Download - Syllabus review
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
SYLLABUS REVIEW
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Syllabus - objectives
During this class You will• Learn about engineering profession and
ethics governing engineers at work• Learn basic concepts of engineering• Learn open-ended problem solving skills
through work on projects in engineering• Learn to work in teams• Learn to use a computational tool: Excel• Learn good engineering communication
skills: written and oral
Debates
Lectures
Homework
In-class tasks
Teardown project
Design project
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Syllabus - policies• Course policies:
– Attendance is mandatory– You may miss 2 classes without penalty– Late work will not be accepted
• Plagiarism: – Plagiarism is a serious offense – Follow ethics guidelines described in student handbook:
http://www.umassd.edu/studenthandbook/academicregs/ethicalstandards.cfm
• Students with Disabilities– In accordance with University policy, if you have a documented
disability and require accommodations to obtain equal access in this course, please meet with the instructor at the beginning of the semester and provide the appropriate paperwork from the Disabled Students Services Office. The necessary paperwork is obtained when you bring proper documentation to the Disabled Students Services Office (DSS), which is located in Group I, Room 016, phone: 508-999-8711.
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Syllabus – schedule (cont’d)Date Topic
Tue 3/23 Engineering Design PracticeThu 3/25 Mass and Force, Ethics Debate 4Tue 3/30 ForceThu 4/1 ForceTue 4/6 Force, Energy & Power, Thu 4/8 Energy & Power, Ethics Debate 5Tue 4/13 Energy & Power Thu 4/15 Energy & Power, Ethics Debate 6Tue 4/20 Review (Area Moment of Inertia)Thu 4/22 Product Teardown, Bring your product!Tue 4/27 Final Design Project-preparation and analysisThu 4/29 Area Moment of InertiaThu 5/4 Area Moment of InertiaTue 5/6 Senior Design PresentationsTue 5/11 Final Design Project-CompetitionTue 5/18 Final Exam (11:30 AM - 2:30 PM)
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Mass and Force
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Mass
• SI unit kg• Weight is a force, unit N• Mass is involved in multiple
engineering principles!
What is the mass of your calculator? How about its weight on Earth? And on Mars?
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Density• Density=mass/volume
• Important in e.g. material selection• Note: Density can change due to e.g. temperature and pressure
V
m
3m
kg
V
m
Which one of these three materials would you choose for a part (size 0.001m3) of an airplane interior decor? How about as a counter weight for an elevator?
Material Density (kg/m3)
Wood (oak) 750
Cement 1920
Aluminum 2740
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Lava Lamp Example
How does the lava lamp work?
www.google-store.com
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Mass Flow
• Mass flow = mass/time
• Remember Volume Flow?
t
mm
s
kg
t
mm
t
VV
Vt
V
t
mm
V Vmm
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Volume or mass flow?
• Depends on application• Volume flow preferred
– when filling a tank of a specific volume with liquids of different densities
– when a process can accept only a limited volume at a time
• Mass flow preferred– in chemical reactions, where the number of
reactant molecules (mass) is important– when measuring gas flow– When goods sold based on weight
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Mass Flow - Task
Estimate the mass flow of a gas pump. Density of regular gasoline is 720 kg/m3.
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Mass Moment of Inertia
• Measure of how hard it is to rotate something with respect to the center of rotation, or resistance to rate of change of rotation
• For a single mass particle:
• For a system of mass particles:
mrI zz2
i
iizz mrI 2
z-axes
r
m2
r2
m
dmrI zz2
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Mass moment of inertia - example
Which one of the following object is harder to rotate around the z-axes? Both are made of steel (=7860 kg/m3).
R=5 cm
Ø=20 cm
h 1=
30 c
m
h 1=
4 cm
z-axis
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
How are these related to mass moment of inertia?
flywheel
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Momentum
• Momentum p (or L)
• Momentum is directionalVelocity (a component of momentum) is
directional
vmp
vmL
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Momentum - Example
www.aerospaceweb.org/question/investigations/columbia/foam-impact.jpg
Investigators into the Columbia accident have estimated that the dislodged foam was about 48 x 29 x 14 cm (19 x 11.5 x 5.5 in) , weighed about 0.75 kg (1.7 lb) and impacted the Shuttle at nearly 850 km/h (530 mph). For the sake of a rough comparison, this block of foam would be about the same size and weight as a large loaf of bread. (www.aerospaceweb.org/question/investigations/q0131.shtml)
p (or L) = mv = 0.75kg * 850,000m/3600s = 177 kg m/s
Same momentum as a 5 kg (11 lb) brick hitting you driving 127.5km/h (80mph) !
