Engineering Science Data Booklet

Transcription

1 Engineering Science Data Booklet Advanced Higher For use in National Qualification Courses leading to the 2015 examinations and beyond. Publication date: 2016 Publication code: BB6957 ISBN: Published by the Scottish Qualifications Authority The Optima Building, 58 Robertson Street, Glasgow G2 8DQ Lowden, 24 Wester Shawfair, Dalkeith, Midlothian EH22 1FD The information in this publication may be reproduced in support of SQA qualifications. If it is reproduced, SQA should be clearly acknowledged as the source. If it is to be used for any other purpose, then written permission must be obtained from SQA. It must not be reproduced for trade or commercial purposes. Scottish Qualifications Authority 2016

2 For an up-to-date list of prices visit the Publication Sales and Downloads section of SQA s website. For further details telephone SQA s Customer Contact Centre on Page two

3 Contents Preface... 3 Quantities, symbols and units... 4 Decimal prefixes... 5 Mathematical Relationships Energy and power formulae... 6 Mechanisms... 6 Pneumatic Systems... 6 Structures... 7 Properties of materials Bending of beams... 8 Second moment of area (I) of common sections... 9 Dimensions and properties of standard sections Electrical and electronic formulae...13 Transistors...13 Typical operational amplifier circuits Converter circuits...19 Ideal transformer...20 Preface This data booklet is intended for use by candidates in examinations in Engineering Science at Advanced Higher. It may also be used as a reference for assignments at Advanced Higher. It is recommended that candidates should become familiar with the contents of the data booklet through use in undertaking Units of these Courses. It should be noted that the range of data contained in the booklet has been limited to the concepts which may be assessed through written question papers. This range should be supplemented by other resource material as necessary during the course, eg by using data sheets. However, should any additional information (or data not included in this booklet) be required in an examination, such information will be included in the question paper. Teachers/lecturers should note that all of the material contained in this booklet is likely to be examined at some time. With regard to tables of information, not every entry in a table will necessarily be involved in examination questions. From the variety of data offered in this booklet, candidates will be expected to demonstrate the ability to select appropriate information or formulae. Page three

4 Quantities, Symbols and Units Quantity Symbol Unit Abbreviation distance d,x metre m height h metre m length l metre m diameter d metre m radius r metre m area A square metre m 2 circumference C metre m time t second s speed, velocity v metre per second ms -1 mass m kilogram kg force F newton N gravitational acceleration g metre per second per second ms -2 work done E w joule J energy E joule J power P watt W torque T newton metre Nm efficiency η pressure P newton per square metre (pascal) Nm -2 (Pa) temperature T kelvin, celsius K, C specific heat capacity c joule per kilogram per degree kelvin voltage, potential difference V volt V current I ampere (amp) A resistance R ohm W Jkg -1 K -1 frequency f hertz Hz rotational speed n revolutions per minute revs min -1 revolutions per second revs sec -1 stress σ newton per square metre (pascal) Nm -2 (Pa) strain Є Page four

5 Decimal Prefixes Prefix Symbol Multiplying factor peta P tera T giga G 10 9 mega M 10 6 kilo k 10 3 milli m 10-3 micro μ 10-6 nano n 10-9 pico p Mathematical Relationships Quadratic Formula 2 ax + bx + c = 0 b b ac x = 4 2a ± 2 Differentiation Conditions for a maximum value of a function y(x) dy dx dy = 0, < 0 2 dx 2 Page five

6 Relationships Energy and power Potential energy E p = mgh g = 9 8 ms -2 (to 2 significant figures) Kinetic energy E k = ½ mv 2 Heat energy E h = cm T c water = 4200 Jkg -1 K -1 (to 2 significant figures) Electrical energy Work done E e = VIt E w = Fd Power P = E t Electrical power P = VI = V2 R = I2 R Mechanical power P = Fv P = 2πnT (n = number of revs per second) Efficiency η = Energy out Energy in = Power out Power in Mechanisms Velocity ratio VR = speed of input speed of output Input speed x input size = output speed x output size Torque Circumference of circle T = Fr C = π d Moment of force M = Fx (x is perpendicular distance) Principle of moments Σ M = 0 Σ clockwise moments = Σ anti-clockwise moments Conditions of equilibrium Σ F h = 0 Σ F V = 0 Σ M = 0 Pneumatic Systems Pressure, force and area P = F A Area of circle A = π r 2 A = π d2 4 π = 3 14 (to 3 significant figures) Page six

