Physics
HS/Science
Unit: 03
Lesson: 01
Suggested Duration: 13 days
Kinematics of 1D and 2D Motion
Lesson Synopsis:
In the last unit, the student gained experience with motion through measurements and graphical techniques. That motion
was limited to one dimension and the emphasis was on graphing techniques and interpretation of the graphs. In this unit,
the emphasis is again on motion, but the student will be expected to perform calculations involving the motion variables.
The student will learn to represent the vector quantities of velocity, acceleration, and displacement with vectors. With
these skills, the variables of projectile motion (an important 2D problem) will be resolved. The motion investigated to date
is translational or linear motion of a point object. Problems involving uniform circular motion of a point and rotation of a
circular object are introduced with similar equations of motion.
TEKS:
P.4
P.4B
P.4C
The student knows and applies the laws governing motion in a variety of situations. The student is expected to:
Describe and analyze motion in one dimension using equations with the concepts of distance, displacement, speed,
average velocity, instantaneous velocity, and acceleration. Readiness Standard
Analyze and describe accelerated motion in two dimensions using equations, including projectile and circular
examples. Supporting Standard
Scientific Process TEKS:
P.1
P.1A
P.2
P.2E
P.2F
P.2G
P.2H
P.2I
P.2J
P.2K
P.2L
P.3
P.3F
The student conducts investigations, for at least 40% of instructional time, using safe, environmentally appropriate,
and ethical practices. These investigations must involve actively obtaining and analyzing data with physical
equipment, but may also involve experimentation in a simulated environment as well as field observations that
extend beyond the classroom. The student is expected to:
Demonstrate safe practices during field and laboratory investigations.
The student uses a systematic approach to answer scientific laboratory and field investigative questions. The
student is expected to:
Design and implement investigative procedures, including making observations, asking well-defined questions,
formulating testable hypotheses, identifying variables, selecting appropriate equipment and technology, and
evaluating numerical answers for reasonableness.
Demonstrate the use of course apparatus, equipment, techniques, and procedures, including triple beam balances,
slotted and hooked lab masses, ring clamps, ring stands, stopwatches, friction blocks, 90-degree rod clamps, metric
rulers, spring scales, meter sticks, scientific calculators, graphing technology, computers, ballistic carts, and other
standard laboratory equipment.
Use a wide variety of additional course apparatus, equipment, techniques, materials, and procedures as appropriate
such as micrometer, caliper, computer, ballistic pendulum, inclined plane, pulley with table clamp, and four inch
ring.
Make measurements with accuracy and precision and record data using scientific notation and International System
(SI) units.
Identify and quantify causes and effects of uncertainties in measured data
Organize and evaluate data and make inferences from data, including the use of tables, charts, and graphs.
Communicate valid conclusions supported by the data through various methods such as lab reports, labeled
drawings, graphic organizers, journals, summaries, oral reports, and technology-based reports.
Express and manipulate relationships among physical variables quantitatively, including the use of graphs, charts,
and equations.
The student uses critical thinking and scientific reasoning, and problem solving to make informed decisions within
and outside the classroom. The student is expected to:
Express and interpret relationships symbolically in accordance with accepted theories to make predictions and
solve problems mathematically, including problems requiring proportional reasoning and graphical vector addition.
GETTING READY FOR INSTRUCTION
Performance Indicator(s):
Graphically represent and analyze a problem situation related to projectile motion. Complete a laboratory report
that includes the proper use of significant figures and error analysis. (P.2H, P.2J, P.2K; P.4B, P.4C)
1C; 5B,
5G
©2012, TESCCC
06/13/12
page 1 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Key Understandings and Guiding Questions:
In two dimensional motion, displacement, velocity, and acceleration must be treated as vector quantities. The
magnitude angle and component forms of vectors are used in studying these motions.
— What are vectors?
— What are the vector quantities describing motion?
— What are the basic equations describing linear motion?
— How are basic kinematics equations used to describe projectile motion?
Vocabulary of Instruction:
speed
displacement
SI unit system
motion detector
vector resultant
angular displacement
error
velocity
vector
acceleration
line graph
radian
angular velocity
centripetal acceleration
position
average speed
uniform circular motion
right triangle
curve fit
vector components
Materials:
golf ball and super ball
Refer to Notes for Teacher section for materials.
Attachments:
Video: Greatest Slide Stunt Ever
Handout: Moving Man Simulation (1 per student)
Handout: Projectile Motion Simulation (1 per student)
Teacher Resource: Projectile Motion Simulation KEY
Handout: Day 2 Kinematics Problems (1 per student)
Teacher Resource: Day 2 Kinematics Problems KEY
Handout: Equation and Symbol Chart (1 per student)
Handout: Significant Digits – Significant Figures (1 per student)
Teacher Resource: Significant Digits – Significant Figures KEY
Handout: Moving Man Problems (1 per student)
Teacher Resource: Moving Man Problems KEY
Optional Handout: Unit 03 Homework Assignment (1 per student)
Teacher Resource: Unit 03 Homework Assignment KEY
Handout: Reliability of Physical Measurements (1 per student)
Optional Handout: Using Excel to find the Standard Error (1 per student)
Handout: Practice Error Calculations (1 per student)
Teacher Resource: Practice Error Calculations KEY
Handout: Measuring g with a Motion Detector – Vernier or Pasco specific (1 per student)
Handout: Lab Report for Measuring g – Vernier or Pasco specific (1 per student)
Teacher Resource: Lab Report for Measuring g KEY – Vernier or Pasco specific
World in Motion: e1962 and e1925
Optional World in Motion: 1910
Handout: Projectile Motion (1 per student)
Handout: Projectile Motion Lab Report (1 per student)
Teacher Resource: Projectile Motion Lab Report KEY
Handout: Hit the Cup Project (1 per student)
Video: Projectile Motion Full
Handout: Vector Tutorial (1 per student)
Teacher Resource: Instructor Vector Addition Tutorial
Handout: Vector Problem Examples (1 per student)
Handout: Acceleration Down a Ramp (1 per student)
Handout: Acceleration Down a Ramp Lab Report (1 per student)
2012, TESCCC
06/13/12
page 2 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Handout: Acceleration Down a Ramp – Photogate (1 per student)
Handout: Acceleration Down a Ramp – Photogate Lab Report (1 per student)
Handout: Rotational Motion Notes(1 per student)
Handout: Rotational Motion Problems (1 per student)
Teacher Resource: Rotational Motion Problems KEY
Handout: Rotation Equation and Symbol Chart (1 per student)
Handout: Hit the Cup Project Report
Teacher Resource: Hit the Cup – Teacher Guide
Handout: Unit 03 Review Questions (1 per student)
Teacher Resource: Unit 03 Review Questions KEY
Resources and References:
Ultrasonic motion detector and computer analysis software. Some of the preferred activities utilize ultrasonic
motion detectors which can be controlled by graphing calculators or computer. Alternate activities are sometimes
given. Pasco or Vernier equipment is described in the lessons.