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Momentum - Task
Which has greater momentum?A)An Olympic 100m runner at
speed 10 m/sB)A 1000kg car pulling out of a
parking lot at 2 km/h
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Mass and Weight
• Mass - scalar (SI unit kg)• Weight – vector, it’s force (SI unit N)
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Basics
• Force is the interaction of two objects, typically one pushes or pulls the other– Direct contact: you pulling a door open– No direct contact: gravity pulling you toward the center
of the earth
• Force causes objects to move, lengthen, shorten, twist, bend, etc.
• SI Unit: Newton [F]=N– F=ma N=kg·m/s2
• U.S. Customary unit: pound force lbf
– F=ma lbf = 1slug·ft/s2 (1lbf=4.448 N)
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Applications
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Force is a vector quantity(on
whiteboard)
F1 F2
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Spring Forces
• Springs widely used in engineering– Store energy– Return to original position– Dampen vibration
• Spring types:– Linear, torsional
www.motorsportscenter.com/uploads/suspension.jpg
www.pleasanthillgrain.com/bag_clip_bag_clips_stainless.asp
www.pharma-pen.com
http://rclsgi.eng.ohio-state.edu/~gnwashin/me481/mech_sys.html
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Hooke’s law
• Applicable in the elastic range of the spring– Elastic means there is no permanent deformation after the force is removed
kxF F = applied force (N)k = spring constant (N/mm, N/m)x = deformation of the spring (mm, m)
x
F
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Whiteboard example
• A compression spring is 10 cm long when no force is applied. When a force is applied, the deformed length is 8 cm. The spring has a spring constant of 10 N/m. Calculated the applied force.
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Determining the spring constant
• In-class task: determine the spring constant of one of the scales in the back of the room
• Plot your data in Excel, explain all the steps you take
• Prepare to present in front of the class• See EF example 10.1 for help
kxF F = applied force (N)k = spring constant (N/mm, N/m)x = deformation of the spring (mm, m)
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Homework and Teardown• Homework – due Thursday 04/01 before the class
– From the course book: 9.5 (10p), 9.6 (less than 1 page typed)(20p), 9.12 (10p), and 9.23 (10p)
• Look for (broken) products to take apart later – good product will replace one bad assignment grade– Bring products early!
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Friction Forces
• “Frictionless” systems, commonly used in physics, do not really exist
• Friction can be useful• Types of friction:
– Dry friction• Static friction• Dynamic (kinetic) friction
– Viscous friction (fluid friction)
www.garageboy.com
www.respo.net/respo_school/respo_school_006/pics/pour_oil_01.jpg
NFfriction
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Applied force and friction
Fric
tion f
orc
e (
N)
Applied force (N)
Maximum static friction force
Dynamic friction force
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Whiteboard Example
• The static coefficient of friction between an object and a horizontal surface is 0.85. The object’s mass is 0.550 kg. If the object is pushed on the surface (force horizontal) of 5N, will the object move?
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Friction In-Class Task
How would you calculate the static coefficient of friction of your calculator starting to slide on your course book?
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Free body diagrams
• Free body diagram shows all external forces acting on the body.
• Commonly used in statics, dynamics, and mechanics of materials
• Steps to draw the free body diagram– Make a simplified drawing of the body in question– Draw all force vectors acting on it
• Do not forget weight, unless gravitational forces are ignored
– Label all forces– Define fore coordinate system
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Practice (white board)
• Steps to draw the free body diagram– Make a simplified drawing of the body in question– Draw all force vectors acting on it
• Do not forget weight, unless gravitational forces are ignored
– Label all forces– Define fore coordinate system
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
In-class task
• Draw a free body diagram for the two pipes in a v-shaped channel.
40 20
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Newton’s Laws
I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it
II.
III. For every action there is an equal and opposite reaction
amF
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Newton’s Laws
I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it
11m
1.5m
v0vy0
100m
vx0
This also applies to an object in rest – they will not move unless acted upon by an unbalanced force
Remember what happened to the cannon ball in both x and y-directions?
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Newton’s LawsI.
II. ,amF
m
a
F
Notice the relation between the magnitudes and directions of F and a!
dt
vdmF
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Newton’s LawsI.
II. ,amF
m
a
1F
dt
vdmF
2F
amFFF 21
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Newton’s LawsI. S
II. s
III. For every action there is an equal and opposite reaction
m
N
mg
gmN
gmN
Why are the absolute value signs on N and g, not mg or m?
Both the magnitude and direction of the two forces are equal
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Force Basics - revisited
• Force is the interaction of two objects, typically one pushes or pulls the other– Direct contact: you pulling a door (from the
handle) open the door pulling the handle so it does not come off
– No direct contact: gravity pulling you toward the center of the earth the surface of the earth (pavement?) pushing you so you do not sink in the earth
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Team Assignment – Due Thu 10/17 12 noon
• Problem/Design project:– Design a mass-spring system that can be taken to Mars
to measure the acceleration due to gravity at the surface of Mars.