7 Structures Stress Strain σ = F A Є = l l Young's Modulus E = σ Є Factor of Safety = ultimate load safe working load = ultimate stress safe working stress General Bending Equation M I σ = = y E R Shear Force F S = dm dx Properties of materials Material Young's Modulus E knmm 2 Yield stress σ γ Nmm 2 Ultimate tensile stress Nmm 2 Ultimate compressive stress Nmm 2 Mild steel Stainless steels Low-alloy steels Cast iron Aluminium alloy Titanium alloy Nickel alloys Concrete 60 Concrete (steel reinforced) Concrete (post stressed) 100 Plastic, ABS polycarbonate Plastic, polypropylene Wood, parallel to grain Wood, perpendicular to grain Page seven

8 Bending of Beams All beams of length L, second moment of area I, and Young s modulus E. Point C is located at mid-span. ω = load per unit length (uniformly distributed load) Configuration Maximum Deflection F 3 A B = FL 3EI at B W = ωl 4 A B = ωl 8EI at B F 3 A C B = FL 48EI at C A W = ωl C B 4 = 5 ωl 384EI at C F 3 A C B = FL 192EI at C W = ωl 4 A C B = ωl 384EI at C Page eight

9 Second Moment of Area (I) of Common Sections Rectangular B x x D 3 BD Ixx = 12 Circular D I D = π 4 64 Page nine

10 Dimensions and Properties of Standard Sections Dimensions and Properties of Square Hollow Sections y D D x x t y Size D D Designation Thickness t Second moment of area mm mm ( 10 4 mm 4 ) Page ten

11 Dimensions and Properties of Rectangular Hollow Sections y B D x x y t Size D B Designation Thickness t Second moment of area ( 10 4 mm 4 ) mm mm Axis x x Axis y y Page eleven

12 Dimensions and Properties of Joists B y D x x y Depth of section (mm) Breadth of section (mm) Second moment of area ( 10 4 mm 4 ) D B Axis x x Axis y y Page twelve

13 Electrical and electronic Ohm s Law V = IR Resistors in series Resistors in parallel R t = R 1 + R 2 + R R t = 1 R R R resistors in parallel R t = R 1 R 2 (R 1 +R 2 ) Kirchhoff s 1st law Kirchhoff s 2nd law ΣI = 0 (algebraic sum of currents at a node is zero) ΣE = ΣIR (algebraic sum of supply voltages = sum of voltage-drops, in a closed loop) Voltage Divider Electrical power V 1 V 2 = R 1 R 2 P=VI= V 2 R =I 2 R Transistors Bi-polar transistor gain MOSFET transconductance h FE = I c /I b g m = I d / V gs Page thirteen

14 Typical operational amplifier circuits V o = output voltage V i = input voltage V cc = supply voltage = feedback resistance R i = input resistance A v = gain = output voltage input voltage Inverting R i +V cc V i -V cc V o A v = V o V i A v = - R i V o = - R i V i Non-inverting +V cc R i V i -V cc V o A v = V o V i A v = 1 + R i V o = 1 + ( ) R i V i Page fourteen

15 Comparator +V cc -V cc V i V ref V o If V i < V ref, then V o saturates positively If V i > V ref, then V o saturates negatively Difference Amplifier R i +V cc V 1 V 2 R i -V cc Rf V o A v = V o (V 2 - V 1 ) A v = R i V o = R i (V 2 - V 1 ) Page fifteen

16 Summing Amplifier R 1 +V cc V 1 V 2 R 2 -V cc V o A v1 = - R1 A v2 = - R2 A vn = - Rn V o = (A v1 V 1 ) + (A v2 V 2 ) +... ( V 1 ) R 2 R 1 V 2 V o = Voltage Follower +V cc V i -V cc V o V o = V i Page sixteen

17 Integrator C R +V cc V in V cc Vout ΔV out 1 = RC V in dt Schmitt Trigger +V cc +V cc V cc V in V out Page seventeen

18 Wien Bridge Oscillator R C +V cc V cc C R V out Frequency : f = 1 2πRC 555 Timer (astable mode) V cc R R 2 C V out Mark: Space: T 1 = 0 7(R 1 + R 2 )C T 2 = 0 7 R 2 C Frequency: f = 1 44 (R 1 + 2R 2 )C Page eighteen

19 4-bit D A converter MSB R 4-bit binary input 2R 4R LSB 8R V out A D converter Clock Binary Digital Output D C B A Binary counter D A converter V in Analogue Input signal Page nineteen

20 Ideal Transformer Relationships I 1 Ф Ф I 2 V 1 N 1 N 2 V 2 Φ = constant V V 2 1 I1 N = = I N [END OF DATA BOOKLET] Page twenty

