Engineering

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Statics Questions

Question 1 – Forces

A force of 5 kN is acting up and to the right at 30° to the horizontal. Determine its horizontal and vertical components.

Hints: start by drawing a diagram

Fx=Fcosθ               Fy=Fsinθ                  

F= Fx2+ Fy2     and     tanθ= FyFx

Question 2 – Forces

If the components of the force acting on a gear tooth are 54.6 N in the radial direction and 150 N in the tangential direction, determine the total force and the angle between the force and tangential direction.

Question 3 – Weight

A man has a mass of 79 kg. What is his weight?

Solution

Question 4 – Weight

What is the force in a cable supporting a load of 1.5 tonnes?

Question 5 – Calculating Forces  

A vehicle having a mass of 1.35 tonnes is standing on an incline at 15° to the horizontal. Determine the components of its weight parallel and perpendicular to the road surface.

Question 6 – Axial loading

Determine all support reactions for the beam shown below.

 

 

 

 

 

 

Question 7 – Shear Stress

Determine the force required to punch a 12 mm diameter hole in a mild steel plate 6 mm thick.

 

Question 8 – Shear stress

If the diameter of the mild steel pin in the figure below is 10 mm, and the maximum force applied to the coupling is 11.3 kN, what is the shear stress in the material of the pin and the factor of safety?

 

 

 

Question 9 – Bolted Joints

A simple lap joint is composed of two steel straps, 40 mm wide x 8 mm thick, held together by a single bolt 16 mm in diameter. calculate the allowable strength of the joint.

 

Assume:

allowable stress in shear: 90 MPa

allowable stress in tension: 110 MPa

allowable stress in compression 220 MPa

 

Question 10 – Torsional Stress

Calculate the torsional sheer stress in a 50 mm diameter shaft if it is subjected to a torque of 1400 N.m.

 

 

Question 11 – Welded Joints

For a fillet weld of 8 mm nominal size and electrode strength of 410 MPa, determine:

a) the throat thickness

b) the allowable stress

c) the allowable load per millimetre of length

d) the legnth of the weld required to carry a load of 52.6 kN

 

 

Question 12 – Bending of Beams

For the beam and loading shown below, determine the bending moments at the three points under the applied forces.

Summation of moments about each of the two supports will show that the bending moment at the supports of a simply supported beam is always zero. It is left to the student to verify this statement by actual calculations. Here it is useful to recognize that if we always work consistently from left to right, i.e. condier moments due to forces acting on the left-hand side portion of the beam only, and use the usual sign convention for moments, i.e. positive-clockwise, negative – anticlockwise, the answers obtained give the correct sign for the bending moments automatically.

Dynamics Questions

Question 13 – Speed

In the last Grand Prix race of the series on his way to the World Driver’s Championship title in 1980, Alan Jones of Australia established a new lap record for the 6 km road course at Watkins Glen, NY, by covering the distance in 1 min 43.8 s. What was his speed in meters per second? What was it in kilometers per hour?

Question 14 – Equations motion/ Linear acceleration

A car starts from rest and accelerates at the rate of 1.2 m/s2 for 15 s. determine the velocity reached after 15 s.

Question 15 – Velocity/acceleration  

If, after travelling for some distance at a constant velocity of 18 m/s, brakes are applied to the car producing a retardation of 2 m/s2, determine the time taken to reduce its velocity to 10 m/s.

Question 16 – Displacement  

Find the total emergency stopping distance of a car and the total time taken from the point where the driver sights danger if the driver’s reaction time before applying brakes is 0.9 s. The initial velocity is 60 km/h and retardation due to the brakes is 7.5 m/s2.

Question 17 – Freely falling bodies

A stone is dropped from the deck of a bridge and strikes the water below after 3.4 seconds of free fall. Neglecting air resistance, calculate the height of the bridge above the water and the velocity with which the stone strikes the water.

Question 18 – Acceleration against Resistance

A train of total mass 120 t is travelling at 60 km/h on a level track. The tractive resistance is 80 N/t. Calculate the tractive effort required to accelerate the train to 100 km/h in 30 s.