AND/OR
Photogates with computer software. An alternate activity is included for Pasco or Vernier photogate equipment.
TEA article on significant digits and/or significant figures:
http://www.tea.state.tx.us/curriculum/science/aboutsigfig.html
Sources of error discussions:
http://www.saburchill.com/physics/chap03.html
http://level1.physics.dur.ac.uk/skills/erroranalysis.php
STATE RESOURCES:
Physics Inquiry Project: www.thetrc.org/trc/projects_tcg.html
Science TEKS Toolkit: http://www.utdanacenter.org/sciencetoolkit
Advance Preparation:
1. Instructional Note: Please check availability of required probeware and all computers for required Pasco
or Vernier lab files. Type of software required is specific to classroom computers, probeware, and
calculators available for your campus. Software files may be downloaded for free at the respective sites.
PASCO and Vernier data files will not open without prior installation of required software.
2. Obtain materials above, and test items to make sure they are working properly. There are various options and
alternate laboratories available in this unit. The teacher should take inventory of his/her equipment and decide on
which activities will be utilized in this unit.
3. Make certain that the software that is needed is installed and compatible with your computers, networks, and IT
personnel. Technology persons often demand significant lead time, and glitches are very common.
4. Students will be graded on laboratory work (participation), a lesson exam, homework, and a project (successful
launch of a marble into a cup) with significant weighting of each component. Instruction should be paced for nearly
three weeks.
5. Install software needed for the activities on the computers that students will use in the laboratory and for
homework.
Microsoft Word and Excel
Ultrasonic motion detector software or photogate software
World-in-Motion (physics toolkit 6.0) software and videos
Internet Explorer with plug-ins for showing videos, etc.
Either Pasco – Data Studio and/or Vernier – Logger Pro software and appropriate experiment files
6. Practice with the specific software for the motion detector and simulations.
7. Prior to Day 11, the project “Hit the Cup” materials need to be gathered – some of the materials are not standard
lab equipment.
8. Edit and copy (potential questions) and other handouts for students.
9. Prepare attachments as necessary.
©2012, TESCCC
06/13/12
page 3 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Background Information:
In this lesson, the student reviews and extends his/her measurement and presentation skills and learns problem-solving
techniques within the context of one- and two-dimensional constant acceleration motion. Kinematics, in large part, does
not emphasize what causes the motion but merely attempts to describe that motion. The dynamics of motion (forces,
energy, and other motion parameters) are studied in later units.
Students learn how to set up and work kinematics problems. The topics of significant digits, unit analysis, metric prefixes,
exponential notation, and error analysis are stressed. These are fundamental to success later, but are typically not much
fun at the time.
Since calculations are a large part of this unit, it is important to instill into the students the value of working problems
systematically and in a clear format. The students will need to draw on some of the skills (graphing, report writing, etc.)
from the last unit.
As in the previous unit, if you do not have the apparatus called for in the activities, you will need to find other approaches
to presenting the material.
GETTING READY FOR INSTRUCTION SUPPLEMENTAL PLANNING DOCUMENT
Instructors are encouraged to supplement, differentiate and substitute resources, materials, and activities to address the needs of learners. The Exemplar
Lessons are one approach to teaching and reaching the Performance Indicators and Specificity in the Instructional Focus Document for this unit. A
Microsoft Word template for this Planning document is located at www.cscope.us/sup_plan_temp.doc. If a supplement is created electronically, users are
encouraged to upload the document to their Lesson Plans as a Lesson Plan Resource for future reference.
INSTRUCTIONAL PROCEDURES
Instructional Procedures
Notes for Teacher
ENGAGE – Introduction to Kinematics
NOTE: 1 Day = 50 minutes
Suggested Day 1
Attachments:
Video: Greatest Slide Stunt Ever
1. Show the Video: Greatest Slide Stunt Ever.
2. Explain that the Video: Greatest slide Stunt Ever is faked, but that the
physics to perform the stunt is within the capability of the class and is
similar to a project they will complete.
3. Announce that for the next three weeks, the class will have another but
different look at motion. The use of graphs will continue, but more detail
and specific information will be utilized. The name of this unit is
“kinematics”.
4. Explain that kinematics is the study of and describing motion using
numbers and equations. In kinematics, we ask how fast, how far, and how
long did it take type questions relating to motion.
5. Introduce the Hit the Cup project, where they will roll a marble down a
ramp and into a cup. The rules of the project will be presented later.
.
6. Indicate that they already know some information, but need to learn how to
put this information together before they can complete the project and
perform calculations on projectiles.
7. Ask questions to show students that they already have significant
knowledge.
