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Principles Of Engineering
Digital Notebook
Table of Contents
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POE Proficiencies
Lesson 1.3 Engineering Careers
Lesson 2.3 – Excel Data
Representation
Lesson 4.1 – Mechanisms & Simple
Machines
Lesson 4.5 – Control Systems ROBO Pro
Free Body Diagrams – Practice
Problems
Activity 5.1a
Working with X and Y Components
of Vectors
Truss Calculations
Practice Exam Problems
Fluid Power
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2
POE Proficiencies
Lesson 1.1 Engineers as Problem Solvers
1.
Students will have an understanding of engineering and be able to identify engineering achievements through history.
2.
Students will be able to identify five historical engineering role models, including minorities and women.
3.
Students will be able to identify problems for engineers to solve in the future.
4.
Students will be able to define attributes associated with being a successful engineer.
Lesson 1.2 Engineering Team
5.
Understand that an engineering team must work together to solve problems, with each team member having individual and collective
responsibilities.
6.
Understand the role of out-sourcing in the engineering process, and how effective communication is essential.
7.
Understand how gender-bias, racial-bias and other forms of stereotyping and discrimination can adversely affect communications within
an engineering team.
8.
Understand how ethics influences the engineering process.
9.
Understand how social, environmental and financial constraints influence the engineering process.
Lesson 1.3 Careers in Engineering
10. Students will have an understanding of the difference between engineering disciplines and job functions.
11. Students will understand the professional and legal responsibilities associated with being an engineer.
12. Students will research and discover the educational requirements to become an engineer.
13. Students will become familiar with an area of engineering by preparing for and conducting an interview with an engineer in that field of
engineering.
Lesson 2.1 Sketching
14. Students will compose sketches use proper sketching techniques in the solution of design problems.
15. Students will select the appropriate sketching styles for presentation of a design problem to a group.
16. Students will use proper proportioning while producing annotated sketches.
Lesson 2.2 Technical Writing
17. Students will plan and compose a written technical report about the research they conduct about a career field in engineering.
18. Students will be able to formulate an organized outline for a technical paper.
Lesson 2.3 Data Representation & Presentation
19. Students will be able to design and create tables, charts, and graphs to illustrate data they have collected.
20. Students will evaluate and select an appropriate type of table, chart, or graph to accurately communicate collected data for written work or
presentations.
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POE Proficiencies
Lesson 2.4 Oral Presentations
21. Students will design and deliver a presentation utilizing appropriate support materials about research they have conducted.
22. Students will create and assemble support materials to appropriate demonstrate concepts used in their presentations.
23.
23.
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25.
Lesson 3.1 Design Process
Students will compose and diagram the product development lifecycle of an invention of their choice and report findings to the class.
Students will trace the history of an invention and evaluate its effects on society and the environment.
Students will examine the evolution of an invention to observe and report on how the design process is applied to continuously redesign
and improve the product.
Lesson 4.1 Mechanisms
26. Students will identify and explain the function of the essential components of a mechanical system on a display they create.
27. Students will create a display of a mechanical system from a household item they disassemble.
28. Students will mathematically explain the mechanical advantage gained and explain the function of the six different types of simple
machines in a presentation on the SMET device.
29. Students will apply simple machines to create mechanical systems in the solution of a design problem.
Lesson 4.2 Thermodynamics
30. Students will conduct an energy analysis on a section of their home and calculate the heat loss through walls and windows.
31. Students will research and evaluate systems undergoing thermodynamic cycles for efficiency and present findings to the group.
32. Students will give an oral presentation incorporating the first and second laws of thermodynamics, describing the concept and function of
a heat engine of their choice.
Lesson 4.3 Fluid Systems
33. Students will evaluate and select specific fluid power sources for different functions.
34. Students will create a flow diagram schematic sketch and compare it to an actual fluid power circuit during a presentation to the class.
35. Students will mathematically calculate and explain the work being done by a specific fluid power device as part of an oral presentation.
36. Students will safely demonstrate proper setup and adjustment of a fluid power system.
Lesson 4.4 Electrical Systems
37. Students will create schematic drawings to facilitate experimental measurements of electrical circuits.
38. Students will apply ohm’s and watt’s laws in designing safe electrical circuits.
39. Students will appraise community needs and evaluate the impact supplying electrical generation has on their communities.
