Es2 Guidance_1012

Engineering Science Guidance Notes FORCES KIT ES2

© TecQuipment Ltd 2012 Do not reproduce or transmit this document in any form or by any means, electronic or mechanical, including photocopy, recording or any information storage and retrieval system without the express permission of TecQuipment Limited. TecQuipment allows you to print and photocopy this document only for use with the Engineering Science Kits. TecQuipment has taken care to make the contents of this manual accurate and up to date. However, if you find any errors, please let us know so we can rectify the problem. TecQuipment supply a Packing Contents List (PCL) with the equipment. Carefully check the contents of the package(s) against the list. If any items are missing or damaged, contact TecQuipment or the local agent.

DB/1012

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ES2 Guidance

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The ES2 Kit - What is it and what can it do? . . . . . . . . . . . . . . . . . . . . 6 List of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 The Work Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Weights, Masses, Weight Hangers and Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 Using the Magnetic Protractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 Accurate Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 Other Things You May Need . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Centre of Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 Triangle of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 Parallelogram of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 Polygon of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

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ES2 Guidance

Introduction

Introduction These Guidance Notes introduce you to the theory for a set of experiments in an engineering science topic. You fit different parts of your kit to a Work Panel to do an experiment. Figure 1 shows a typical experiment.

Work Panel

Parts of your Kit

Figure 1 A Typical Experiment Each kit can do more than one experiment. Each experiment has Worksheets that tell you how to do the experiment. You must use the Worksheets with the Guidance Notes as they: • Introduce the parts in the kit, and list the experiments that it can do. • Give you important information you need to do the experiments or complete your Worksheet.

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The ES2 Kit - What is it and what can it do?

ES2 Guidance

The ES2 Kit - What is it and what can it do? This kit helps you to understand how to predict the centre of gravity and the relationship between angles and forces. It uses different shapes, cords, pulleys and weights to show you how: • Forces must balance for equilibrium • You can use known angles and forces to calculate other forces • You can predict centre of gravity by drawing or find it by simple experiment Scientists and engineers used experiments to prove their theories for forces and angles. Textbooks show these experiments and the theory, giving them popular names. The experiments and theory for this kit try to follow these names (for example ‘the Triangle of Forces’) so you can easily compare them with the information you will find in textbooks or in your classroom lessons. The kit comes in a plastic box with a lid and contains all the parts you need to do the experiments shown in Table 1. Refer to the Parts List in your kit to see what parts are included. Your tutor may decide to ask you to do all the experiments or just a few. You must be sure what you need to do.

List of Experiments

Does my teacher need me to do this experiment?

Experiment 1. Centre of Gravity 2. Forces 3. Parallelogram of Forces 4. Polygon of Forces

Table 1 List of Experiments

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Have I got the Worksheet?

ES2 Guidance

General Notes

General Notes The Work Panel

Thumbscrews

Supports

Figure 2 The Work Panel Mounted in Two Typical ways (Portrait and Landscape) The Work Panel mounts on its Supports in different ways as needed by each experiment. The Worksheets show you which way TecQuipment recommends you to fit the Supports but you may find an alternative that fits better on your desk. To change how the Supports hold the Work Panel, ask your Teacher or a classmate to help you hold the Work Panel while you change the Supports around. However you mount the Work Panel, you must always use two Thumbscrews and Thumbnuts to hold each Support to the Work Panel.

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General Notes

ES2 Guidance

Weights, Masses, Weight Hangers and Forces

Hook

= 10 g Securing clip

Masses

Base plate Figure 3 A Weight Hanger The masses supplied with the Engineering Science Kits have markings in grams (or grammes). For your calculations, you use the unit of force (Newton - N) caused by the pull of gravity (downward) on the masses. 1 kg = 9.81 N or 100 g = 0.98 N Note: Each weight hanger itself weighs 10 g, so you only need to add 9 x 10 g masses to get 100 g.

Weights

Force (N)

1 x 10 g = 10 g

0.098

10 x 10 g = 100 g

0.98

20 x 10 g = 200 g

1.96

30 x 10 g = 300 g

2.94

40 x 10 g = 400 g

3.92

50 x 10 g = 500 g

4.90

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ES2 Guidance

General Notes Using the Magnetic Protractor

Roughly 25 degrees from horizontal.

Roughly 25 degrees from horizontal.

Roughly 75 degrees from horizontal

Figure 4 Using the Protractor See Figure 4, showing a typical experiment with three forces. Slide the protractor on the Work Panel so that its centre is directly behind the Split Ring. Gently pull the split ring up and down to make sure the cords and pulleys have ‘settled’. Align the protractor so the 180 to 0 degree line is horizontal and the 270 to 90 degree line is vertical (use the holes in the Work panel as a guide). Look directly at the Split Ring and measure the angles with respect to vertical or horizontal.