Question 19 – Acceleration again Gravity

A loaded lift has a total mass of 1500 kg. Determine the forces in the cables when:

a)      The acceleration of 2 m/s2 is upwards

b)     The acceleration of 2 m/s2 is downwards

 

Question 20 – Acceleration against dry sliding friction

A block of mass 26.3 kg is sliding along a horizontal supporting surface with an acceleration of 1.7 m/s2 when pulled by a horizontal applied force FP. If the coefficient of kinetic friction between the clock and the surface is 0.35, what is the magnitude of the applied force?

Question 21 – Centrifugal Force

In an amusement park, a car travels in a vertical circular path of diameter 30 m as shown in the figure below. determine the minimum speed of the car so that there is no tendency for it to fall off the track.

 

 

Question 22 – Angular rotation  

A Cam in a mechanism makes 500 revolutions in 2 minutes 37 seconds. What is its average angular velocity per minute and in radians per second?

 

Question 23 – Angular Acceleration  

A flywheel starts from rest and is accelerated at the rate of 2.4 rad/s2 for 30 s. determine the angular velocity reached after 30 s.

 

Question 24 – Angular displacement

A flywheel turns at a constant angular velocity of 150 revolutions per minute for 45 seconds before a brake is used to bring it to rest with a retardation of 0.5 radians per second squared. Determine the total time and the total angular displacement of the wheel.

 

Question 25 – Inertia

Determine the mass moment of inertia of a flywheel in the form of a disc, 50 mm wide x 300 mm diameter, if the material is steel (density of steel is 7800 kg/m3).

 

Question 26 – Torque

Determine the net torque required to give a flywheel with a mass moment of inertia of 0.75 kg.m2 an angular acceleration of 16 rad/s2.

 

Question 27 – Law of a machine

A simple machine is represented diagrammatically below. The load is 450 N and the effort is 50 N. the distances moved by the load and by the effort are 100 mm and 1200 mm respectively. Calculate the mechanical advantage and the velocity ratio.

 

 

Question 29 – Work/energy

A hoist lifts a load of 1.5 t through a vertical distance of 20 m. determine the amount of work done against gravity.

 

 

Question 30 – Power

If it takes 27 s to lift the load in the previous question, what is the average power required?

 

 

 

 

 

 

 

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Instructions

Draw free hand sketches of the following diagrams:

 

For all of the problems, the items shown in Figure 1, Figure 2, and Figure 3 are 2 centimetres  wide, 1.5 1 centimetres high, and 1 centimetres deep.

 

The holes in:

Figure 1(b), Figure 1(c), Figure 1(d),

Figure 2(c), and Figure 2(d) are through holes.

The hole in Figure 2(b) is through the front face only

 

Question 1 – Free Hand Drawing Basics

 

Question 1.1  – You may use graph paper for the following exercises

1.            Draw a series of 10 parallel lines approximately 100mm long and 15mm apart on an A4 sheet.

2.            Draw a series of 10 vertical lines approximately 100mm long and 15mm apart on the same A4 sheet.

3.            Draw a series of 10 parallel lines approximately 100mm long and 15mm apart on the same A4 sheet at an angle of 45°.

4.            Draw a series of 10 parallel lines approximately 100mm long and 15mm apart on the same A4 sheet at an angle of 135°.

5.            Draw a series of 10 parallel lines approximately 100mm long and 15mm apart on the same A4 sheet at an angle of 60°.

6.            Draw a series of 10 parallel lines approximately 100mm long and 15mm apart on the same A4 sheet at an angle of 120°.

 

 

Question 1.2 – You may use graph paper for the following exercises

1.            Draw a 100mm x 100mm square on an A4 sheet.

2.            Draw a 50mm x 50mm square on the same A4 sheet.

3.            Draw a 25mm x 50mm rectangle on the same A4 sheet at an angle of 45°.

4.            Draw a 60mm x 30mm rectangle on the same A4 sheet at an angle of 135°.

5.            Draw a 75mm x 75mm square on the same A4 sheet at an angle of 60°.

6.            Draw a 10mm high x 100mm long rectangle parallel bottom of the A4 sheet.

 

 

Question 1.3 – You may use graph paper for the following exercises

Create freehand oblique sketches of the objects in Figure 1. (The objects are shown as oblique projections, so you must simply recreate the drawing by freehand sketching.)