21 Engineering Science Data Booklet Advanced Higher For use in National Qualification Courses leading to the 2015 examinations and beyond. Publication date: 2016 Publication code: BB6957 ISBN: Published by the Scottish Qualifications Authority The Optima Building, 58 Robertson Street, Glasgow G2 8DQ Lowden, 24 Wester Shawfair, Dalkeith, Midlothian EH22 1FD The information in this publication may be reproduced in support of SQA qualifications. If it is reproduced, SQA should be clearly acknowledged as the source. If it is to be used for any other purpose, then written permission must be obtained from SQA. It must not be reproduced for trade or commercial purposes. Scottish Qualifications Authority 2016

22 For an up-to-date list of prices visit the Publication Sales and Downloads section of SQA s website. For further details telephone SQA s Customer Contact Centre on Page two

23 Contents Preface... 3 Quantities, symbols and units... 4 Decimal prefixes... 5 Mathematical Relationships Energy and power formulae... 6 Mechanisms... 6 Pneumatic Systems... 6 Structures... 7 Properties of materials Bending of beams... 8 Second moment of area (I) of common sections... 9 Dimensions and properties of standard sections Electrical and electronic formulae...13 Transistors...13 Typical operational amplifier circuits Converter circuits...19 Ideal transformer...20 Preface This data booklet is intended for use by candidates in examinations in Engineering Science at Advanced Higher. It may also be used as a reference for assignments at Advanced Higher. It is recommended that candidates should become familiar with the contents of the data booklet through use in undertaking Units of these Courses. It should be noted that the range of data contained in the booklet has been limited to the concepts which may be assessed through written question papers. This range should be supplemented by other resource material as necessary during the course, eg by using data sheets. However, should any additional information (or data not included in this booklet) be required in an examination, such information will be included in the question paper. Teachers/lecturers should note that all of the material contained in this booklet is likely to be examined at some time. With regard to tables of information, not every entry in a table will necessarily be involved in examination questions. From the variety of data offered in this booklet, candidates will be expected to demonstrate the ability to select appropriate information or formulae. Page three

24 Quantities, Symbols and Units Quantity Symbol Unit Abbreviation distance d,x metre m height h metre m length l metre m diameter d metre m radius r metre m area A square metre m 2 circumference C metre m time t second s speed, velocity v metre per second ms -1 mass m kilogram kg force F newton N gravitational acceleration g metre per second per second ms -2 work done E w joule J energy E joule J power P watt W torque T newton metre Nm efficiency η pressure P newton per square metre (pascal) Nm -2 (Pa) temperature T kelvin, celsius K, C specific heat capacity c joule per kilogram per degree kelvin voltage, potential difference V volt V current I ampere (amp) A resistance R ohm W Jkg -1 K -1 frequency f hertz Hz rotational speed n revolutions per minute revs min -1 revolutions per second revs sec -1 stress σ newton per square metre (pascal) Nm -2 (Pa) strain Є Page four

25 Decimal Prefixes Prefix Symbol Multiplying factor peta P tera T giga G 10 9 mega M 10 6 kilo k 10 3 milli m 10-3 micro μ 10-6 nano n 10-9 pico p Mathematical Relationships Quadratic Formula 2 ax + bx + c = 0 b b ac x = 4 2a ± 2 Differentiation Conditions for a maximum value of a function y(x) dy dx dy = 0, < 0 2 dx 2 Page five

26 Relationships Energy and power Potential energy E p = mgh g = 9 8 ms -2 (to 2 significant figures) Kinetic energy E k = ½ mv 2 Heat energy E h = cm T c water = 4200 Jkg -1 K -1 (to 2 significant figures) Electrical energy Work done E e = VIt E w = Fd Power P = E t Electrical power P = VI = V2 R = I2 R Mechanical power P = Fv P = 2πnT (n = number of revs per second) Efficiency η = Energy out Energy in = Power out Power in Mechanisms Velocity ratio VR = speed of input speed of output Input speed x input size = output speed x output size Torque Circumference of circle T = Fr C = π d Moment of force M = Fx (x is perpendicular distance) Principle of moments Σ M = 0 Σ clockwise moments = Σ anti-clockwise moments Conditions of equilibrium Σ F h = 0 Σ F V = 0 Σ M = 0 Pneumatic Systems Pressure, force and area P = F A Area of circle A = π r 2 A = π d2 4 π = 3 14 (to 3 significant figures) Page six