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General Notes

ES2 Guidance

Accurate Results For best results: • Do not rush your experiment. • Double-check each reading. • Repeat the experiment if you are not sure of your results. • Unless the instructions say otherwise, gently tap the Work Panel before taking a reading. Sometimes, mechanical parts ‘stick’ against each other (caused by friction). This is often called ‘stiction’ or static friction. Tapping the Work Panel helps to reduce this. Do not expect your results to be exactly as shown in the theory. Theory always shows ‘perfect’ or ‘ideal’ results, based on perfect scientific conditions. Your ‘actual’ results will be slightly different to theory, based on the accuracy of the equipment and how carefully you do your experiment. You may learn more about your experiments by making and finding mistakes than getting things right first time!

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ES2 Guidance

General Notes Other Things You May Need

These are things that are not in the Kit but you may need to complete your experiments. You should already have these things as part of your normal student equipment (pencil case) or your teacher may supply them:

Part

Image

Pencil

150 mm Rule

Protractor

A Pair of Compasses

Table 2 Other Things you May Need

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General Notes

ES2 Guidance

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ES2 Guidance

Theory

Theory Centre of Gravity

Supporting Force

Centre of gravity (C of G)

Gravity Figure 5 Centre of Gravity Note: Centre of Gravity is often called ‘Centre of Mass’. These are not exactly the same, but can be considered identical for this experiment. Gravity is the downward pull of the Earth on a body. When gravity acts on a body, it pulls all the particles of the body downwards. These particle forces are equivalent to a single force, equal to the weight of the body, acting through a point called the Centre of Gravity (C of G). So, from this, a single force acting upwards through the centre of gravity can support the body. The diagram shows an example of this, where a rope supports a mass. Since the weight of a body acts vertically downwards, the direction of the supporting force must also be vertical (see Figure 5). Because of this, a small weight or plummet (sometimes called a ‘plumb bob’) on a string, called a plumb-line, always hangs vertically. This small weight helps to find the centre of gravity of a body, as shown in the experiment. When engineers design a machine that has parts that move or rotate, the weight of the part is taken to be concentrated at its centre of gravity, and it is important to know the position (or positions) of the centre of gravity. Often the parts are metal plates, so the centre of gravity lies somewhere on the plate. However, on certain shapes, the centre of gravity may be outside the area of the plate. The shape of the plate determines the exact location of its centre of gravity. You can find the centre of gravity of a shaped plate by experiment (as follows), but when you have a simple symmetrical shape or one that easily divides into other simple shapes, you can also use a simple drawing method to find the theoretical centre of gravity. This method follows two useful rules: Rule 1 - If a body is symmetrical (its area is distributed evenly about a line), then the centre of gravity lies on the line of symmetry. Rule 2 - If a body has two parts, then the centre of gravity of the body lies between the centres of gravity of the two parts. If the two parts are the same area, the centre of gravity is midway between them. If the two parts are not the same area, the centre of gravity will be nearer the larger part, the distance being proportional to the relative areas. Figure 6 shows these rules and the basic drawing skills needed to find centres of gravity.

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Theory

ES2 Guidance

Line of symmetry

Line of symmetry

Centre of gravity is along this line

Rule 1

Centre of gravity for a triangle

Centre of gravity for a rectangle

Divide the length of each by two Centre of gravity for this part of the shape

Centre of gravity for the whole shape is along this line

Rule 2 Centre of gravity for this part of the shape

Figure 6 Using Basic Drawing Skills to find the Centre of Gravity of Shapes

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ES2 Guidance

Theory Forces

Forces are vectors. Vectors have both magnitude and direction. This means we can represent a force as a line with an angle from a known reference. The length of this line is the magnitude and the angle is the direction of force.

Triangle of Forces

Space Diagram

Triangle of Forces Force = Y

Force = X

Length = Y q1 O

q3

q2

q2 q3

Length = Z

Length = X q1

Force = Z Figure 7 Space Diagram and Triangle of Forces The forces you use in this activity are in equilibrium, all coplanar and all pull on the same point (concurrent). You can use standard drawing skills to draw these forces as a ‘space diagram’ and a ‘triangle of forces’ diagram. Space Diagram or ‘Free Body’ diagram (see Figure 7) - this is a simple diagram of the three forces at the correct angles showing the relative angles of the forces, but not necessarily the magnitude. You use this as a guide to help you draw the equivalent force diagram. Force Diagram or ‘Triangle of Forces’ (see Figure 7) - this diagram shows the relative forces (as lengths) and the correct angles. If the ends of the triangle do not meet, then you have not correctly drawn the triangle, or the forces are not in equilibrium. You start this drawing by picking one of the known forces, usually the vertical force, then draw the other two forces, working clockwise. You can use this method with good drawing skills to find an unknown force and its angle when you know the other two forces and their angles. This is not the only method to find unknown forces - a mathematical approach can be used, but the drawing method is the simplest to use to introduce the topic.