 


 

Question 2 –  You may use graph paper for the following exercises

Create freehand isometric sketches of the objects in Figure 1. (The objects are shown as oblique projections.)

 

 

Figure 1

 

 

 

 

 

 

 

 

Question 3 – orthographic sketches

Create freehand orthographic sketches of the objects in Figure 1.  (The objects are shown as oblique projections.)

Question 4 – Isometric and Oblique Sketching

Create freehand oblique sketches of the objects in Figure 2. (The objects are shown as isometric projections.)

 

Figure 2

 

Question 5 – Orthographic Sketches

Create freehand orthographic sketches of the objects in Figure 2.

(The objects are shown as orthographic projections, so you must simply recreate the drawing by freehand sketching.)


 

Question 6 – Oblique Sketches

Create freehand oblique sketches of the objects in Figure 3. (The objects are shown as orthographic projections.)

 

Question 7  – isometric sketches

Create freehand isometric sketches of the objects in Figure 3. (The objects are shown as orthographic projections.)

Figure 3

 

 


 

Question 8 – Perspective Sketching

Question 8.1

Reproduce the Tee Block on an A4 sheet using two-point perspective looking in the direction of the arrow.

 

Question 8.2

Reproduce the Sliding Socket on an A4 sheet using two-point perspective looking in the direction of the arrow.

 

Question 8.3

Reproduce the Slotted Wedge on an A4 sheet using two-point perspective.

Question 8.4

Reproduce the Corner Stop on an A4 sheet using two-point perspective looking in the direction of the arrow.

 


 

Samples

 


 

 

 


 

Types of Sketches

 


 

Line Types

 

 

Chapter 3 of Modern Graphics Communication by Giesecke, Mitchell, Spencer, Hill, Dygdon, Novak, and Lockhard, 3rd edition.  Prentice-Hall, 2004.

Technical Drawing by Giesecke, Mitchell, Spencer, Hill, Dygdon, and Novak, 9th edition.  Macmillan, 1991

 

 

 

 

 

 

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MEM12025A – Use graphical techniques and perform simple statistical computations

 

Question 1 –  Statistical Data

   

Question 1.1

A company manufactures 025mm steel bars cut into 1.8 metre lengths. The diameter of each bar is measured at the middle of the length for the purpose of quality control. The results for the bars are 19.9, 19.8, 20.1, 19.9, 19.7, 20.1, 20.0, 19.6, 19.7, 20.1, 20.2, 20.0, 19.9, 19.8, 20.1, 20.0, 19.7, 19.6, 19.9 and 20.2.

Determine the Median, Mode, upper, lower and mid quartiles.

 

Question 1.2 

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint.

3.4

2.5

4.8

2.9

3.6

2.8

3.3

5.6

3.7

2.8

4.4

4.0

5.2

3.0

4.8

 

Calculate the Median, Mode, upper, lower and mid quartiles for this data

 

Question 1.3

According to the journal Chemical Engineering, an important property of a fibre is its water absorbency. A random sample of 20 pieces of cotton fibre was taken and the absorbency on each piece was measured.

The following are the absorbency values:

 

18.71

21.41

20.72

21.81

19.29

22.43

 

20.17

23.71

19.44

20.50

18.92

20.33

 

23.00

22.85

19.25

21.77

22.11

19.77

 

18.04

21.12

 

 

 

 
                   

 

Calculate the Median, Mode, upper, lower and mid quartiles for this data

 

 

Question 1.4

A certain polymer is used for evacuation systems for aircraft. It is important that the polymer be resistant to the aging process. Twenty specimens of the polymer were used in an experiment. Ten were assigned randomly to be exposed to an accelerated batch aging process that involved exposure to high temperatures for 10 days. Measurements of tensile strength of the specimens were made, and the following data were recorded on tensile strength in kPa:

No aging:

227

222

218

217

225

 

218

216

229

228

221

Aging:

219

214

215

211

209

 

218

203

204

201

205

 

Calculate the Median, Mode, upper, lower and mid quartiles for both conditions of aging.