40. Students will be able to estimate current consumption by a circuit and be able to compare estimates to accurate measurements they
perform.
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POE Proficiencies
Lesson 4.5 Control Systems
41. Students will design, diagram and implement a program to control a device they construct to perform a sorting operation.
42. Students will select and apply concepts of mechanical, electrical, and control systems in solving design problems.
43. Students will formulate a plan for evaluating the functioning of their sorting device and to make appropriate changes in design, circuitry or
programming.
44. Students will demonstrate and defend their solution to the design problem in an oral presentation to the class.
Lesson 5.1 Statics
45. Students will
46. Students will
47. Students will
48. Students will
design.
mathematically analyze a simple truss to determine types and magnitude of forces supported in the truss.
be able to define, describe and analyze the stresses and forces acting on an object.
design, construct and test a model bridge to support the greatest amount of weight per gram of bridge mass.
prepare and present a mathematical analysis of a truss design as part of a 5 minute oral presentation about their bridge
Lesson 5.2 Strength of Materials
49. Students explain the use of factors of safety in the design process.
50. Students will be able to explain the difference between the area of a cross section of an object and the second moment of the area
(Moment of Inertia) and predict the relative strength of one shape vs. another.
51. Students will be able to use a computer aided engineering package to analyze a shape.
52. Students will explain the effects that stress has on a material and explain how the material will react.
Lesson 6.1 Categories of Materials
53. Students will be able to identify and differentiate the five basic categories of solid engineering materials.
54. Students will be able to compare and contrast the physical properties of organic, metals, polymers, ceramics, and composites.
55. Students will be able to trace the production of raw material to finished product.
56. Students will be able to identify practical applications of each material category to engineered products and processes.
57. Students will be able to collect, analyze, and test samples of the four basic materials.
58. Students will be able to document and present laboratory data related to studies of material classifications.
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POE Proficiencies
Lesson 6.2 Properties of Materials
59. Students will be able to identify and document the properties of materials.
60. Students will be able to design an experiment to identify an unknown material.
61. The student will be able to formulate conclusions through analysis of recorded laboratory test data for presentations in the form of charts,
graphs, written, verbal, and multi-media formats.
62. Students will be able to analyze word problems about forces acting on materials.
Lesson 6.3 Manufacturing Processes
63. Students will be able to define and state examples of the major categories of Production Processes.
64. Students will be able to analyze a component of a product and describe the processes used in its creation.
65. Students will be able to interpret a drawing and produce a part.
66. Students will give an oral presentation on the production processes used to create products from a category of materials and a
demonstration about one of the processes.
Lesson 6.4 Quality Control
67. Students will be able to state the difference between mass and weight.
68. Students will be able to utilize a variety of precision measurement tools to measure appropriate dimensions, mass, and weight.
69. Students will be able to understand and explain why companies have a need for quality control and will describe what customers and
companies refer to when the term “quality” is used.
70. Students will be able to calculate the mean, median, mode, and standard deviation for a set of data and apply that information to an
understanding of quality assurance.
71. Students will be able to explain the difference between process and product control.
72. Students will be able to distinguish between the characteristics of quality in a final product and the control of quality in each step of a
process.
73. Students will understand how control charts are used in industry and will be able to predict whether a process is “out of control,” or not by
using a control chart.
Lesson 6.5 Material Testing
74. Students will be able to describe and safely conduct destructive and non-destructive material testing and will be able to use the data
collected through these tests to compute and document mechanical properties.
75. Students will be able to analyze a product that breaks and be able to explain how the material failed.
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POE Proficiencies
Lesson 7.1 Reliability
76. Students will be able to diagram a system and identify the critical components.
77. Students will be able to mathematically estimate chance of failure of a system given information
on certain components.
78. Students will list the causes of failure and be able to propose solutions.
79. Students will prepare and defend a position on an ethical engineering dilemma.
Lesson 7.2 Case Study
80. Students will research the engineering, legal, social, and ethical issues related to a final design
developed in a case study.