• Explain the basis of your design – The governing equations & law’s of physics and how they relate to your design– Decisions on materials, components, attachment methods or working principle– Decisions that relate to the ability to take it to Mars
• Include a drawing of your design– Include rough dimensions– Include a parts list. The level of detail can be “spring, glue, screw, metal plate”, so no
need to find the actual part numbers and exact materials for the components.
• Explain how your design should be calibrated and used• No need to build the system.• Hand in a report including equations and figures. The length can be
anything from 2-4 pages typed. The length will not be graded. Only content is graded. Max 50p.
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Assignment
• Individual assignment (=homework)• Due Tue 10/22 12 noon• Problems:
– 10.11, 10.15, 10.19, 10.21, 10.22 (10p each)
• Follow format in course book EF chapter 4
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Reminders
• Look for (broken) products to take apart later – good product will replace one bad assignment
grade
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Newton’s Law - Application
• Equilibrium of forces and moments
System:
If F is 50N, what is FA+ FB, why?
i
ixF 0, i
iyF 0, i
iOM 0,
FBX
FFree Body Diagram:
FBYFA
F
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Whiteboard example
System: jiF 43
i
j
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Whiteboard example 2You are pushing a lawn mower with force of 703N. The lawn mower weighs 30 kg. The mower is not moving in the y-direction. What is the acceleration of the mower on the grass? The friction coefficient between the wheels and the grass is 0.60. At what angle should you push to maximize the acceleration? What is a reasonable angle if you were to redesign the mower?
45°
F
mg
N
F
y
x
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Pressure
• Pressure: Force acting over an area
• SI unit Pascal:
• US customary unit:
• Pressure analogous to stress
A
Fp
Pa
m
N
A
Fp
2
A1=r12 A2=r2
2A
F F=mg
F=mg
psi
in
lb
A
Fp f
2
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Pressure in Engineering
• Pressure and stress
• Hydrostatics
• Hydrodynamics
• Hydraulics/Pneumatics
• Aerodynamics
AP
www.howstuffworks.com
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Pressure - Fluids
• Pascal’s law: for fluid at rest, pressure at a point is the same in all directions.
• For a fluid at rest, pressure increases with the depth of fluid:
h
ghp
Pam
N
ms
mkgm
s
m
m
kghgp
22223
1
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Pressure - Air
• Analogous to fluids• Atmospheric pressure 101.325 kPa (14.696
psi)– Based on the weight of air in the atmosphere above the
surface of the earth divided by the area at the base of the column
hhh1
h2
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Measuring Pressure
• Absolute pressure vs gauge pressure
atmospheregaugeabsolute ppp
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Pressure Application
• Hydraulic systems
F1 F2
1
11 A
Fp
2
22 A
Fp
11
22
2
2
1
121 F
A
AF
A
F
A
Fpp
www.immersivetechnologies.com/Images/machine/cat5130.jpg
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Hydraulic system – whiteboard example
F1
F2
r1 = 1 cmr2 = 3 cmF1 = 10 NF2 = ?
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Example (whiteboard)
F1
A1
A2 = 20.0 A1
F1 = ?k=3000.0 N/mx=5.00 cm
Rigid beam
How much force (F1) do you need to apply to compress the spring by 5.00cm?How much force (F1) do you need to apply to compress the spring by 5.00cm?
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda• Mass
– Mass– Density– Mass Flow– Mass Moment of Inertia– Momentum
• Force– Force basics and applications– Spring forces– Friction forces– Newton’s laws– Pressure
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Hooke’s law - revisited
• Applicable in the elastic range of the spring– Elastic means there is no permanent deformation after the force is removed
kxF F = applied force (N)k = spring constant (N/mm, N/m)x = deformation of the spring (mm, m)
x
F
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Hooke’s law cont’d
• Applicable in the elastic range of the material– Elastic means there is no permanent deformation after the force is removed
kxF F = applied forcek = a constant x = deformation
x
F
Elastic stress is not typically visible
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Stress-Strain curve
Str
ess
(Pa)
Strain (mm/mm)
Upper yield stressLower yield stress
Ultimate stress
Elastic stress
Fracture stress
L
LE
Remember: Hooke’s law valid in “elastic range”
Hooke’s law restated:
E
Modulus of Elasticity E
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Modulus of Elasticity & Shear Modulus
• Material property• Modulus of elasticity, E,
for linear pulling (or pushing) of material
• Shear modulus for shearing or twisting material
F F
F
F
FF
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Tensile Strength & Compressive Strength
• Tensile strength is the stress when a material is pulled apart– Yield strength in the elastic region
(commonly used in engineering)– Ultimate stress in the maximum
stress material can handle before failure
• Compressive strength is the stress when a material is compressed
F F
F F
F
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Modulus of elasticity of materials
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Stress-Strain curve Brittle and Ductile material
Str
ess
(Pa)
Strain (mm/mm)
Str
ess
(Pa)
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Strength of materials
• When designing a piece, it is typically designed to withstand loads to its yield stress + a factor of safety
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Example (whiteboard)
• A rod is pulled in a tensile testing machine with force 50.0 kN. The rod has a diameter of 4.0 cm. The stain is 0.00001 What material could the rod be?