 

 

 

Question 2 –   Types of Charts

Question 2.1

Create a bar chart for the following set of data on the items contained in a storage cabinet; Sheers – 45, Pliers – 26, Hack Saws – 48, Ball Peen Hammers – 15, Claw Hammers – 34, Jack Planes – 18, Panel Saws – 59, Wire Cutters – 29, Bastard Files – 18, Cross-cut File – 38, Spoke Shave – 11, Panel Saw – 39, Rip Saw – 6, Scribes – 19, Gouge – 33, Welding Mask – 44.

 

Question 2.2

Create a 3D column chart showing the following salaries of a local company; President – $145000, General Manager – $189000, Secretary – $84500, Office Workers – $61250, Section Leaders – $62750, Production Workers – $42500, Cleaners – $35000.

 

Question 2.3

Produce an Exploded 3D Pie Chart showing the distribution of marks from a set of class exercises; John – 59%, Mary, 86%, Thai – 53%, Tran – 63%, Ahmed – 74%, Sohail ­85%, Barry – 49%, Janice – 38%, Ingrid – 92%, Mohammed – 81%, George – 16%.

 

Question 2.4

Create an Area chart to suit the distribution of Gold, Silver and Bronze medals awarded during the inception of the Olympic Games.

Team

Gold

Silver

Bronze

Team

Gold

Silver

Bronze

USA

929

729

638

Sweden

142

160

173

Russia

395

319

296

Australia

131

137

164

UK

207

255

253

Hungary

159

141

159

France

191

212

233

Japan

153

129

127

Germany

163

163

203

China

123

112

126

Italy

190

157

174

Austria

163

117

105

Skill Practice Exercise MEM-SP-0205.

Create a 3D Line Chart showing the following interest rates at the local “loan shark”; Day 1 – 15.00%, Day 2 – 15.25, Day 3 – 16.15, Day 4 – 17.02, Day 5 – 18.59, Day 6 ­22.34%, Day 7 – 35.50%.

 

Question 2.5

The revenues of a manufacturing business are laid out in the following table:

 

2010

2011

2012

Total Revenue

$382837

$383291

$375682

Total Expenses

$257190

$259726

$268645

Profit/Loss

$125647

$123565

$107037

Create a Column chart showing the Total Revenue, Total Expenses and the Loss/Profit for the indicated years.


 

 

Question 2.6

Create a Pie Chart showing that 10% of students travelled to college by car, 45% rode a bycicle, 30% came by bus, and 15% walked.

 

 

Question 2.7

Create a Line Chart showing the distribution of marks for a set of skill practice exercises obtained by Joel; MEM09202A – 72%, MEM09208A – 75%, MEM16008A – 81%, MEM30001A – 80%, MEM30004A – 39%, MEM30004A – 69%, MEM30012A – 83%, MSAENV272B – 91%, MSATCS501A – 70%, MSATCS502A – 76%.

 

Question 2.8

The projected water usages for three development sites are estimated in the following table. From the given data create a 3D Area chart.

Year

Balmoral

Cowan

Maitland

Year

Balmoral

Cowan

Maitland

2004

17953300

6284563

3902433

2015

20551668

7915423

4031375

2005

18387170

6239591

3698998

2016

20565653

7982723

4113504

2006

18750805

6421633

3519683

2017

20595611

8015628

4186249

2007

19062302

6767108

3377652

2018

20641383

8023235

4246885

2008

19391817

7027177

3379175

2019

20701978

8020414

4287144

2009

19756036

7157013

3487413

2020

20776360

8014522

4308337

2010

20071776

7247387

3639514

2021

20841000

8017312

4316377

2011

20292625

7304345

3718734

2022

20894663

8031845

4317904

2012

20433568

7488245

3804250

2023

20937841

8055989

4315765

2013

20513902

7661745

3871708

2024

20971290

8085462

4317193

2014

20549048

7807797

3946975

2025

20995736

8116568

4324264

 

 

 

Question 2.9

The number of products, sales and market share are provided in the following table:

Number of
Products

Sales

Market Share

14

$12200

15%

20

$60000

33%

18

$24400

10%

22

$32000

42%

Create a Bubble chart to display the Industry Market Share data with the Number of Products forming the horizontal axis and the Sales forming the vertical axis.