81. Students will analyze an engineering failure for the purpose of presenting an aural report which
identifies; causes, damage done, design failures, and other areas where the failure has impacted
the environment or society.
82. Students will prepare a written report explaining their analysis of an engineering failure.
Lesson 8.1 Linear Motion
83. Students will be able to explain the difference between distance traveled and displacement.
84. Students will design and build a device for the purpose of conducting experiments of acceleration,
displacement, and velocity.
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Engineering Careers
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Lesson 2.3 – Data Representation and Presentation
Key Terms
Directions:
• Use the Internet to identify the definitions of the terms below.
• Add a link to this slide in your table of contents named Key Terms Lesson 2.3– Data Representation and
Presentation
• (Delete this text box once you get started and stretch the text box below to fill the slide)
Bar Chart
Cell
Chart
Data
Graph
Histogram
Line Graph
Pictograph
Pie Chart
Plotting
Qualitative
Quantitative
Spreadsheet
Statistics
Table
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Lesson 4.1 – Mechanisms & Simple Machines
Key Terms
Directions:
• Use the Internet to identify the definitions of the terms below.
• Add a link to this slide in your table of contents named Lesson 4.1 - Mechanisms
• (Delete this text box once you get started and stretch the text box below to fill the slide)
Cam
Crankshaft
Force
Friction
Gear
Gear Train
Inclined Plane
Lever
Linkage
Mass
Pitch
Pulley
Screw
Simple Machine
Compound Machine
Spring
Sprocket
Fulcrum
Thread
Torque
Effort
Load
Wedge
Wheel and Axle
Mechanical Advantage
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Lesson 4.1 – Energy & Work
Key Terms
Directions:
• Use the Internet to identify the definitions of the terms below.
• Add a link to this slide in your table of contents named Lesson 4.1 - Mechanisms
• (Delete this text box once you get started and stretch the text box below to fill the slide)
Work/ Equation
Units of Force
English - Foot pounds
Metric – Newton
Power/ Equation
Watt
Killowatt
Energy
Chemical Energy
Electrical Energy
Solar Energy
Radiant Energy
Potential Energy
Kinetic Energy
Law of Conservation of Energy
Nuclear Energy
Efficiency/ Equation
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Levers (E X LE = R X LR)
Load (R)
1
?
Resistance Arm
(LR)
Effort Arm (LE)
Effort (E)
2 feet
6 feet
1 lbs.
4 feet
4 lbs.
2
8 lbs.
3
13 lbs
2 feet
4
50 lbs.
3 feet
5
113 lbs.
2 feet
6
?
1 foot
?
?
4 lbs.
5 feet
?
?
10 feet
40 lbs.
1 ton
Use the GUESS Method to solve the problems in the table above.
G
1 G
2 G
3
U
U
U
E
E
E
S
S
S
S
S
S
G
4
G
5
G
U
U
U
E
E
E
S
S
S
S
S
S
6
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GUESS Method – Wheel and Axle
1. A wheel is used to turn a valve stem on a water valve. If the wheel radius
is 1 foot and the axle radius is .5 inches, what is the mechanical
advantage of the wheel and axle?
G)
U)
E)
S)
S)
Wheel
Radius 1’
Axle
Radius .5”
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GUESS Method – Wheel and Axle
2. How much resistance force can be overcome when an effort of 80 lbs
is applied to the wheel of the water valve in problem 1?
G)
U)
E)
S)
S)
Effort
80 lbs.
Wheel
Radius 1’
Axle
Radius .5”
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GUESS Method – Wheel and Axle
3. What is the linear distance traveled when a 2.5’ diameter wheel makes
one revolution?
Linear distance of one revolution is equal to the circumference of the
wheel.
G)
U)
E)
S)
S)
Dia. = 2.5’
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GUESS Method – Wheel and Axle
4. On an automobile how could you increase the distance traveled for each
revolution of the axle while keeping bearing friction constant?
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GUESS Method – Pulley Problems
1. Using a block and tackle pulley system, determine the number of strands
that will be needed to lift a weight of 1092 lbs. by applying 80 pounds of
force.
G)
U)
E)
S)
S)
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GUESS Method – Pulley Problems
2. Using a block and tackle pulley system, with 7 strands and an input force
of 45 pounds, what is the maximum weight that can be lifted?