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Theory

ES2 Guidance

Parallelogram of Forces

Resultant

Figure 8 Parallelogram of Forces When two forces act on a body in different directions, they are equivalent to a single force (the resultant) acting somewhere in between them. An example of this is when two horizontal ropes spread at an angle pull a sledge. The sledge will move in a direction between the ropes along the line of their resultant force. Also, until the sledge moves, its frictional forces will pull back against the ropes with a single force equal and opposite to the resultant of the two rope forces. When three such forces are in equilibrium, and coplanar, their lines of action all meet at a point (O). Using this fact, a graphical method called the Parallelogram of Forces finds the resultant of two coplanar forces at given angles. See Figure 9. To find the resultant of the two forces caused by two weights at A and B: 1. Draw the space diagram of the lines of action (see theory for Forces), at the correct angles. 2. On each line, mark off a distance equivalent to the magnitude of the force caused by the weight. In Figure 9 these are the distances A0, B0 and C0. 3. From the distance marks, draw lines parallel to A0 and B0. The lines will cross at D. OR Use a pair of compasses to draw arcs with radius of OA and OB. In Figure 9, the parallel lines or the compass arcs cross at D. 4. Draw the resultant from O to D. The line between O and D gives the resultant force direction and magnitude. When the system is in equilibrium (not moving), this should be equal and opposite to that of the line OC.

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ES2 Guidance

Theory

D

B

A

B

A

B

A

O

O

O

C

C

C

OR D AO

AB B

A

B

A

B

A

O

O

O

C

C

C

Figure 9 Drawing the Parallelogram

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Theory

ES2 Guidance

Polygon of Forces

Idealised diagram Typical Roof Truss

Figure 10 Polygon of Forces - Roof Truss When engineers design structures such as girders, bridges and roof trusses (see Figure 10) they need to predict the forces acting in each member, allowing them to make the frame strong enough. The Polygon of Forces method helps to find the forces in each member in turn. This experiment shows that in a system containing four or more concurrent coplanar forces, you can find an unknown force if you know the magnitude and direction of the others. This follows on from the Triangle of Forces. However, the force diagram becomes a polygon force diagram, which becomes complicated if you do not draw it in the correct order. For this reason, engineers use ‘Bows Notation’ (devised by R.H. Bow in the 1870s), which uses a simple numbering system.

Space Diagram

Force Diagram d

W2

W3 C

a

B

D

c

A b

W1

W4

d

W2

W3

e

C

c

B

D

E A

a W1

W4 W5

b

Figure 11 Drawing the Polygon of Forces - four and five forces, anticlockwise

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ES2 Guidance

Theory

Figure 11 shows how this works: You draw a space diagram with lines at the known angles (see theory for Triangle of Forces). You then label each sector between the lines with the letters A, B, C etc, deciding whether you will follow a clockwise or anticlockwise direction. Then you start with the force line (W1) that passes between sectors A and B. You draw a line of length equal to the force magnitude (or scale of the magnitude) and label its ends a and b. You then move in your chosen direction to draw the next force line (W2) that passes between sectors B and C, until you complete the force diagram. You leave any unknown force until last, allowing the missing part of the diagram to show its angle and magnitude. Non-concurrent Forces A more advanced force polygon includes non-concurrent forces, where groups of forces pull on two or more points, linked together. You can use the Bow’s notation method to prove this ‘linked polygon’, but it needs an additional point of reference called the ‘Polar Point’. Figures 12 and 13 show you how this works. 1. Start by drawing the Free Body or Space Diagram as shown in the Triangle of Forces theory, deciding whether to work clockwise or anticlockwise. 2. Draw the Force Diagram, ignoring the force in the link (Fx). 3. Pick any point (0) inside the Force Diagram. This is the Polar Point. 4. Draw dotted lines from the Polar Point to each of the points in the Force Diagram. 5. Draw another Space Diagram, identical to the first. 6. Starting with sector A of the Space Diagram, draw a line across it parallel to line 0A of the force diagram. The position is not critical for this first line. 7. Now in sector B of the Space Diagram, draw a line across it parallel to line 0B of the force diagram, so that its end crosses the end of the 0A line. 8. Continue around the Space Diagram until you complete the link polygon. If all lines meet, you have done the task correctly and confirmed that the theory works for equilibrium. Again, just as with the Triangle of Forces and other polygon theory, this method can help to find a missing force and angle.

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Theory

ES2 Guidance

W2

W3 C

Free Body Diagram D

B

Fx

W1

W4 A

E

W5

d

Force Diagram

e

Forces taken anticlockwise

c

a b Figure 12 Linked Polygon Theory 1

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ES2 Guidance

Theory

d

Force Diagram with Polar Point

e

c

0

a

Forces taken anticlockwise

b

W2

W3

0

d

C

0

c

Free Body Diagram with Link Polygon

B

Fx D

e

0 W1

W4 A

E

0

a W5

b

0

Figure 13 Linked Polygon Theory 2 22

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Theory

ES2 Guidance

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