Transcript Quiz Notes - Catapult Physics and Role of Engineer

• Which step of EDP evaluates the pros and cons of
different ideas?
•
•
•
•
A. STEP 3
B. STEP 4
C. STEP 5
D. STEP 6
Question of the DAY DEC 11
• Discuss the quantities of velocity
involved in the throwing of a projectile
(THINK Vectors!!!).
• Explain your answer using mathematic
principles.
DO NOW
DEC 11
• Both Vx and Vy are equally important.
• Equal horizontal and vertical velocities will provide the
projectile with the maximum distance in travel.
• If Vx is greater than Vy, the projectile’s trajectory will
push it downward into the ground.
• If Vy is greater than Vx, the projectile’s trajectory will
push it upward causing it to lose energy and shorten the
distance it travels.
• How do you achieve equal horizontal and vertical
velocities?
DO NOW ANSWERED
DEC 11
• BIG QUESTION: How does EDP affect the design and
construction of a solution to a proposed problem?
• 1. Question of the Day and DO NOW
• 2. Newspaper Tables Challenge II
• Once you finish your 2nd Design, work on rolling the
newspaper and shaping the supports into a square/triangle
shape and RETEST.
• 3. Introduce Catapult Challenge Project
• 4. Review and Homework
AGENDA
DEC 11
• Torsion can be defined as a
•
•
•
•
A. Rotational Force
B. Twisting force
C. Linear Force
D. Pulling force
Question of the DAY DEC 12
• What is the acceleration of an object due to gravity in SI
units?
• Discuss the effects gravity has on the workings of a catapult
or trebuchet.
DO NOW
DEC 12
• 9.8 meters/second squared
• Gravity is the force exerted on all objects by the Earth that are on
or near its surface.
• Gravity will ultimately pull any object including a projectile
launched by a siege engine to the ground.
• It is also the simple force used to power the trebuchet.
• The device believed to be the most effective siege weapon prior to the
advent of gunpowder and the cannon.
DO NOW ANSWERED DEC 12
• BIG QUESTION: How does EDP affect the design and
construction of a solution to a proposed problem?
•
•
•
•
1. Question of the Day and DO NOW
2. Newspaper Tables II Results/Questions
3. CATAPULT CHALLENGE PROJECT
4. Medieval Siege Video
• Complete Video Guide
• 5. Review and Homework
• Tomorrow: Meet in 417
• We will then go to the library.
AGENDA
DEC 12
CATAPULT
CHALLENGE
STEM Trimester 2
2013
• You will work in your teams to complete
this project.
CATAPULT CHALLENGE
TEAMS
• Watch the following video documenting the
tedious and very demanding process of
building a medieval trebuchet.
How to build a catapult in
eight easy steps
• http://www.youtube.com/watch?v=5WDiW1WDyrA
MEDIEVAL SIEGE
• BIG QUESTION: How does EDP allow you to build a
working solution to a proposed problem?
• 1. LIBRARY Research Day
• We are on the island
• 2. Catapult Teams
• 3. Objectives
AGENDA
DEC 13
• Begin some informal research on the CATAPULT
CHALLENGE PROJECT
• Write down websites and other useful links.
• Make a team decision to build a CATAPULT or a
TREBUCHET
• Any research, brainstorming, discussion, ideas, sketches,
websites, video clips, or anything else to do with this project
must be recorded.
•
•
•
•
Elect a Note Taker (Remember the EDP!)
Use your notebook like a journal
Write EVERYTHING down
Required to earn maximum points for project
TODAY’S OBJECTIVES DEC 13
• When constructing a trebuchet, which component
design will be most critical to a successful throw?
•
•
•
•
A. Framework
B. Wheels
C. Throwing arm
D. Sling
Question of the Day DEC 16
• Work with your Catapult teams.
• BRAINSTORM for 10 minutes about websites
and ideas you have found through your
RESEARCH.
• Ask yourselves which part of the project will
be most challenging for you.
• GET ORGANIZED!!!
DO NOW
DEC 16
• BIG QUESTION: How does EDP affect the design and
construction of a solution to a proposed problem?