G)
U)
E)
S)
S)
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GUESS Method – Inclined
Plane
1. Using the diagram below find the force and mechanical advantage. Be
sure to show your work and use the GUESS Method.
Mechanical Advantage
G)’
U)
E)
S)
S)
Force
G)
U)
E)
S)
S)
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GUESS Method – Inclined
Plane
2. Using the diagram below find the mechanical advantage and effort
needed to move the object up the inclined plane. Be sure to show your
work and use the GUESS Method.
Mechanical Advantage
G)
U)
E)
S)
S)
Force
G)
U)
E)
S)
S)
20
Activity 4.1d Pulley and Gear
Problems
Unit 4 – Engineering Systems
Pulley Problems
Use a blank piece of paper to solve for the unknown quantities in the problems below.
Use the GUESS Method to show the equations and all work.
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Solving Problem 1 - Pulleys
Identify how you are going to solve for each missing variable using the formulas
provided.
Where do I start?
1. Start with a problem that you have 3 of the 4 variables given.
2. Let’s start with the Tout.
3. List the variables provided and solve for the missing one.
G: D in = 2, D out = 8, T in = 100
U: T out
E: Tin/Tout = Din/Dout
S: 100/ Tout = 2/8
S: Tout = 400 ft lb
Formulas:
Win/Wout = Dout/Din
Tin/Tout = Din/Dout
SR = Win/Wout
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Solving Problem 1 - Pulleys
400 ft lb
Identify how you are going to solve for each missing variable using the formulas
provided.
What’s next? Now solve for Wout.
List the variables provided and solve for the missing one.
G: D in = 2, D out = 8, w in = 200
U: Wout
E: Win/Wout = Dout/Din
S: 200/Wout = 8/2
S: Wout = 50 rpm
Formulas:
Win/Wout = Dout/Din
Tin/Tout = Din/Dout
SR = Win/Wout
24
Solving Problem 1 - Pulleys
50 rpm
400 ft lb
Identify how you are going to solve for each missing variable using the
formulas provided.
What’s next? Solve for SR
List the variables provided and solve for the missing one.
G: w in = 200, Wout = 50 rpm
U: SR
E: SR = Win/Wout = 200/50 = 4
S: 200/50 = 4
S: Speed ratio = 4
Formulas:
Win/Wout = Dout/Din
Tin/Tout = Din/Dout
SR = Win/Wout
Continue this method to solve for each
problem.
25
Gear Problems
Use a blank piece of paper to solve for the unknown quantities in the problems below. Use
the GUESS Method to show the equations and all work.
26
Solving Problem 1 –gEARS
There are four unknown variables to solve for. Here is how it is done:
G: Nout = 28, Nin = 12
U: GR
E: GR = Nout/Nin
S: GR = 28/12 = 2.33
S: Gear Ratio = 2.33
G:Win=1800, Nin=12, Nout=28
U:Wout
E: Win*Nin = Wout*Nout
S: 1800*12=Wout*28
S: Wout=771 rpm
G: Win =1800, Wout=771, Din=6
U: Dout
E: Win/Wout = Dout /Din
S: 1800/771= Dout /6
S: Dout = 14 in
G:Tin100, Din=6, Dout=14
U:Tout
E:Tin/Tout=Nin/Nout
S:100/Tout=12/28
S:Tout = 233 ft lb
Formulas (Gears)
GR=Input Rate /Output Rate
GR=Nout/Nin
SR=W in/Wout
W in/Wout=Dout/Din
Tin/Tout=Din/Dout
Nin/Nout=Din/Dout
Tin/Tout=Nin/Nout
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Lesson 4.5 – Control Systems - ROBO Pro
Key Terms
Directions:
• Use the Internet to identify the definitions of the terms below.
• Add a link to this slide in your table of contents named Lesson 4.5 – Control Systems - ROBO Pro
• (Delete this text box once you get started and stretch the text box below to fill the slide)
Series Circuit
Parallel Circuit
Analog signal
Digital signal
Switch
Loops
Variables
Transistor
Photocell
Photoconductive
Current
Voltage
Resistance
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Fischertechnik Interface
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Lesson 4.5 – Control Systems - ROBO Pro
Function Blocks
Directions:
• Use the Internet to identify the definitions of the terms below.