 

 

Question 3 – 3 – Histograms & Box Plots

Question 3.1

A sample of concrete slump test results for the construction of a bridge connecting the North and South Heads at the entrance to Sydney Harbour yielded the following results:

Safety

Deck

Guards

Arch

—-1

79

79

82

81

80

78

80

79

80

80

79

82

81

82

80

81

83

84

80

79

82

83

79

78

78

82

80

 

Test I      Piles

1

Deck Beams

82

79

81

83

82

78

77                    81         J

79         1         79

75         j          78

80                   76

82                   82

9             781                 81

Create a histogram with bins of 74, 76, 78, 80, 82 & 84 and a Box Plot of the results.

Question 3.2

The lengths of steel beams required for a construction project were measured as follows:

6.55m, 8.6 m, 10.5 m, 9.2 m, 7.4 m, 6.2 m, 10.6 m, 9.25 m, 9.1m, 10.4 m, 6.2 m 9.0 m, 9.3 m, 8.5 m, 7.0 m, 10.6 m, 10.25 m, 8.6 m, 10.4 m, 7.4 m, 7.0 m, 10.6 m.

Create a histogram of the results with bins of 6, 7, 8, 9, 10 & 11.

 

Question 3.3

Samples of water from Lake Alexandrina in South Australia were tested for salinity content and gave the following results:

50.64

47.55

50.62

60.00

50.67

49.11

52.22

57.40

62.58

51.14

45.41

56.86

53.77

48.53

49.59

43.91

51.17

54.28

46.99

58.41

40.24

60.02

44.38

45.44

54.82

40.79

50.13

47.00

48.03

42.82

49.63

42.31

51.69

38.13

51.66

43.91

42.86

60.51

51.15

52.17

40.24

49.62

52.69

47.52

52.74

51.18

52.21

49.08

50.10

42.82

Create a histogram containing 6 bins and a Box Plot of the results.

 


 

A study into the use of gelcoat colouring agents by a manufacturer of glass reinforced plastic products identified the usage of the following colours:

White – 42%, Black – 14%, Red- 8%, Brown – 7%, Orange – 5%, Yellow 3%, Green – 3%, Grey 2%, Brown – 2%.

Create a histogram of the results with bins of 7, 14, 21, 28, 36, 42 & 49.

 

 

Question 3.4

The removal of municipal solid waste (garbage) is a growing environmental concern. Recent figures from the United States give the following breakdown of materials:

Material

Weight

(million tonnes)

Percentage of
total (%)

Recycled
Percent (%)

Food Scraps

31.7

12.5

1.6

Glass

13.6

5.3

5.7

Metals

20.8

8.2

26.8

Paper and Cardboard

83.0

32.7

54.5

Plastics

30.7

12.1

6.8

Rubber, Leather & Textiles

19.4

7.6

10.7

Timber

14.2

5.6

9.3

Lawn & Garden Trimminqs

32.6

12.8

54.1

Other

8.2

3.2

0.0

Total

254.2

100.0

 

Create a histogram with bins of 10, 20, 30, 40, 50 & 60 and a Box Plot of the results.

 

Question 3.5

The acidity levels (measured by pH) in 105 samples of rainwater are given in the following table. Distilled water has pH 7.00; as the water becomes more acidic, the pH goes down. The pH of rainwater is important to environmentalists because of the problem of acid rain.