• 1. Question of the Day and DO NOW
• 2. CATAPULT CHALLENGE PROJECT Presentation
• 3. Medieval Siege Video
• Complete Video Guide
• 4. Review and Homework
AGENDA
DEC 16
• http://www.youtube.com/watch?v=5WDiW1WDyrA
MEDIEVAL SIEGE
• A block and tackle utilizing a double pulley
reduces the amount of force required to lift
objects. How much force is required to lift a
automobile with a mass of 5400 kg?
• A. 5400 N
• B. 2700 N
• C. 1350 N
• D. 900 N
Question of the DAY Dec 17
• Work with your Catapult Teams to design your
presentation.
• Lay out each section of your presentation and what you
want to include in each one.
• Include diagrams, video clips, images, and other useful
information.
• GET ORGANIZED!!!
TEAMWORK!!!
• We will be in the library on Friday.
• Presentations are DUE on MONDAY DEC 23.
• BE PREPARED TO PRESENT!!!
DO NOW
DEC 17
• ALL TEAMS MUST BE PREPARED TO
PRESENT.
• ANY TEAM NOT READY WILL LOSE 20%
OF THEIR GRADE.
• Refer to the grading rubric for a breakdown
of scoring categories.
PRESENTATIONS
• BIG QUESTION: How can energy be used to launch
a projectile?
•
•
•
•
•
1. Question of the DAY and DO NOW
2. Hand in Medieval Siege Video Questions
3. Catapult Physics – Forces
4. Measurements and Scaling
5. Catapult Teams – Presentations
• DUE MONDAY DEC 23
AGENDA
DEC 17
• You are asked to design a new touring
bicycle for the US Postal Service team.
• Describe how you would go about this
process. Use EDP as a framework
DO NOW
Jan 2
• Find out if the riders have any specific
requests (Step 1)
• Determine a budget, building materials, and
how quickly they need it (2).
• Research existing models and share new ideas.
Collect data on what works (3).
• Choose a few ideas to develop. Different frame
materials (aluminum, titanium, carbon fiber).
Notes and drawings (4)
DO NOW ANSWERED Jan 2
• List pros and cons of each bicycle design (5).
• Pick the best idea with your team. Use
multiple parts from different ideas (Frame
material from one idea and frame geometry
from another idea 6).
• Build a bike. Does it all fit together? (7)
• Get out and RIDE! Make improvements based
upon rider feedback, input, suggestions (8)
DO NOW Answered Jan 2
• Catapults use stored energy to hurl a projectile
without the use of an explosive charge. The three
primary energy storage mechanisms are tension,
torsion, and gravity. (Real-World Physics)
THE PHYSICS OF A
CATAPULT
• Tension is the pulling force exerted by a string, cable,
chain, or similar solid object on another object.
• Tension is the opposite of compression force.
• Measured in Newtons (N).
• PE when drawn or taut (C)
• Energy = 0 at rest (B)
• KE when released (A)
TENSION
• Bows and Crossbows
• Composite bow is a traditional bow laminated together.
• When the bow is drawn, the sinew (stretched on the
outside) and horn
• (compressed on the inside) store
• more energy than wood for the
• same length of bow.
Examples
of Tension
• Muscle Fibers create tension during a muscle
contraction.
• Muscle fibers slide
across one another
producing tension.
Examples of Tension
• Torsion is the twisting of an object due to
an applied torque.
• Torque is a rotational force.
• An object tends to rotate
about a fixed object.
Torque = Force x Lever Arm Distance
TORSION
Torque
• Flexible elastic object that stores mechanical
energy when it is twisted.
• Torsion bar suspensions
Examples of Torsion
Examples of Torsion
• A counterweight is an equivalent counterbalancing weight
that balances a load.
Counterweight
• Which of the following is not measured in
Newtons?
• A. Tension
• B. Compression
• C. Weight
• D. Stress
Question of the DAY
DEC 18
• You have been asked to build a workbench for the
Art Department.
• List five factors you would consider when
designing/assembling the table.
• Briefly explain why each factor is important.
• Cost of the table is not a factor.
DO NOW
DEC 18
• 1. Size of the table
• 2. Type of material to build it with
• Must meet the demands of the class environment
• 3. Location of the table (Space limitations)
• Indoor/Outdoor (will also affect the materials used)
• 4. Uses of the table
• Art work, painting, sculpting, pottery
• 5. Dimensions of the table (Height, width, Length)
• 6. Ease of maintenance and cleaning.
• 7. Who will be using it?