Ask:
If you travel 50 mi/hr for 3 hours – how far did you go?
Wait for answers, and then add these conditions:
In a straight line. (150 miles)
In a circle. (0 miles)
1.5 hours each way. (0 miles)
©2012, TESCCC
06/13/12
Instructional Notes:
Limit the introduction discussion to 10
minutes to allow the students to have
time to interact with the simulations. If
necessary, the vector discussion can be
conducted at another time.
The introduction of the kinematics
equations is only necessary to show
that there are just a few ideas that are
used over and over.
Misconceptions:
Students may think that acceleration
and velocity are always in the same
direction.
Students may think that an object
thrown into the air has zero
acceleration at the highest point.
Students may think that velocity is a
force.
page 4 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
How did you get the answer? What would the equation be? (d =
vav t), where vav is the average velocity
If you traveled in a straight line for 150 miles and it took 3 hours,
how fast did you drive? (50 mi/hour)
What was the average velocity?
How did you get the answer? What equation did you use? (vav =
d/t )
Is this different from the other equation?
Convince students that these are the same equation and that it is easier to
remember one equation rather than two, but some thinking is necessary.
8. Remind students that displacement is a vector and it is important to be
clear about the real question being asked. Is it distance or displacement?
Ask:
What do we mean by vector and scalar?
Give examples. (Bring out the idea that time is not a vector because
forward is not a direction!)
In one dimensional motion, how do we designate the direction of
a vector? Positive or negative number within a coordinate system
9. Remind students of some of the fine points about vectors and scalars, and
give examples of quantities that are vectors and examples of quantities
that are scalars. Include discussions of (speedometer, average,
instantaneous, and average values).
EXPLORE – Introduction to Kinematics
Suggested Day 1 (continued)
1. Quickly go over the kinematics equations below which describe motion in
1D for constant acceleration. Just identify the symbols, and stress that
these apply for constant acceleration motion like falling objects. These
equations are part of the chart handed out tomorrow
Δd = vav t
2
Δd = vo t + ½ a t
v = vo + a t
2
2
v – vo = 2 a Δd
vav = (v + vo)/2
2. Instruct the student to groups run the two simulations.
3. Explain that they will explore two simulations that will be used heavily
during the next couple of weeks and they should answer specific questions
on the Handout: Moving Man Simulation and the Handout: Projectile
Motion Simulation. There will be a post-lab discussion at the end of the
period to go over any questions. This document may or may not be turned
in for credit.
4. Very briefly demonstrate the moving man simulation.
5. Distribute the Handout: Motion Man Simulation and the Handout:
Projectile Motion Simulation.
6. Assist students with the simulations, and answer questions as needed.
7. When there is10 minutes left in class, discuss any problems with the
simulations and questions on the handouts.
©2012, TESCCC
06/13/12
Materials:
marbles
marble launch materials
Attachments:
Handout: Moving Man Simulation
(1 per student)
Handout: Projectile Motion
Simulation (1 per student)
Teacher Resource: Projectile
Motion Simulation KEY
Instructional Notes:
The simulation activities are intended
primarily to introduce these specific
simulations which will be used later.
Do not take up the simulation sheets,
but allow students to keep them for
informational purposes when they run
the simulations later.
The projectile motion simulation
reinforces that the horizontal motion
speed remains constant.
page 5 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
8. Stress that there are only two significant digits for time and up to three for
acceleration, velocity, and displacement on the moving man simulation.
(This concept may or may not have much meaning at this point.)
9. Stress that the horizontal motion on the projectile motion is the (d = vav t)
equation, where v is constant and d is the distance coordinate. So, half of
the projectile motion problem is already solved.
EXPLAIN – Working Physics Problems
1. Ask:
2
If a car starts from rest and accelerates at 5 m/sec for 6.0
seconds, how far did it travel and how fast was it moving at the
end of the 6.0 seconds? 90m at 30m/sec
2
How is this problem worked? d = v0t + ½(5)(6) = 90m; v = v0 +
(5)(6) = 30 m/sec
Emphasize that it is not the answer, but the technique, that is being
requested. That is what today is about.
2. Distribute the Handout: Day 2 Kinematics Problems. These are to be
worked in class and handed in today. They will be critiqued and returned
tomorrow. The problem above is the first of the problems on this sheet.
Students are to work all problems.
3. Lead a discussion on how the problems should be solved and presented in
class. Use this problem as an example. A common approach has the
following steps. More or less steps can be required.
Read the problem once or twice to get a general idea of what is being
asked. You may want to read it several times for this purpose. Not
understanding the problem is the most common source of error.
Include any assumptions not clearly stated.
Write down the information in symbol form, and write down what is
being asked in symbol form with a question mark or blank to
emphasize that when this blank is filled, the problem is solved.
Ensure all of the quantities are in proper (SI) units.
Sketch the motion. For now, this is a necessary step to assure that the
problem is properly understood. Later, it may not be necessary for all
problems. Visualize the motion in your head.
Write down equations that describe this motion (from the five
equations on the handout), and determine a strategy about which
equation to use. Narrow down choices to an equation with a single
unknown and the other symbols known.
If the equation being used can solve for the unknown easily, solve the
equation for the unknown algebraically. Isolate the unknown on the left
side of the equation by itself, with the known quantities on the other
side.
Insert the numbers, and perform the calculations with a calculator.
Repeat as needed until all of the question parts have been answered.
Check to make sure that the answers have the proper units and
significant figures. (At this point, do not have the students worry about
the significant digits, which will be discussed later. Now, just have
them focus on doing the problem correctly.)