27 Structures Stress Strain σ = F A Є = l l Young's Modulus E = σ Є Factor of Safety = ultimate load safe working load = ultimate stress safe working stress General Bending Equation M I σ = = y E R Shear Force F S = dm dx Properties of materials Young's Yield Ultimate Ultimate Material Modulus stress tensile compressive E σ γ stress stress knmm 2 Nmm 2 Nmm 2 Nmm 2 Mild steel Stainless steels Low-alloy steels Cast iron Aluminium alloy Titanium alloy Nickel alloys Concrete 60 Concrete (steel reinforced) Concrete (post stressed) 100 Plastic, ABS polycarbonate Plastic, polypropylene Wood, parallel to grain Wood, perpendicular to grain Page seven

28 Bending of Beams All beams of length L, second moment of area I, and Young s modulus E. Point C is located at mid-span. ω = load per unit length (uniformly distributed load) Configuration Maximum Deflection F 3 A B = FL 3EI at B W = ωl 4 A B = ωl 8EI at B F 3 A C B = FL 48EI at C A W = ωl C B 4 = 5 ωl 384EI at C F 3 A C B = FL 192EI at C W = ωl 4 A C B = ωl 384EI at C Page eight

29 Second Moment of Area (I) of Common Sections Rectangular B x x D 3 BD Ixx = 12 Circular D I D = π 4 64 Page nine

30 Dimensions and Properties of Standard Sections Dimensions and Properties of Square Hollow Sections y D D x x t y Size D D Designation Thickness t Second moment of area mm mm ( 10 4 mm 4 ) Page ten

31 Dimensions and Properties of Rectangular Hollow Sections y B D x x y t Size D B Designation Thickness t Second moment of area ( 10 4 mm 4 ) mm mm Axis x x Axis y y Page eleven

32 Dimensions and Properties of Joists B y D x x y Depth of section (mm) Breadth of section (mm) Second moment of area ( 10 4 mm 4 ) D B Axis x x Axis y y Page twelve

33 Electrical and electronic Ohm s Law V = IR Resistors in series Resistors in parallel R t = R 1 + R 2 + R R t = 1 R R R resistors in parallel R t = R 1 R 2 (R 1 +R 2 ) Kirchhoff s 1st law Kirchhoff s 2nd law ΣI = 0 (algebraic sum of currents at a node is zero) ΣE = ΣIR (algebraic sum of supply voltages = sum of voltage-drops, in a closed loop) Voltage Divider Electrical power V 1 V 2 = R 1 R 2 P=VI= V 2 R =I 2 R Transistors Bi-polar transistor gain MOSFET transconductance h FE = I c /I b g m = I d / V gs Page thirteen

34 Typical operational amplifier circuits V o = output voltage V i = input voltage V cc = supply voltage = feedback resistance R i = input resistance A v = gain = output voltage input voltage Inverting R i +V cc V i -V cc V o A v = V o V i A v = - R i V o = - R i V i Non-inverting +V cc R i V i -V cc V o A v = V o V i A v = 1 + R i V o = 1 + ( ) R i V i Page fourteen

35 Comparator +V cc -V cc V i V ref V o If V i < V ref, then V o saturates positively If V i > V ref, then V o saturates negatively Difference Amplifier R i +V cc V 1 V 2 R i -V cc Rf V o A v = V o (V 2 - V 1 ) A v = R i V o = R i (V 2 - V 1 ) Page fifteen

36 Summing Amplifier R 1 +V cc V 1 V 2 R 2 -V cc V o A v1 = - R1 A v2 = - R2 A vn = - Rn V o = (A v1 V 1 ) + (A v2 V 2 ) +... ( V 1 ) R 2 R 1 V 2 V o = Voltage Follower +V cc V i -V cc V o V o = V i Page sixteen

37 Integrator C R +V cc V in V cc Vout ΔV out 1 = RC V in dt Schmitt Trigger +V cc +V cc V cc V in V out Page seventeen

38 Wien Bridge Oscillator R C +V cc V cc C R V out Frequency : f = 1 2πRC 555 Timer (astable mode) V cc R R 2 C V out Mark: Space: T 1 = 0 7(R 1 + R 2 )C T 2 = 0 7 R 2 C Frequency: f = 1 44 (R 1 + 2R 2 )C Page eighteen

39 4-bit D A converter MSB R 4-bit binary input 2R 4R LSB 8R V out A D converter Clock Binary Digital Output D C B A Binary counter D A converter V in Analogue Input signal Page nineteen

40 Ideal Transformer Relationships I 1 Ф Ф I 2 V 1 N 1 N 2 V 2 Φ = constant V V 2 1 I1 N = = I N [END OF DATA BOOKLET] Page twenty

41 Published: September 2016 Change since last published: Removal of MOSFET characteristics curve section on page 13.