• Add a link to this slide in your table of contents named Lesson 4.5 – Control Systems - ROBO Pro – Function
Blocks
• (Delete this text box once you get started and stretch the text box below to fill the slide)
What block is this and what does it do?
What block is this and what does it do?
What block is this and what does it do?
What block is this and what does it do?
What block is this and what does it do?
What block is this and what does it do?
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Lesson 4.5 – Control Systems - ROBO Pro
Function Blocks
Directions:
• Use the Internet to identify the definitions of the terms below.
• Add a link to this slide in your table of contents named Lesson 4.5 – Control Systems - ROBO Pro – Function
Blocks
• (Delete this text box once you get started and stretch the text box below to fill the slide)
What block is this and what does it do?
What block is this and what does it do?
What block is this and what does it do?
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Lesson 4.5 – Control Systems - ROBO Pro
Command Buttons
What
does this
do?
What does
this do?
What does
this do?
What does
this do?
What does
this do?
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Lesson 4.5 – Control Systems - ROBO Pro
Activity 4.5c - Basic Programming
Add Brief Description of what
each program does here.
•BP1A:
•BP1B:
•BP1C:
Add ROBO Pro Screen Shot here!
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Lesson 4.5 – Control Systems - ROBO Pro
Activity 4.5d - Basic Programming 2
Add Brief Description of what
each program does here.
•BP2A:
•BP2B:
•BP2C:
Add ROBO Pro Screen Shot here!
34
Lesson 4.5 – Control Systems - ROBO Pro
Activity 4.5e - Basic Programming 2
Add Brief Description of what
each program does here.
•BP3A
Add ROBO Pro Screen Shot here!
35
Lesson 4.5 – Control Systems - ROBO Pro
Activity 4.5g - Closed Loop Control 1
Add Brief Description of what
each program does here.
•45G1:
•45G2:
Add ROBO Pro Screen Shot here!
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Fluid Power Introduction
Open the Fluid Power Introduction PowerPoint from the assignment log and
add your notes from that in this section.
Define the following terms:
Fluid Power Hydraulics Pneumatics What do the following Fluid Powered Components do?:
Reservoir / Receiver Fluid Conductor Pump / Compressor –
Valve –
Actuator -
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Fluid Power Physics
Define the following terms: add equations were applicable
Energy –
Energy Transfer –
Work –
Power –
Horsepower –
Torque Flow –
Rate of Flow –
Pressure Law of conservation of energy:
Pascal’s Law:
Schematic -
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Fluid Power Schematics
Drag the appropriate schematic symbol next to the term in the table below.
Component
Symbol
Vented Reservoir
Pressurized
Reservoir
Rotary Device
Pump
Variable Pump
Fixed Orifice Flow
Control Valve
Adjustable Orifice
Control Valve
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Fluid Power Schematics
Drag the appropriate schematic symbol next to the term in the table below.
Component
Symbol
3 position valve
Free Flow Check
Valve
Blocked Flow Valve
Motor
Bi-directional or
reversible Motor
Motor with a drain
line
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Fluid Power Schematics
Drag the appropriate schematic symbol next to the term in the table below.
Component
Symbol
Single Acting
Cylinder
Double Acting
Cylinder
Double Rod
Cylinder
Large Rod Dia.
Cylinder
41
Pneumatic Power
Properties of Gases
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Identify the following terms:
Gauge Pressure:
Standard Atmospheric Pressure (barometric pressure):
Standard atmospheric pressure equals 14.7 lb/in.2
Absolute Pressure (p) (lb/in.2 or psi):
Absolute Temperature:
42
Perfect Gas Laws
Law – (Add description)
Equation (Add Equation)
Boyle’s Law -
Charles’ Law -
Gay-Lussac’s Law -
43
Hydraulic Power
Why are Hydraulic Systems more precise than pneumatic systems?
What are the key characteristics of a Hydrodynamic System?
What are the key characteristics of a Hydrostatic System?
44
The image to the right shows an ammeter being used to
measure the current flowing through a circuit.