Suggested Day 2
Attachments:
Handout: Day 2 Kinematics
Problems (1 per student)
Teacher Resource: Day 2
Kinematics Problems KEY
Handout: Equation and Symbol
Chart (1 per student)
Instructional Notes:
Today is the day to look at how physics
problems are solved. It is largely a
technique intensive day. At the end of
the day, students will have worked a few
problems using proper technique,
including the appropriate units. Students
will have started an equation sheet
(many instructors allow this sheet to be
used with tests). Some problems will be
worked in class and then turned in so
that you may evaluate the technique of
students. These problems and your
critique (including a trial grading
scheme) will be handed back and
discussed tomorrow.
It is suggested that a wrong
multiplication or non-logic mistake
produces only a slight loss of grade.
Although these are standard formulas
for physics, they need to correlate with
STAAR Reference Materials used by
students on assessment.
4. For this specific problem, the motion is 1D with v and x being requested, vo
and t are given. The motion is straight line, and the equations are the
©2012, TESCCC
06/13/12
page 6 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
constant acceleration motion equations. Thus, the information and
unknown lines might look like:
v = _____ m/sec
2
d = _____ m
1. Δd = vo t + ½ a t
vo = 0
2. v = vo + a t
v = (0 + 5.0 * 6) = 30 m/sec
2
2
a = 5.0 m
3. v – vo = 2 a Δd
t = 6.0 sec
4. vav = (v + vo)/2
5. It should be clear that equation 2 gives the value of v and equation 1 gives
the value of d. The number of significant digits is two and should eventually
be reflected in the answers (discussed later) which could be placed in the
blanks. Do not give full credit unless all of the important steps are followed.
6. For the second problem, ask the class to direct your hand in working the
problem according the method outlined above.
7. Divide the students into pairs, or small groups, and have them work the
remaining problems and turn in before the end of the class. These are for
you to critique.
8. If time permits, you should have the students start a symbol-equation
sheet. The Handout: Equation and Symbol Chart is a good start and
should be distributed to the students.
EXPLAIN – Significant Digits
1. Hand back the student problems worked in class yesterday, and describe
to the class what is needed to do better. Explain any comments placed on
the student papers.
2. Announce to the class that today will emphasize problem solving of
constant acceleration kinematics problems, but with attention to the
number of significant digits in the information and in the answers.
3. Make a brief presentation on significant digits, and indicate your policy on
how they are to be used. Also, indicate what penalty (partial credit
removed from a correct answer) is applied if they are not handled correctly
on homework and test answers. (Specific decisions are left up to the
teacher.)
4. Use the problems handed back as examples of how to handle the
significant digits, and have the students correct their answers according to
your policy.
5. Break students into small work groups, and hand out problems due
tomorrow, but with a clear directive that there should be time to finish the
assignment in class today. The Handout: Moving Man Problems would
be appropriate for this assignment.
6. If the students need the help, do the first problem or two as a class
discussion. It is instructive to check the answers with the moving man
simulation either as a demonstration or in student groups.
If Internet access and time is available for the students, allow them to
check their answers with the moving man simulation.
Encourage the students to pay attention to the graphs from the
simulation to aid in the understanding.
Suggested Day 3
Attachments:
Handout: Significant Digits –
Significant Figures (1 per student
and teacher)
Teacher Resource: Significant
Digits – Significant Figures KEY
Handout: Moving Man Problems
(1 per student)
Teacher Resource: Moving Man
Problems KEY
Optional Handout: Unit 03
Homework Assignment (1 per
student)
Teacher Resource: Unit 03
Homework Assignment KEY
Instructional Notes:
Although not specifically addressed in
current physics standards, the use of
Significant Figures is taught in chemistry
and used in the field of physics.
Today’s goal is to cover the topic of
significant digits and continue working
kinematics problems. This is done
through a review of yesterday’s
problems, a discussion and drill on
significant digits, and through checking
answers using the simulations.
The Handout: Significant Digits –
©2012, TESCCC
06/13/12
page 7 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
7. Assist students, and encourage them to stay on task during the class time.
Significant Figures is taken from the
web, and many other similar documents
are available. It is included as a possible
aid for the students or for the instructor
as a source of ideas. As noted below,
the emphasis on significant digits in the
classroom is an open question to be
answered by the instructor in the room.
The Handout: Moving Man Problems
can be worked in class and the answers
checked by the simulation. Now is a
good time to re-emphasize the use of
graphs in understanding motion. If the
students do not have access to the web,
using the moving man simulation as a
class activity is also useful.
The Handout: Significant Digits –
Significant Figures addresses the
topic of significant digits and/or
significant figures. This TEA article
addresses some of the difficulties
involved with teaching significant
figures.
http://www.tea.state.tx.us/curriculum/sci
ence/aboutsigfig.html.
Most teachers agree on the following:
Students should formally know the
number of significant digits in
different numbers and in different
formats. (scientific notation or other)
Calculations (because it is so easy)
should be carried out with more
than the “official” number of
significant digits.
Students should formally know that
the “official” answer contains as
many significant digits as the least
significant number used in the
calculation.
Many teachers allow one more
than the “official” number of
significant digits, with the last digit
underlined to designate it as
doubtful.
EXPLORE/EXPLAIN – Measuring g and Error Analysis
1. Remind students that the unit project is to hit a cup with a projectile and
that task requires knowledge of how things fall under the influence of
gravity and how precise (accurate) predictions are done.
2. Announce that today the class will measure the acceleration due to gravity
and use that data to examine error analysis and how to report
measurements. The class will measure the acceleration of gravity using a
©2012, TESCCC
06/13/12
Suggested Day 4
Materials:
meter sticks
stopwatches
golf ball(s)
page 8 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
“super” ball(s)
stopwatch and meter stick.
3. Review a little about bodies falling under the influence of gravity and
neglecting air friction. The class will (with help) devise the procedure,
estimate the error, improve the technique, and do the error analysis on the
measurements.