• Age of students
DO NOW Answered DEC 18
• BIG QUESTION: How can energy be used to
launch a projectile?
• 1. Question of the DAY and DO NOW
• 2. Catapult Physics – Forces
• 3. Measurements and Scaling
• 4. Review and Homework
• 5. Catapult Teams – Presentations
• DUE MONDAY DEC 23
AGENDA
DEC 18
When a counterweight is greatly overbalanced on one end
of a lever, it can produce large amounts of energy.
Potential Energy vs. Kinetic Energy
Counterweight is not
moving vs. moving.
Counterweight
• Catapults work by storing energy in twisted ropes.
• They function much like an archery bow.
• The tension stored is released as kinetic energy.
The Mangonel Catapult
• The trebuchet uses a counter-balance weight to rapidly
rotate the throwing arm when the weight is released.
The Trebuchet
• The twisted rope is commonly referred to as a torsion
bundle.
• It consists of several lengths of rope with the arm inserted
in between them.
• The rope is then twisted manually on both sides of the
arm using levers.
• Upon release, the torsion bundle rotates the arm at high
speed, launching the payload.
Generating Energy
• A wooden bridge has a width of 28 feet and a length of
120 feet. Accurate testing of the bridge’s efficiency
requires you to build a scale model of it. If the scaled
width of the bridge is 7 feet, what is the scaled length of
the bridge?
• A. 20
• B. 28
• C. 30
• D. 40
Question of the DAY
Dec 19
• List the eight steps of the EDP.
• Which step do you believe is the
most important to the success of
your Catapult Challenge?
• Explain your answer.
DO NOW
DEC 19
• Big QUESTION: How do scale model drawings assist you in
building a successful catapult/trebuchet?
• 1. Continue Measurements and Scaling
• 2. Project Presentations: DUE Monday DEC 23
• ALL TEAMS MUST BE PREPARED TO PRESENT. ANY
TEAM NOT READY WILL LOSE 20% of THEIR GRADE.
• Practice your presentations!!!
• Share your presentation with each other.
HOMEWORK: Measurements/Scaling Activity DUE Tomorrow
Complete Designing a Garden: DUE MONDAY DEC 23
AGENDA
DEC 20
• 1. All teams should finish their presentations first.
• 2. I will check with every team in the Media Center to
make sure you are on task.
• 3. I am looking for completed presentations including
diagrams, video clips, animations, as well as an order of
presentation. Slides each team member will be presenting.
Know your information. PRACTICE. Being unprepared
will affect your grade.
• 4. All team members must have a copy of the presentation.
Being ABSENT is NOT an EXCUSE!!!
• 5. Continue with your RESEARCH. BE ORGANIZED!
Media Center
Expectations for Sept 20
• BIG Question: What benefits do research provide
to the completion of the Catapult Challenge?
•
•
•
•
•
1. Catapult Challenge Progress Presentations
2. All teams must be prepared to present.
3. HOMEWORK
HAPPY HOLIDAYS!!!
MERRY CHRISTMAS and HAPPY NEW YEAR!!!
AGENDA
DEC 23
• You need to review two designs for a project you are
working on. It is necessary to reevaluate the pros and
cons of each design.
• You would check your notes for which EDP step to do
this…
• A. Step 4
• B. Step 5
• C. Step 6
• D. Step 3
Question of the DAY Jan 2
• Underwater exploration is the new frontier for
many kinds of research.
• A new type of self-contained submersible is
needed to expand current capabilities of
exploration.
• Apply the steps of EDP to the plan and design of
a deep-sea vehicle.
• What questions need to be asked throughout the
process?
DO NOW
Jan 2
• Special requests/requirements (Step 1)
• Determine a budget, building materials, and
how quickly they need it (2).
• Research existing models and share new ideas.
Collect data on what works (3).
• Choose a few ideas to develop. Include life
support systems, power/fuel sources, and
frame construction.
DO NOW ANSWERED Jan 2
• Weight he pros and cons of each design. Which is
the most efficient at solving the problem (5).
• Move forward with the best idea. Include facets of
working models and improve upon them (6).
• BUILD IT! Remember the difference between a
fault and a weakness.(7)
• Test it. Use it in various underwater conditions.
Unmanned and manned controlled tests. Invite
experts in the field to review and critique your
designs . Make improvements based upon their
input and your test results. (8)
DO NOW Answered Jan 2
• BIG QUESTION: How does engineering evolve to build
safer machines?