4.33

4.38

4.48

4.48

4.50

4.55

4.59

4.59

4.61

4.61

4.75

4.76

4.78

4.82

4.82

4.83

4.86

4.93

4.94

4.94

4.94

4.96

4.97

5.00

5.01

5.02

5.05

5.06

5.08

5.09

5.10

5.12

5.13

5.15

5.15

5.15

5.16

5.16

5.16

5.18

5.19

5.23

5.24

5.29

5.32

5.33

5.35

5.37

5.37

5.39

5.41

5.43

5.44

5.46

5.46

5.47

5.50

5.51

5.53

5.55

5.55

5.56

5.61

5.62

5.64

5.65

5.65

5.66

5.67

5.67

5.68

5.69

5.70

5.75

5.75

5.75

5.76

5.76

5.79

5.80

5.81

5.81

5.81

5.81

5.85

5.85

5.90

5.90

6.00

6.03

6.03

6.04

6.04

6.05

6.06

6.07

6.09

6.13

6.21

6.34

6.43

6.61

6.62

6.65

6.81

 

 

 

 

 

Make a histogram of pH with 14 classes, using class boundaries 4.2, 4.4,…, 7.0.

Make a second histogram, also with 14 classes, using class boundaries 4.14, 4.34,…, 6.94. The classes are those from the previous moved 0.06 to the left.

 


 

Question 4 – Control Charts

Question 4.1

In a plant hours a sample is taken from a production process every two hours. Each sample consists of 3 measurements of pressure in kPa (pounds per square inch). The results are repo

 

8.00 a.m.

10.00 a.m.

12.00 a.m.

2.00 p.m.

255.1

979.1

455

648.1

227.5

992.8

420.6

661.9

241.3

999.7

413.7

682.6

 

 

Question 4.2

A series of special machinery applying force between two surfaces to be adhered have recorded the following data from automatically generated validation tests.

Create a Control Chart and indicate which machines fail by performing below the LLC.

Sample

Test 1

Test 2

Test 3

Test 4

Test 5

Machine 1

10.68

10.689

10.776

10.798

10.714

Machine 2

10.79

10.860

10.601

10.746

10.779

Machine 3

10.78

10.667

10.838

10.785

10.723

Machine 4

10.59

10.727

10.812

10.775

10.730

Machine 5

10.69

10.708

10.790

10.758

10.671

Machine 6

10.75

10.714

10.738

10.719

10.606

Machine 7

10.79

10.713

10.689

10.877

10.603

Machine 8

10.74

10.779

10.110

10.737

10.750

Machine 9

10.77

10.773

10.641

10.644

10.725

Machine 10

10.72

10.671

10.708

10.850

10.712

Machine 11

10.79

10.821

10.764

10.658

10.708

Machine 12

10.62

10.802

10.818

10.872

10.727

Machine 13

10.66

10.822

10.893

10.544

10.750

Machine 14

10.81

10.749

10.859

10.801

10.701

Machine 15

10.66

10.681

10.644

10.747

10.728

 

 

Question 4.3

A company producing high quality scientific instruments has a high rate of products with defects on a daily basis. Produce a Line Chart plotting the defect rates.

Day

Defective
Components

Day

Defective
Components

1

67

8

24

2

28

9

25

3

45

10

27

4

32

11

28

5

30

12

29

6

48

13

65

7

32

 

 

 


 

Question 5 – Parabolic Charts

Question 5.1

The data in the following table was taken from official Road and Transport figures and shows the reaction Distance, Braking Distance and the Total Stopping Distance at various speeds and are based on tests of cars having brakes in first class working condition and on dry level hard surfaces.

The Reaction Distance is the distance that the car travels from the time that the driver sees the need to do so until their foot applies pressure to the brake.

The braking distance is the distance that the car travels after the brakes are applied until it comes to a stop.

The Total Stopping Distance is the sum of the Reaction Distance and the Braking Distance.

Speed km/h

Total Stopping
Distance

Reaction
Distance

Breaking Distance

40

17.98

8.23

9.75

60

30.78

11.58

19.20

75

46.94

15.24

31.70

90

65.84

18.59

47.24

105

87.78

21.64

66.14

As a guide to stopping distances at speed, the bar chart below indicates the stopping distances compared to a 100 metre long rugby league, rugby union or soccer field, or the length of an Olympic 100 meter sprint race.

 

Question 5.2

Create a Parabolic curve using the equation x2 +3 between -5 and 5

Question 5.3

Create a parabolic curve using he equation -0.292 + 6.26 between -8 and 8