1. How much resistance does the fischertechnik® lamp provide against the flow of electricity
through this circuit? (B –S09)
a) 12V
b) 2.0A
c) 24V
d) 6.0Ω
2. What is the power supply voltage if the ammeter (which is wired in series with the circuit)
displays a value of 2A every time the momentary switch is pressed? (Accuracy = 0) (B –
S09)
a) 12V
b) 2.0A
c) 24V
d) 6.0Ω
45
Unit 5 Statics and Strength of Materials-Activity 5.1g Bridge Building
Learning Activity #1-Build a Model of a Truss Bridge
Directions:
• Use the Activity sheet provided to identify the definitions of the terms below.
• Add a link to this slide in your table of contents named Learning Activity #1 Bridge Building
• (Delete this text box once you get started and stretch the text box below to fill the slide)
Truss
Pinned Connections
Members
Gusset Plate Connections
Tension
Foundation
Compression
Abutments
Structural Engineer
Piers
Elevation View
Geotechnical Engineer
Isometric View
Through Truss
Top Chord
Pony Truss
Bottom Chord
Deck Truss
Verticals
Diagonals
Struts
Lateral Bracing
Floor Beams
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Bridge Components
1.
2.
7.
3.
8.
4.
5.
6.
9.
10.
11.
12.
13.
47
Activity 5.1b – Free Body
Diagrams
Student practice problems
Free Body Diagrams Worksheet Problem 1
Draw free body diagrams (force diagrams) for each of the following:
What forces need to be identified to draw the free body diagram?
What about the normal force of D, G, &
H on the spheres?
What about the weight of each object?
B
H
G
A
All of these things need to be
taken into consideration.
C
WB
D
N WA
WC N
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Free Body Diagrams Worksheet Problem 1
Draw free body diagrams (force diagrams) for circle A:
Isolate circle A
What forces are in the x direction?
What forces are in the y direction?
Don’t forget the weight of A!
B is acting on A in both the x an y directions!
FB
B
H
G
A
FG
A
C
FN WA
D
N WA
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Free Body Diagrams Worksheet Problem 1
What are the sum of the forces on circle A?
B has forces in both the x and y directions.
FB
Here is how we write the equations:
FX=0=FG-FBX=0
-FBY
FG
The sum of the forces in the x direction equals the
force of G – force of B in the x direction.
FY=0=FN-WA-FBY=0
A
-FBX
FN W
A
The sum of the forces in the y direction equals the normal
force –the weight of A, – force of B in the y direction.
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Free Body Diagrams Worksheet Problem 1
Draw free body diagrams (force diagrams) for circle B:
Draw each force
Isolate circle B
B
What forces are acting on B from A?
H
G
A
C
This includes the weight of B.
What forces are acting on B from C?
Now calculate the sum of all forces.
D
52
Free Body Diagrams Worksheet Problem 1
If this object is not accelerating, what are the sum of the forces on
circle B?
What are the sum of the forces in the X direction?
FX=
The sum of the forces in the X direction
=Force of FA in the x direction – the force of
FC in the x direction.
What are the sum of the forces in the Y
direction?
FY=
The sum of the forces in the Y direction
=Force of FA in the Y direction + the force of
FC in the Y direction – the weight of WB.
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Free Body Diagrams Worksheet Problem 1
Draw free body diagrams (force diagrams) for circle C:
Isolate circle C
Draw each force
B
H
G
What forces are acting on C from B?
What forces are acting on C from H?
A
C
What forces are acting on C from D?
There is also the weight of C.
D
Now calculate the sum of all forces.
54
Free Body Diagrams Worksheet Problem 1
If this object is not accelerating, what are the sum of the forces on circle C?
What are the sum of the forces in the X
direction?
FX=
What are the sum of the forces in the Y
direction?
FY=
55
Free Body Diagrams Worksheet Problem
2
Draw a free body diagram for member AB.
What about pivot A?
What is affecting the weight of AB?
Lets start with Cord CB.
The cord is pulling on point B
Vector FD has forces in both the X and Y directions.
Cord
C
B
D
A
56
Free Body Diagrams Worksheet Problem
2 diagram for pivot A.
Draw a free body
The weight of D causes the
following forces on pivot A.