• 1. Question of the Day and DO NOW
• 2. Finish Presentations
• 3. The duty of responsible engineering
• 4. Introduce Engineering Critique Project
• 5. Closing Thoughts and Review
AGENDA
Jan 2
• The role of the engineer is to respond to a
need by building or creating something
along a certain set of guidelines (or
specifications) which performs a given
function.
• Devices, plans, or creations should perform
its function without fail.
Engineering
• Engineers weigh different design choices on their merits
and choose the solution that best matches the
requirements.
• The crucial and unique task of the engineer is to identify,
understand, and interpret the constraints on a design in
order to produce a successful result.
• It is usually not enough to build a technically successful
product; it must also meet further requirements.
Engineering
• BIG QUESTION: How does engineering evolve to build
safer machines?
• 1. Finish Presentations
• 2. Hand in homework
• 3. Research Day – Center Island in Library
• 4. Engineering Disasters Critique Project
• 5. Closing Thoughts and Review
AGENDA
Jan 6
• Research and Select an Engineering Disaster for your Project.
• Be sure that the disaster you choose meets all of the criteria of the project as per
the handout.
• Begin working on sketches and diagrams of a buildable and working
catapult/trebuchet design.
• Consider the following…
•
•
•
•
•
•
Size of overall device
Parts you will need
Dimensions of components
Energy mechanisms – Torsion or Counterweight
Sling Assembly, Length of throwing arm, torsion, Placement of Axle
Frame design/reinforcements
Research Day: Expectations and
Objectives
JAN 6
• The most important responsibility an engineer has is
to
•
•
•
•
A. create the most cost-efficient (cheapest) design.
B. meet all of the constraints and criteria of the project.
C. create a design with the greatest factor of safety
D. create the safest design while considering cost and
materials
Question of the Day
Jan 7
• 417 Enterprises is a company that specializes in producing extreme
conditions equipment. One of their products is a high tensile
braided rope used for rescue operations and high-altitude
expeditions. They recently chose a new supplier for the nylon used
in the rope. It is cheaper and the new supplier says the nylon fibers
are the strongest available today.
• Two climbers were recently killed in an accident on Mt. Everest
when one of the ropes purchased from 417 was unable to support
the weight of three climbers and their gear. The weight was well
under the maximum limit of the rope. Upon investigation, the rope
did not appear to be cut or damaged.
• Which party is at fault? Support your answer.
DO NOW
Jan 7
• 417 Enterprises is liable for the defective rope they manufactured
and sold.
• The climbers did not exceed the recommended maximum load
rating of the rope.
• The fault most likely lies with the new nylon purchased for the
rope.
• It is the responsibility of 417 to retest the ropes using the new
nylon.
• Main component (nylon) of the rope has been changed.
• The manufacturing process of the rope may have weakened the
overall strength of the nylon.
• The nylon manufacturer may also have some liability.
DO NOW ANSWERED
Jan 7
• BIG QUESTION: How does engineering evolve to build
safer machines?
• 1. Finish Presentations
• 2. Role and Responsibilities of an Engineer
• 3. Catapult Challenge EDP Steps 5 and 6
• 4. Closing Thoughts and Review
AGENDA
Jan 7
• Engineers take on the responsibility of producing designs that will
perform as well as expected and will not cause unintended harm to
the public at large.
• Engineers typically include a factor of safety in their designs to
reduce the risk of unexpected failure.
• However, the greater the safety factor, the less efficient the design
may be.
• What factors may affect limitations of a factor of safety?
Engineering
Material Strength
Factor of Safety = _________________
Design Load
• Design load is maximum load a part should ever see in service.
• I-beam material strength = 3000 tons (Maximum before failure)
• Design load applied to I-beam = 1000 tons
• Factor of Safety = 3
Factor of Safety
• Engineers must struggle to design in such a way
as to avoid failure, and, more importantly,
catastrophic failure.
• Result in loss of property, damage to the
environment, and possibly injury or loss of life.
• With analysis and study of engineering disasters,
modern engineering designers can learn what not
to do and how to create designs with less of a
chance of failure.
Engineering
• When calculating factor of safety, the material strength is defined
as
• A. the least amount of weight a material should be exposed to
• B. the maximum amount of load that a part will see in service
• C. the maximum load a material can withstand before failure
• D. the safest amount of weight a part should be exposed to
Question of the Day
Jan 8
• A new proposal has been given to your engineering firm.