4. Introduce the topic of reporting measurements and errors.
Ask: (5 minutes)
If I were to measure the height of a desk and report the value as
85.1 cm ± 0.2 cm, what do these numbers mean? (Value and
estimated error)
If another person measures the value to be 85.4 cm ± .4 cm, do
these measurements agree or disagree?
Try to get students to agree that the measurements are compatible.
Which is correct? (Both – if correctly stated)
Why do we report an error? (It is customary and useful.)
If my best measurement of a mass is 2.31 kg and the known mass
is 2.40kg, how would I report the measurement? (Percent error)
How is percent error figured? % = errors difference (100)
standard
When do you report percent error and when do you report
absolute error? (Depends upon the situation)
5. Lead a brief discussion on reporting error and kinds of error. The Handout:
Reliability of Physical Measurements can be used as a reference for the
students and should be distributed at this time or a teacher-created
document can be substituted. The last page summary will be useful for the
students later. Include precision and accuracy terms in your discussion.
(10 minutes)
6. Introduce the topic and materials to measure g – the acceleration due to
gravity.
Ask:
Which falls faster a nickel or a golf ball? Does the mass of the
object affect the rate of fall?
Most classes will correctly say the same rate. Demonstrate the fact
anyway that mass is not a factor.
7. Develop a procedure, and measure g as a class – Method I. (15 minutes)
Ask:
Given the materials (meter sticks, stopwatches, balls), how could
we measure the acceleration due to gravity?
Let the class brainstorm different ideas. Choose one. Probably someone
drops a ball from a known height. Use several timers across the class, etc.
Involve as many students as possible in the process.
In the process, do not be afraid to throw out obviously bad data. Have
fun, and discuss possible errors. Have a student record the times on
the board.
Ask which student’s time measurement to use? Class will say average.
Ask if the class did the process again, will it get the same answer?
How close? What is the error value to use? Will we get better with
practice? Discuss the role of percent error and data scatter in this
measurement.
Arrive at some conclusion about the error that should be attached to
©2012, TESCCC
06/13/12
Attachments:
Handout: Reliability of Physical
Measurements (1 per student)
Optional Handout: Using Excel to
find the Standard Error (1 per
student)
Handout: Practice Error
Calculations (1 per student)
Teacher Resource: Practice Error
Calculations KEY
Instructional Notes:
Like significant digits, the degree to
which error analysis is presented is
highly dependent upon the goals of the
class and background of the students.
The information presented in this lesson
is probably minimal, but some reference
documents are made available if the
class goals demand more. In addition,
there are a number of good sources of
error discussions on the web.
Two such websites are:
http://www.saburchill.com/physics/chap
03.html
and
http://level1.physics.dur.ac.uk/skills/erro
ranalysis.php
The documents provided as reference
for the class are:
Handout: Reliability of Physical
Measurements
An overview of error analysis
with examples and summary
Handout: Practice Error
Calculations
The complicated standard error
calculation is not too bad if
Excel functions are used.
The information presented for the
classroom activities is intended to keep
the class involved in a dialogue on error
analysis and allow you to assess the
skills of the students in making simple
measurements.
You may not want to emphasize the
formal standard error equations and
procedure. It is adequate to mention
that there is a standard way to present
the information.
Save the standard error discussion for
page 9 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
this technique. (Likely 10% or more)
8. Develop an improved procedure, and measure g as a class – Method II.
(10 minutes)
9. In Method I, there is uncertainty in when the student (ball dropper) will let
the ball drop. This affects the timers. Try to get the dropper(s) out of the
error process. Ask if it would be valid to let the ball roll off the edge of a
table so that the timers could anticipate the starting time?
Ask:
If an object is launched sideways at the same height as another
object is dropped straight down, which hits the ground first?
The class has already found the time of fall to be the same from
simulations but may need convincing with videos. Make sure that they
understand that the question does NOT ask which goes faster or farther.
10. Illustrate the independence of the vertical and horizontal motion.
11. Show the Video: X and Y Motion, and/or run the simulation of the two
balls falling at the URL given here.
12. Measure g using an improved technique, discuss the error sources, and
develop a new measured value and error.
Hopefully, this value will be more accurate and the data scatter will be
less than that from Method I.
later, if you want to emphasize that
method at all. A good activity to use for
this purpose would be to measure the
height of a table at different locations by
different people, or you may use the
data in the Excel Handout: Practice
Error Calculations.
Video: X and Y Motion
http://www.upscale.utoronto.ca/GeneralI
nterest/Harrison/Flash/ClassMechanics/
TwoBallsGravity/TwoBallsGravity.html
13. Review class policy on error reporting.
2
14. Indicate that since you have a standard value of g = 9.81 m/sec , giving a
percent error or an absolute value is appropriate. However, if you did not
have that value, you would need to determine a reasonable value for the
error based upon common sense and data scatter.
15. If it fits your class policy, finish the presentation on random errors and the
use of standard error in reporting measurements and/or using Excel to
calculate the standard error.
Most teachers will not require the use of the standard error, but rather
use an educated guess at random error in their classroom.
16. Assign as homework or in-class work the Handout: Practice Error
Calculations.
EXPLORE/EXPLAIN – Measuring g with a Motion Detector
1. Review any questions or leftovers from yesterday in terms of:
The importance of g, and when it applies
Error analysis in your classroom
2. Tell the students that they will use the motion detector to measure g and
will hopefully get a more accurate value than with the stopwatch. One
purpose is to confirm that the global value of g applies to your local
classroom.
3. Divide the class into normal lab groups, distribute the apparatus and
handouts, and perform the laboratory investigation Measuring g with a
Motion Detector. Each lab group should hand in one lab report.
Emphasize that the error analysis is important, as is explaining error
sources such as air friction.