Cord
C
B
D
A
57
Free Body Diagrams Worksheet Problem
Draw a free body diagram 2
for the forces on cylinder D.
Cord
C
B
D
What are the forces in the x direction?
What are the forces in the y direction?
What about the force of AB?
A
58
Free Body Diagrams Worksheet Problem
3
Draw a free body diagram for member
AB which is pin connected at A
and supported by member BC.
C
B
A
Force
59
Truss Calculations
Practice Problem
Spring 2006
Practice Problem Test C-Spring 2006 #1
To receive full credit on any problem that requires calculations, you must:
1)
identify the formula you are using
2)
show substitutions
3)
state the answer with the correct units.
61
Practice Problem Test C-Spring 2006 #1
1. Study the truss in Figure 1 and its free body diagram in Figure 2, and answer the following
questions.
a. Draw a point free body diagram for joint C and label all of the given information for that
node (assume all member forces are tension).
[2 points]
b. Calculate the length of truss member BC. (answer precision = 0.000)
[3 points]
c. Using joint C, determine the magnitude and type of force (tension or compression) that is
being carried by truss member BC. (answer precision = 0.0) [4 points]
62
Practice Problem Test C-Spring 2006 #1-A
1.
2.
3.
Isolate Point C
What forces are acting on C in the X
direction?
What forces are acting on C in the Y
direction?
FBCX
FAC
30°
FBC
FBCY
C
F1 100 lbs
63
Practice Problem Test C-Spring 2006 #1-A
1. Study the truss in Figure 1 and its free body diagram in Figure 2, and answer the following
questions.
a. Draw a point free body diagram for joint C and label all of the given information for that
node (assume all member forces are tension).
[2 points]
64
Practice Problem Test C-Spring 2006 #1-B
1. Study the truss in Figure 1 and its free body diagram in Figure 2, and answer the
following questions.
b. Calculate the length of truss member BC. (answer precision = 0.000) [3 points]
Sketch the triangle and label everything you know about it from the illustration and
FBD.
4 ft
Use the GUESS Method!
G: C = 30 °, AC = 4 ft, B = 90 °
A
C
30°
U: BC
E: BC = cosine θACB x AC
S: BC = cosine 30° x 4 ft
S: BC = 3.464 ft
B
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Activity 5.1a
Working with X and Y
Components of Vectors
Next
Concepts
• To analyze a truss, we must be able to
mathematically relate the angles of a triangle
to the lengths of its sides.
• Vectors are described with a direction and
force
• Fx = force in the x (horizontal) direction
• FY = force in the y (vertical) direction
• N = metric unit for force (pounds)
67
Next
1. Find the x and y components of vector V.
To find VX, notice there is a right triangle. The value of the hypotenuse is 5 and the opposite angle is
30. (SOHCAHTOA)
Use sine:
VX needs to be broken into its X and Y
components, let’s solve for X first
Y-axis
X-axis
30
V=5N
VX = 2.5N
G
= Angle 30, V=5N
U
= VX
E
= sin  =
opposite
hypotenuse
Vx
5
S
= sin 30 =
S
= VX = 5 * sin 30 = 2.5
Solution Hint: Think of the vector as pointing southeast. You will need to split it up into its y
component (pointing south, and its x component (pointing east).
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Next
1. Find the x and y components of vector y.
To find VY, notice there is a right triangle. The value of the hypotenuse is 5, the
adjacent angle is 30 and we know the opposite side is 2.5. (SOHCAHTOA)
Use cosine:
Y-axis
G =  = 30°, VX=2.5, V=5N, 90°
X-axis
U = VY
E = cos  =
VY =-4.3N
30
V=5N
S = cos 30 =
VY
adjacent
hypotenuse
Vy
=2.5
5
S = VY = 5 * cos 30 = 4.3
VX = 2.5N
Why is this a negative value?
69
Next
2. Find the x and y components of vector W. Can you predict
the solution based on Problem 1?
Use the GUESS Method to show all work
Y-axis
X-axis
W=5N
30
Solution Hint: Think of the vector as pointing southwest. You will
need to split it up into its y component (pointing south, and its x
component (pointing west).