A new product has been designed with flexible, gold (Au)
joints. These joints need to flex in order to withstand
various environmental conditions the product will be
exposed to. The product is a new type of “rover” which
can collect data and specimens within extremely hot or
cold conditions. It has the same capabilities as other
“rovers” available on the market. Most rovers of this type
cost anywhere between $50,000 to 60,000. This new
“rover” will cost $80,000.
• Evaluate the proposal before it can go into production.
DO NOW
Jan 8
• Considerations….
• 1. COST – Gold will drive up price of the product.
• Is this the only reason why it costs $20,000 to 30,000 more than other
models?
• 2. Need for Gold – why is gold needed?
•
•
•
•
Gold is a malleable metal with a low melting point.
Is this the best material for the job?
Alternate material that can be used?
Still needs to be tested!
DO NOW Answered Jan 8
• BIG QUESTION: How does engineering evolve to build
safer machines?
• 1. Question of the Day and DO NOW
• 2. Role and Responsibilities of an Engineer
• Engineering Disasters Video Clips
• 3. Catapult Challenge EDP Steps 5 and 6
• 4. Closing Thoughts and Review
AGENDA
Jan 8
• Consider the various forms of transportation and travel
available to us.
• Which method of transportation do you believe is the
most dangerous?
• SUPPORT your answer with facts/data/examples.
• BE READY to share your answer with the class.
Identifying Potential Risk
• What are the general opinions and fears of the public?
Disasters are
identified by the
public’s perception
of risk.
Modern Engineering
• In 1992, roughly the same number of fatalities occurred
(in the United States) in transportation accidents
involving
airplanes (775)
trains (755)
bicycles (722)
• Public perception of risk is by far the greatest with air
travel.
Perception of Risk
• BIG QUESTION: How does engineering evolve to build
safer machines?
• 1. RESEARCH DAY – On the Island
• 2. Role and Responsibilities of an Engineer
• Engineering Disasters Video Clips
• 3. Catapult Challenge EDP Steps 5 and 6
• 4. Closing Thoughts and Review
AGENDA
Jan 9
• http://www.youtube.com/watch?v=e6PKIiT_T8Q
• 8:52
• 17:55
Engineering Disasters
• Which of the following is most difficult for engineers to
account for when designing a solution to a problem?
•
•
•
•
A. Maximum load applied to the structure
B. Quality of building materials
C. Integrity of foundation materials
D. Natural phenomenon
Question of the Day Jan 14
• You have been asked to design a new type of rocket car. It will be
used to attempt to break the current land speed record held by
Royal Air Force pilot Andy Green. It stands at an average of
763.05 mph (1227.96 km/h) over a 1 mile distance. This is the
only supersonic land speed recorded to date.
• Brainstorm with your teammates and compile a list of factors and
considerations that must be included in a design for this type of
vehicle.
DO NOW
Jan 14
• Materials to build the vehicle (what is the cost constraint if any)
• Tires for maximum traction (where will vehicle be tested)
• Type of propulsion system (Turbofan)
• Safety mechanisms to slow and stop vehicle (drag chute)
DO NOW ANSWERED Jan 14
• BIG Question: What is the role of an engineer?
• 1. Question of the Day and DO NOW
• 2. Role of the Engineer
• 3. FRIDAY Jan 17 QUIZ on Physics of a Catapult and
Role of the Engineer
• 4. Blueprints and Parts Lists – Special Parts
• 5. STUDY for QUIZ
AGENDA
Jan 15
• http://www.youtube.com/watch?feature=endscreen&NR=1&v=
gWGLAAYdbbc
The Speed of Sound
• BIG Question: What is the role of an engineer?
• 1. Question of the Day and DO NOW
• 2. Space Shuttle Challenger Disaster
• 3. FRIDAY Jan 17 QUIZ on Physics of a Catapult and Role of
the Engineer
• 4. Blueprints and Parts Lists – Special Parts
• 5. STUDY for QUIZ
AGENDA
Jan 16
• January 28, 1986
• The Challenger disintegrated 73
seconds into its flight after lift-off.
• All 7 crew members were killed.