©2012, TESCCC
06/13/12
Suggested Day 5
Materials:
basketball or similar object
stand to position the motion
detector
coffee filter
alternate* files for “World in Motion”
program (if you do not use the
motion detector apparatus)
Attachments:
Handout: Measuring g with a
page 10 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
4. Assist the students with the data taking, analysis, and saving the graphs to
a Word document.
5. It is likely that students remember how to handle the programs, but they
may need reminding. If necessary, remember that the entire screen can be
saved (copied) by hitting Ctrl-Print Screen.
6. The program gets slopes through a subtraction of previous data points and
then does some smoothing. Thus, the velocity graph tends to be offset
from the position graph and so on. The same time portions of the all
graphs may not produce the best results.
7. Most classes will not have time to perform the coffee filter portion of the
lab, but it may serve as a demonstration topic and introduce free fall, air
friction, and parachutes.
10. Perform a post-lab discussion on the experiment and questions at the end
of the lab report.
8. It should be clear that the "free fall” motion up after the bounce can also
provide a value of g. This motion agrees with the previous study of graphs.
9. The dramatic negative “bounce” acceleration can provide a conversation
topic for collisions, and the negative direction should be emphasized – up
is negative.
10. Remind students of the homework assignment due on Day 9.
EXPLORE – Projectile Motion Concepts
1. If the activities from yesterday are not complete, summarize or otherwise
close out that topic.
Ask:
If a ball rolls off the table at a speed of 2 m/sec and is in the air
for 0.15 seconds, how far does it land from the table? Since the
d motion is simply d = vot, the class should respond .3 meters.
How high is the table?
Again, they should answer correctly.
2. Not to be answered, only ask!
0
If the ball left at an angle of 30 , where would it land? (More difficult
but farther from the table)
At what angle and speed would it need to be shot to hit a target at
1.1 m from the table? (More difficult)
3. Explain that on Day 12, each lab team will roll a ball down a tube and hit a
target placed on the floor by the instructor. The team will also provide
calculations detailing how they calculated the parameters necessary to be
successful. Most will roll the ball horizontally off the table but some may
want to launch at an angle.
4. The lab today gives experience with launch speeds and angles.
5. In addition, the knowledge and skills will be tested on the unit exam.
6. Break the class into lab groups, and distribute the Handout: Projectile
©2012, TESCCC
06/13/12
Motion Detector – Vernier or
Pasco specific (1 per student)
Handout: Lab Report for
Measuring g – Vernier or Pasco
specific (1 per student)
Teacher Resource: Lab Report for
Measuring g KEY – Vernier or
Pasco specific
World in Motion: e1962 and e1925
Optional - World in Motion: 1910
Instructional Notes:
While it is suggested that the motion
detector apparatus be used, similar
concepts can be presented using the
“World in Motion” program and video
“e1962” for the falling ball with bounce
and “e1925” for a body falling with
extreme air friction.
Students should remember how to use
the motion detector and computer to
report data, but may need a review. This
is a standard activity and is presented to
enhance the student’s laboratory skills.
It should also give some reality to the
2
idea that g really is 9.8 m/sec and that
measurement error really does exist.
Suggested Day 6
Attachments:
Handout: Projectile Motion (1 per
student)
Handout: Projectile Motion Lab
Report (1 per student)
Teacher Resource: Projectile
Motion Lab Report KEY
Handout: Hit the Cup Project (1
per student)
Instructional Notes:
One goal for today is to remind students
about “hit the cup” project and generate
some enthusiasm for learning about
vectors and projectile motion. The
Walter-Fendt projectile motion
simulation works well and can be used
by students to check homework
problems.
By now the students have familiarity
with the basic kinematics equations for
one dimension and recognize that 2D
motion is more complicated. They also
have an appreciation for vectors, but are
probably not proficient in their use. This
page 11 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
Motion. Remind students that the x and y motions are independent and
that this program splits up the total motion into x and y motions using
vector techniques. The class will study these techniques more tomorrow.
Send the students to the computers to run the simulation found at
http://www.walter-fendt.de/ph14e/projectile.htm.
7. Assist the students in setting up the simulation and filling out the data
sheet using Handout: Projectile Motion Lab Report.
8. Continue with the lab exercises to the end of the period or until you decide
a lecture is called for based upon student questions.
9. Encourage the students to read the material carefully.
10. Each student should keep a separate lab report which will be discussed
tomorrow.
class period is used to discuss rules for
the project, discuss what things must be
learned, and to get a start on the
learning about projectile motion through
a simulation program.
If your students are not familiar with the
use of scientific or graphing calculators
to find the sine and cosine of angles, a
few minutes should be taken just
handling the mechanics of punching in
numbers. The right triangle logic will be
covered tomorrow. The simulation
activity requires calculations with sines
and cosines. The meaning is not
needed explicitly today.
11. Distribute the Handout: Hit the Cup Project to the students at the end of
the class so they may begin to think about it. They will be expected to
devise a procedure on Day 11 then perform the task on Day 12.
EXPLAIN – Working with Vectors
1. Ask:
Name some vectors and some scalar quantities. Force, velocity,
etc.; time, mass, etc.
Who uses vectors in their work? (Pilots, engineers, architects,
graphic artists)
2. Explain that today is dedicated to developing vectors formally. They will
use vectors on the project and also in later chapters. There are also vector
problems on the pending homework assignment. There will be some inclass group work on vectors, and if not completed today, they should be
worked at home and handed in tomorrow.
3. Lead a discussion similar to that found in the Teacher Resource:
Instructor Vector Addition Tutorial. Present numerous examples to
illustrate the equations and stress the skills needed.
4. Provide the URLs from the tutorial or other study sources.
5. Provide the Handout: Vector Tutorial.
6. Have the students work the example problems in small groups, and go
over these as additional examples as time permits. If the students are not
finished with these problems, they should take them home and hand in
tomorrow.