Next
Problem
70
Previous
3. Find the x and y components of vector W. Can you predict
the solution based on Problem 1? Use the GUESS Method
to show all work
Nail
30
30
W=5N
30
30 V=5N
F = resultant force
Sir Isaac Newton
Next
Problem
71
Previous
4. Find the x and y components of vector A. Use the GUESS
Method to show all work
Y-axis
A = 50 N
20
X-axis
Solution Hint: Think of the vector as pointing northeast. You need to
split it up into the y component (pointing north, and the x
component pointing east).
Next
Problem
72
Previous
5. Find the x and y components of vector B. Use the GUESS
Method to show all work
Y-axis
B = 100 N
15
X-axis
Solution Hint: Think of the vector as pointing northeast. You need to
split it up into the y component (pointing north, and the x
component pointing east).
Next
Problem
73
Previous
6. Two ropes are attached to the screw eye hook in this picture.
Robe B is being pulled with a force of 100N at an angle of 15
degrees to the y-axis. Rope A is being pulled with a force of 50 N
at an angle of 20 degrees to the x-axis. Use your solutions from
Problems 4 and 5 to find x and y components of the resultant
force, F:
Next
Problem
74
Previous
7. Two ropes are attached to the screw eye hook in this shipping crate. Rope B
is being pulled with a force of 5200N at an angle of 30 degrees to the x-axis.
Rope A is being pulled with a force of 3000N at an angle of 45 degrees to the
x-axis. Find the x and y components of the resultant force, F:
A = 3000 N
45
30
B = 5200 N
Next
Problem
75
Previous
8. This plane is suspended from the wires shown. Calculate the resultant forces
with the information provided.
1800 lbs.
1484 lbs.
60
45
385 lbs.
90
2300 lbs.
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Previous
Important Key Terms
1.3 Careers in Engineering
Engineering Profession:
4.2 Thermodynamics
Convection:
Conduction:
Radiation:
R-value:
4.3 Fluid Systems
Pneumatic:
Hydraulic:
Pascal’s Law:
Bernoulli’s Law:
4.4 Electrical Systems
Series Circuit:
Parallel Circuit:
Voltage:
Current:
77
Important Key Terms
5.1 Statics
Torque (Formula/ definition):
5.2 Strength of Materials
Moment of inertia:
Cross-sectional area:
6.1 Categories of Materials
Ferrous:
Non-ferrous:
Polymer:
Organic:
6.3 Production Processes
Injection Molder:
Milling Machine:
Forging:
Annealing:
6.5 Material Testing
Plastic deformation
Brittle material
78
Important Key Terms
6.4 Statics
Torque (Formula/ definition):
7.2 Reliability
Product Failure:
Ethics:
7.2 Case Studies
Case Study:
Design Brief:
8.1 Linear Motion
Velocity:
Acceleration:
Displacement:
79
Practice Problems
Simple Machines
2005 B # 1
Below are two simple machines. In each case the
weight of the load is 120 lbs.
For each one, identify the type of simple machine (1
pt), the Mechanical Advantage of the device (1 pt), the
Effort Force, F, needed to support the weight. (1 pt)
Show all Work (1 pt each).
(a) Identify the following:
• Simple Machine
• MA =
•E=
(b) Identify the following:
• Simple Machine
• MA =
•E=
81
2005 C # 4
The jack pictured below has a ¾-10 screw thread and a 9-inch effort
arm. It can lift an object that weighs up to 600 lbs. Calculate the
mechanical advantage of this device. [4 points]
Picture this as a lever and solve.
82
Study the technical drawing below, and use
auto-shapes to fill in the missing center
lines and hidden lines in the orthographic
views. Assume the circle represents a thru
hole.
83
2006 B # 6
2006 B # 7
7a. What class of lever is shown in
Figure 5? Justify your answer.
Figure 5
7b. How much effort force is needed to balance the 100 lb load? (show work)
84
Study this technical drawing below, and
use auto-shapes to fill in the missing center
lines and hidden lines in the orthographic
views.
2007 B # 7
85
2007 B # 8
8a. What class of lever is shown in
Figure 5? Justify your answer.
8b. How much effort force is needed to balance 20.8 pounds of resistance?
(answer precision = 0.0)
86