Space Shuttle Challenger
• The O-rings, as well as many other critical components, had no test
data to support any expectation of a successful launch in such
conditions.
• The lowest safe launch temperature was confirmed at 4o degrees F.
• The morning of the launch was 18 degrees F.
• Insufficient knowledge ............................... 36%
Underestimation of influence ......................... 16%
Ignorance, carelessness, negligence .................. 14%
Forgetfulness, error ................................. 13%
Relying upon others without sufficient control ....... 9%
Objectively unknown situation ........................ 7%
Poor definition of responsibilities ............. 1%
Choice of bad quality ................................ 1%
Other ................................................ 3%
Conducted by the Swiss Institute of Technology, Zurich
Causes of Failure
• BIG Question: What is the role of an engineer?
• 1. Question of the Day and DO NOW
• 2. Space Shuttle Challenger Disaster
• 3. FRIDAY Jan 17 QUIZ on Physics of a Catapult and Role of
the Engineer
• 4. Blueprints and Parts Lists – Special Parts
• 5. STUDY for QUIZ
AGENDA
Jan 16
• http://www.youtube.com/watch?v=diaZFIUBMBQ
GOOGLE buys Robotics Firm
• BIG QUESTION: How can building a prototype
provide you with opportunities to improve your
design?
• 1. CATAPULTS
• 2. Other materials
• 3. Objectives
• 4. Closing Thoughts and Homework
• Model Airplane Challenge and Webquest
AGENDA
NOV 5
• If you need to finish testing your model airplanes, you
must do so today!
• Results and your design notes/diagrams are due
TODAY by the end of this period.
• Please place them in the HOMEWORK BOX before you
leave class.
MODEL AIRPLANE CHALLENGE
• When assembling your catapults, it is important to be
careful when placing screws because
• A. they won’t secure the wood if they are too close
together
• B. the wood may split if the screws are placed along
the outer edges of the wood
• C. they may protrude along the length of the wood
• D. components of your catapult may be weakened
QUESTION of the DAY
• BIG Question: How can building a prototype provide
you with opportunities to improve your design?
• 1. SAFETY!!! WEAR PROTECTIVE EYEWEAR AT
ALL TIMES!!!
• 2. Assembly of your catapults
• 3. Preparing components
• 4. Closing Thoughts
AGENDA
NOV 6
• http://www.matscieng.sunysb.edu/disaster/
• Measure and mark where you will need holes drilled into the
components of your catapult.
• GLUE your framework and base together.
• Place paper towels under any glue points – Let’s keep the
classroom clean.
• Once your frame has been glued together and has dried, you
may them begin to place screws into the wood.
CONSTRUCTION of
CATAPULTS
• Be careful with where you insert screws to hold your framework
together.
• Avoid placing screws too close together or along the edges of the
wood.
• Place one screw and then wait before adding a second.
• This may cause components to crack or split.
• Inspect the components as you begin putting everything together.
Placing Screws
• If you require any replacement parts, you must write it
down on a separate sheet of paper with the quantity/specs
you need.
• Include the names of the members in your team.
• State the reason why you require new parts.
NEW PARTS
• EDP STEPS 7 and 8
• YOUR HOMEWORK
• Bring in screwdrivers (Phillips
Head) and any other materials/tools
you will need to complete your
catapults.
CATAPULT CHALLENGE
•
•
•
•
1. Get your CATAPULT Parts
2. Inspect all of your components.
ALL PARTS were cut as per your diagrams/specs.
Make sure they match the Specifications on your Parts
Lists.
• 3. Clean up all of your parts… SAND them down to
remove any rough/sharp edges.
• 4. Organize all of your notes/information from your
design steps.
• I will return your parts list and spec sheets.
TODAY’S OBJECTIVES
If you need any additional components not on your
parts list
OR
If you are missing anything/something is not cut
to your specs.
I NEED TO KNOW!!! So I can get teams what
you need.
MISSING PARTS
• Lay out all of your parts to make sure your
catapult can be constructed.
• DO NOT begin to assemble anything with
screws yet!!!
• Remember to include parts for the
projectile basket and the torsion handle or
handles.
PRE-BUILD INSPECTION
• Measure and mark where you need holes drilled
• Indicate the diameter of the hole.
• Angled supports may require angled cuts.
• Measure these cuts and mark them on the wood
sections. (USE PROTRACTORS/RULERS)
PLANNING