramid, how many corners and how many edges? Are all the faces the same shape? What is the shape of the sides and of the base?

      8 7 2012-01-02T14:29:00Z 2012-03-21T09:45:00Z 3 516 2946 eptsoft 24 5 3617 9.3821

      SURFACE AREA and SYMMETRY: Cube.

      The cube is another example of being able to produce two objects with an identical size and shape. Are there any other planes of symmetry for this shape?

      How many faces has a cube, how many corners and how many edges? Are all the faces the same shape? What is the shape of each face?

      VOLUME: Cylinder Volume.

      Interactive Content!

      The volume of a solid geometric object is the amount of space it occupies, measured in terms of length, width and height.

      First find the end surface area and multiply by the length. The volume in this case will be measured in cubic centimetres.

      The measurement of volume can be useful when we need to calculate how many objects or component parts can be fitted into a known container. In practice this is often an estimate as there is always unused space between the items. Nevertheless it can provide a useful guide.

      VOLUME: Triangular Prism Volume.

      The prism is an object with a triangular cross-sectional area and length.

      The calculations for the volume or the space it occupies is based on the surface area of a triangle multiplied by its length. A rectangular shaped box of the same dimensions divided by two would give the same answer.

      VOLUME: Pyramid Volume.

      The volume of a pyramid will always be one third of that for a cube or rectangular solid of the same dimensions.

      It is therefore easy to calculate if you multiply the base area by the height and divide by three. As it's a volume measurement the result is shown as cubed.

      VOLUME: Cone Volume.

      The cone volume will always be one third of the volume of a cylinder with the same dimensions.

      VOLUME: Sphere Volume.

      A sphere could be considered a complex shape.

      It would be difficult to accurately produce a net diagram from which calculations could be made. We have to rely on the formula to find the volume.

      An alternative which could apply to any irregular shape would be to use displacement of a liquid.

      Taking a container with a known volume, which can be calculated, insert the object and measure the amount a liquid left when the sphere is removed. Simple subtraction will confirm the volume of the object.

      COMPOUND MEASURES: Density.

      Interactive Content!

      Compound measures are those with two or more variables. Covering the resultant in the triangle exposes the formula to be used.

      Density of a material is the mass contained within the volume. This is usually called the weight and refers to how heavy the object is. A piece of lead of would be much heaver than a block of plastic with the same dimensions. Density is measured in grams per centimetre cubed (g/cm³) and is found by dividing the Mass by the Volume.

      Mass is the quantity of matter and measured in grams and is a product of Density and Volume.

      Volume is a measure of the amount of space an object occupies. Found by dividing the mass by the density.

      COMPOUND MEASURES: Mass.

      Compound measures are those with two or more variables. Covering the resultant in the triangle exposes the formula to be used.

      Density of a material is the mass contained within the volume. This is usually called the weight and refers to how heavy the object is. A piece of lead of would be much heaver than a block of plastic with the same dimensions. Density is measured in grams per centimetre cubed (g/cm³) and is found by dividing the Mass by the Volume.

      Mass is the quantity of matter and measured in grams and is a product of Density and Volume.

      Volume is a measure of the amount of space an object occupies. Found by dividing the mass by the density.

      COMPOUND MEASURES: Volume.

      Compound measures are those with two or more variables. Covering the resultant in the triangle exposes the formula to be used.

      Density of a material is the mass contained within the volume. This is usually called the weight and refers to how heavy the object is. A piece of lead of would be much heaver than a block of plastic with the same dimensions. Density is measured in grams per centimetre cubed (g/cm³) and is found by dividing the Mass by the Volume.

      Mass is the quantity of matter and measured in grams and is a product of Density and Volume.

      Volume is a measure of the amount of space an object occupies. Found by dividing the mass by the density.

      COMPOUND MEASURES: Speed.

      Compound measures are those with two or more variables. Covering the result variable in the triangle leaves the required formula.

      Speed of an object is the rate of travelling and measured in miles per hour (mph) or kilometres per hour measured (kph) and is found by dividing the Distance by the Time taken.

      Distance is the length covered and measured in miles in this instance and is a product of the speed the object is moving and time taken.

      Time is the total period the object is moving and found by dividing the distance by the speed the object is travelling.

      COMPOUND MEASURES: Distance.

      Compound measures are those with two or more variables. Covering the result variable in the triangle leaves the required formula.

      Speed of an object is the rate of travelling and measured in miles per hour (mph) or kilometres per hour measured (kph) and is found by dividing the Distance by the Time taken.