L
LE
Hooke’s law restated:
E
Modulus of Elasticity E
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Replacing an engine - problem
You are replacing an engine in your car using a rope as shown in figure. How much force do you need to lift the engine? What is the tension force on the supporting cable? Choose a rope diameter to accommodate the largest stress. Use a reasonable factor of safety. The tensile strength of the rope is 42 MPa.The engine weighs 321 kg.
Engine
10°
80°
ring, not a pulley
Supporting cable
To solve, draw a free body diagram, make the sum of forces (as vectors or as components) add to 0 (equilibrium), and solve for unknown forces. From forces, calculate the needed diameter for the worst case. Mathematical answer for diameter is 1.0 cm, what is your engineering answer?
To solve, draw a free body diagram, make the sum of forces (as vectors or as components) add to 0 (equilibrium), and solve for unknown forces. From forces, calculate the needed diameter for the worst case. Mathematical answer for diameter is 1.0 cm, what is your engineering answer?
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Reminders
• Look for (broken) products to take apart later – good product will replace one bad assignment
grade
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda
• Force basics and applications• Spring forces• Friction forces• Free body diagrams• Newton’s laws• Pressure• Stress and strain• Moments• Work
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Moment
• Moment is force acting at a distance
FdM NmdFM
F
dF
r
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Moment & Torque in Engineering
http://eml.ou.edu/Photo/Struct/Traffic%20light2.jpg www.craneoperator.com
www.mech.uwa.edu.au/DANotes/gears/intro/gearbox.jpeg
http://content.answers.com/main/content/wp/en/thumb/b/b4/500px-The_Little_Belt_Bridge_(1935).jpeg
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Calculating moments
1. Draw a free body diagram2. Write the force and moment
equilibrium equations3. Solve for unknowns
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Moment – Example 1
FSystem:
L
L/2
FFree Body Diagram:
FByFA
FBx
1. Draw a free body diagram2. Write the force and moment
equilibrium equations3. Solve for unknowns
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Moment – Example 2
FSystem:
L
L/2
FFree Body Diagram:
FAy
M
FAx
1. Draw a free body diagram2. Write the force and moment
equilibrium equations3. Solve for unknowns
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Moment – Example 3
• EF problem 10.25
1. Draw a free body diagram2. Write the force and moment
equilibrium equations3. Solve for unknowns
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Moment – in class task
m1g
Calculate the forces and moments in terms on given mi , L, and g. L
L
FAyM FAx
L/2
L/4
L/8
m2g
1. Draw a free body diagram2. Write the force and moment
equilibrium equations3. Solve for unknowns
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Agenda
• Force basics and applications• Spring forces• Friction forces• Free body diagrams• Newton’s laws• Pressure• Stress and strain• Moments• Work
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Work
• Work is the force to the direction of the movement need to move an item
FdW JNmdFW
F
d
F
Fwork Fwork
dFW
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Work in Engineering
www.otis.com
mowabb.com/aimages/images/2005/07-15-05.jpg
www.mhinfo.com/mhi_new/images/conveyor.jpg
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Work - Example
• How much work is required to push a lawn mower for 100m? How much force do you need to push the mower? F=200N. Pushing angle is 60°.
Fwork
60°
F
Fy
mg
N
F
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Work - Example
• How much work is required to push a lawn mower for 100m?
=200i+231jF
mg
N
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Work – In class task
• How much work is required to push w/ force F the crate 1m down the ramp at constant speed. Friction force is 800N. The crate weighs 100 kg.
F
mg
NF
40
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
Assignment
• Individual assignment (=homework)• Due Thu 4/16 8:00am• Problems:
– 10.23, 10.24, 10.27, + the pulley problem on the next slide (10p for each problem in EF + 20p for the pulley problem)
• Follow format in course book EF chapter 4
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
• A pulley is hanging on 2 cables on the ceiling. You are pulling a known mass on a rope as shown in the figure. What percentage of the effort (force) you use goes to work done to lift the mass? Which rope/cable is under most stress?
40 30
m
25
Cable A Cable B
Rope
You
are
pul
ling
here
© Katja Hölttä-Otto 2009
EGR 102 03/24/2009
40 30
25
TA
G
Fpul
l
TBTAy
TAx
TBy
TBx
40 30
Fpull_x
Fpull_y