©2012, TESCCC
06/13/12
Suggested Day 7
Attachments:
Handout: Vector Tutorial (1 per
student)
Teacher Resource: Instructor
Vector Addition Tutorial
Handout: Vector Problem
Examples (1 per student)
Instructional Notes:
Today’s goal is to introduce vectors
formally in 2 and 3 dimensions. Quickly
limit the discussion to 2 dimensions, and
then look at:
vector addition graphically,
vector conversion between
magnitude angle format and the
component formulation, and
vector addition in components.
From the projectile motion activities, the
students should be aware of the
usefulness of breaking the vectors into
components and have a feel for the
process. The students should also be
aware that vectors will be useful in
analyzing the motion of the “marble”
down the ramp used to launch the
projectile in the project. Today, formally
present vector theory, and work through
some examples. Determine the
background of your students, and tailor
your presentation accordingly.
page 12 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
EXPLAIN – Working Homework, Getting It Clear
Notes for Teacher
1. This session should not be a “teacher works the problem and students
copy it from the board” session. A variety of presenters and student
participation is recommended.
2. Determine where the students are in the homework assignment and what
is causing the most trouble.
3. Use the period to help the students get the homework ready to turn in and
understand the wide range of problems.
4. One possible approach would be for the teacher to work one problem –
emphasizing techniques then this could be followed by the class “directing
the teacher’s hand” for a problem and followed by a student being at the
board and the class directing the hand of the student presenter.
Suggested Day 8
Instructional Notes:
The goal for today is to help the
students to understand and be able to
complete the homework that is due
tomorrow. Problems like those on the
homework have been introduced and
practiced at times earlier, but now a
variety of different types of problems are
now all due at the same time. This
creates some pressure. In addition, the
correct method of working the problems
has been stressed and the students
need to know that this is still an
important part of the procedure.
5. The idea is to keep the students involved.
6. An alternative approach is to pair the students and have each pair work a
different problem on the board during the first half of class. Then, they’ll
present their work, round robin style, the second half of class.
7. Tomorrow, the lab activity is to measure the acceleration due to gravity (g)
by measuring the acceleration down a ramp and applying vector concepts
to obtain g. Spending some time on a problem resembling this situation
would set the stage for that lab activity.
EXPLORE/EXPLAIN – Acceleration Down a Ramp
1. Ask:
Which will take longer? Falling off the height of a ramp or rolling
down the ramp? (It takes longer to roll down the ramp.)
Will the time depend upon the slope of the ramp? (Yes)
2. After taking up homework and answering any last minute questions, inform
the class that today you are going to measure the acceleration due to
gravity by measuring the acceleration of a cart down a ramp. This will give
them some practice and experience with vectors.
Develop ramp concepts – 5 min
3. Arrange for two cart track setups to be at the front of the room for some
preliminary demonstrations. Ask questions, then demonstrate the answers
of the different situations running side-by-side races down the ramps. The
starting technique for the races is very important. A ruler, blocking the
start, then quickly removed works well.
Ask:
If we have a steep ramp and one not so steep, which cart will win
the race? (Which accelerates more?) Steep
If we have an empty cart and a loaded (heavy) cart, which will win
the race? They are mostly the same.
0
What would be the acceleration if the ramp was at a 90 angle? (g
2
– 9.8 m/sec )
Can we use vector components to find g by measuring the
acceleration down the ramp? Yes, this is the point of the lab.
It typically takes much longer to work
problems as a class than anticipated, so
spend some time inquiring about where
the students are and what concepts are
giving students difficulties. Concentrate
the class time on the areas of difficulty.
Work those specific homework
problems or problems of that type.
Suggested Day 9
Materials:
stopwatch
protractor
meter stick
cart and track
motion detector apparatus
Attachments:
Handout: Acceleration Down a
Ramp (1 per student)
Handout: Acceleration Down a
Ramp Lab Report (1 per student)
Handout: Acceleration Down a
Ramp – Photogate (1 per student)
Handout: Acceleration Down a
Ramp – Photogate Lab Report (1
per student)
Instructional Notes:
The standard lab activity utilizes motion
detectors but there is a version for
photogates using a picket fence and
software.
The ramp demonstration races need to
be set up and ready for class.
©2012, TESCCC
06/13/12
page 13 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
Develop the equations for the lab – 5 min
Make sure that the apparatus, including
the computer software and motion
detector apparatus or photogates, is
available. Students should be proficient
with the apparatus, but may need some
additional help.
4. Show the students the diagram of the apparatus, and go through the
equations needed in the lab to understand the use of vectors to find g.
Indicate that one report per group is needed.
Perform the lab activity with post-lab – 40 min
5. Divide the class into lab groups, provide the following handouts and start
lab.
Handout:
Handout:
Handout:
Handout:
student)
Acceleration Down a Ramp (1 per student)
Acceleration Down a Ramp Lab Report (1 per student)
Acceleration Down a Ramp – Photogate (1 per student)
Acceleration Down a Ramp – Photogate Lab Report (1 per
This activity gives useful practice now
for when Newton’s laws are examined.
The normal force concept will be easier
if the student has had the experiences
gathered today.
6. Assist students as needed.
7. Perform a post-lab discussion. There should be time to do both parts of the
lab, but the post-lab is more important than completing both methods. If
even one group completes the motion detector portion of the lab, the
results from that group can be discussed.
8. Stress that breaking the motion into components (perpendicular) is
important, the motion down the ramp is constant acceleration, and the
motion normal to the ramp is zero.
Ask:
How might friction affect the results? Slow down – g measure small
Which measurement approach is better? Could be either, if the
technique is good
EXPLORE/EXPLAIN – Rotational Motion Concepts
1. Explain that today the class looks at rotational or circular motion. So far in
the course, the motion has been that of a point, or a point in an object,
traveling in a straight line or (for projectile motion a combination of straight
line motions). That motion is referred to as translational motion, and now
we study rotational motion.