      Distance is the length covered and measured in miles in this instance and is a product of the speed the object is moving and time taken.

      Time is the total period the object is moving and found by dividing the distance by the speed the object is travelling.

      COMPOUND MEASURES: Time.

      Compound measures are those with two or more variables. Covering the result variable in the triangle leaves the required formula.

      Speed of an object is the rate of travelling and measured in miles per hour (mph) or kilometres per hour measured (kph) and is found by dividing the Distance by the Time taken.

      Distance is the length covered and measured in miles in this instance and is a product of the speed the object is moving and time taken.

      Time is the total period the object is moving and found by dividing the distance by the speed the object is travelling.

      GEOMETRY: Bisecting a Line at Right Angles.

      Interactive Content!

      Each of these topics shows how its possible to accurately draw lines and angles using nothing more than a straight edge and a pair of compasses.

      Beginning with bisecting a line i.e. to find the centre of the line from two distant points here labelled A and B.

      Note that this process finds the centre between points A and B, but also produces two lines at exactly 90° to one another.

      GEOMETRY: Construct a Perpendicular Line.

      A perpendicular line (shown as a vertical) is at right angles to another line (shown as horizontal) and found by creating a mirrored point on the opposite side of the horizontal line before joining them together.

      Note it is possible to connect with the horizontal line from point P anywhere along its length.

      The perpendicular will only be found for a point exactly in the middle of points A and B which is the shortest distance between P and the horizontal line.

      GEOMETRY: Dividing Longer Lengths or Distances.

      Sometimes it is necessary to find the centre or subdivisions of a much longer distance. To make it easier, remove the bulk of the distance so more accurate attention can be applied to a much smaller and manageable section.

      Say you have a vertical wall and you need to find the mid point. Taking a stick slightly longer than half the vertical distance and marking off from both top and bottom will produce an area of overlap to which the previous bisecting technique can be applied. In practice it would most likely be possible to guess by eye the centre point between these two marks on the wall. The closer the length of the stick to half way the more accurate your final estimation will be.

      A similar technique can be applied to very long distances shown here as a running track. A rope is first connected one end to scribe a mark along the track. The same rope is then positioned at the opposite end and a second mark made. The centre will be between these two scribed lines. It's unlikely that any closer accuracy will be required other than a good guess between the marks.

      Sometimes it may be necessary to find sub multiples of a given distance, say a quarter or eighth locations. Each can be found through bisecting the previous sub division. The result can never be more accurate than any previously bisected distances.

      GEOMETRY: Bisecting an Angle.

      This topic will show how any acute angle between 0 and 90° can be divided by two or bisected.

      In the diagram we have labelled the angles produced for explanation, but in practice they could be unknown or at best guessed at.

      To be able to accurately determine a point half-way between the two original lines is usually all that is required when bisecting an angle.

      GEOMETRY: Finding the Centre of Rhombus.

      A Rhombus is a parallelogram where all sides are equal and where the diagonals always bisect at right angles.

      Also diagonals bisect the angles through which they pass i.e. the angles at the corners either side of the red line will always be equal at opposite corners.

      Angles 'A will always equal C' and 'B will always equal D'.

      GEOMETRY: Finding the Centre of a Circle.

      Making constructions using a circle can be made much easier if you can accurately locate the centre from which all other measurements are then taken.

      A simple technique is to construct a box around the circle and mark across the corners.

      Another method would be to draw two lines at right angle touching the perimeter of the circle and bisect the 90 degree angle formed. This will place one line across the centre of the circle. This would then need to be repeated from another direction to form a cross in the centre

      Alternatively use one of the constructions for bisecting angles, again this will need to be completed at least twice at right angles to one another.

      GEOMETRY: Repeating an angle.

      As the length of a chord across a circle (distance between two points on the circumference) represents the angle drawn within the circle, this measurement can be copied and used to draw one or more angles with identical dimensions using the same radius.

      GEOMETRY: Draw Fixed Angles of 30° and 60°.

      Note that for an equilateral triangle all sides are equal and all internal angles added together total 180°.

      We also know that the length of the chord will equal the radius for an angle of 60°, producing an equilateral triangle.

      It is these properties that enable us to accurately draw first, a 60° triangle and then by applying the method shown previously for bisecting any angle we can determine that for 30°.

      GEOMETRY: Draw Fixed Angles of 90° and 45°.

      The semicircle shown extends to 180°. That is made up of three chords each representing 60°.

      Taking the distance from E to F as the base of a triangle then two arcs can be scribed to form point G. This will be exactly centred at the middle of the second chord. Therefore

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