Ask:
What are some things that rotate or move in circles? Tires,
planets, CDs, pulleys, rolling balls
Which objects rotate and translate? Tires and rolling balls
What is the relationship between the number of rotations and the
linear distance rolled? With more turns, the farther the distance
The rotational speed and the linear speed? The faster the rotational
speed, the faster the linear speed.
Most students will have a qualitative idea, but may not have formal
equations. That will be covered later.
If the disk rolls through 1 rotation across a desk, how far has it
traveled on the desk? 2πr
Is this the same as the circumference? Yes
What are some of the words that describe circular or rotational
motion? Answers may vary, but include angle, rotation, etc.
©2012, TESCCC
06/13/12
Suggested Days 10 and 11
Materials:
demonstration wheel (with
reference line)
Attachments:
Handout: Rotational Motion Notes
(1 per student)
Handout: Rotational Motion
Problems (1 per student)
Teacher Resource: Rotational
Motion Problems KEY
Instructional Notes:
Today is basically a lecture-discussiondemonstration day to develop the
concepts and equations of uniform
rotational motion. The students will have
ideas about this topic, but will need
formal guidance and vocabulary
page 14 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
2. Announce that they are going to look at strictly rotational motion first and
then look at the connection between rotational motion and the motion of
moving wheel a little later. Have the two URLs below readily available.
discipline. Since rotational motion will be
studied later in connection with
Newton’s laws and satellite motion, the
goal is to develop vocabulary, concepts,
and some kinematics equations.
3. Bring up the Ladybug simulation:
http://phet.colorado.edu/simulations/sims.php?sim=Ladybug_Revolution
http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ClassMech
anics/RollingDisc/RollingDisc.html
4. Present the concepts and equations for this topic. Students should be
encouraged to add these equations and concepts to their “equation and
symbol chart”. The URL of hyperphysics has good resources for this topic
under rotational motion.
http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
5. If time permits, assign selected questions from the “rotational motion”
problems to work in class. It is unlikely that there will be time, and you
should use the first half of class tomorrow for that task.
6. Inform the students that questions like these will be on the unit exam.
A large disk with a line visible on the
side as a reference which can roll on the
desk or in the air helps demonstrate
some of the ideas. In addition, you
should have the Phet Ladybug
simulation opened on an Internet
connection with classroom display. This
simulation can clarify some of the
concepts efficiently.
In the discussion, try to use terms such
as linear speed and angular speed to
connect the angular concepts to the
related linear concepts in the student’s
minds.
7. Ask the students if they have any questions before they continue working
on the assignment.
8. Divide the students into groups to work together, or send students to the
board in groups, to report their results to the class or work the problems as
a group.
9. The question on orbital motion (#7) should be discussed, as it ties several
concepts together that are classic confusion points for students.
ELABORATE – Hit the Cup
Suggested Day 11 (continued)
Performance Indicator
Graphically represent and analyze a problem situation related to
projectile motion. Complete a laboratory report that includes the proper
use of significant figures and error analysis. (P.2H, P.2J, P.2K; P.4B,
P.4C)
1C; 5B, 5G
1. View the video: Project Projectile Full to introduce the activity, and if
needed, redistribute the Handout: Hit the Cup Project.
2. Allow students to practice with the materials but stipulate that tomorrow the
cup will be placed at a specified location and they must adapt to that
location. They will then be expected to hit the cup from their procedure and
calculations.
If possible, leave the equipment set up for tomorrow to save time.
Assist students with their equipment and in developing a procedure,
but inform them that they are expected to have the procedure in place
at the beginning of class.
Materials:
stand and clamps to hold projectile
ramp
marbles
projectile ramps (tubing)and tape to
hold them in place
meter stick
washer and string as plumb line
Attachments:
Video: Project Projectile Full
Handout: Rotation Equation and
Symbol Chart (1 per student)
Handout: Hit the Cup Project (1
per student)
Handout: Hit the Cup Project
Report
Teacher Resource: Hit the Cup
Teacher Guide
Instructional Notes:
©2012, TESCCC
06/13/12
page 15 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
Working rotational motion problems and
preparing for the “Hit the Cup” Project:
Reserve 20 minutes at the end of class
to prepare for the Hit the Cup project
performance which will take place
tomorrow.
It is assumed that the lecture
demonstration on uniform rotational
motion did not leave time to complete
the in-class problem set. The first part of
class is dedicated to completing
thoughts on that subject, allowing
students additional time to work the
problem set, and to discuss some of
those problems in class.
Project Projectile Full Video:
This brief introduction into rotational
kinematics will be helpful to understand
topics to be visited later and should not
be neglected. Adding these equations
and concepts to the equation sheet is
recommended. A separate Handout:
Rotation Equation and Symbol Chart
is included as an example.
The goal for the second half of class is
for the groups to do all that is necessary
to be successful in the hit the cup
“presentation” tomorrow.
EVALUATE – Hit the Cup
Suggested Days 12 and 13
1. This should be a fun day as student groups show off their skills.
2. Have each group take their opportunity with the “Hit the Cup” activity.
3. Instruct each student to complete a laboratory report over the “Hit the Cup”
activity.
4. Distribute copies of the Handout: Unit 03 Review to the students.
Materials:
stand and clamps (to hold projectile
ramp)
marbles
projectile ramps and tape (to hold in
place)
meter stick
washer and string (as plumb line)
stop watches
Attachments:
Handout: Unit 03 Review
Questions (1 per student)
Teacher Resource: Unit 03 Review
Questions KEY
Instructional Notes:
The room arrangements will dictate the
real conditions for the “presentations”,
but having each student group perform
©2012, TESCCC
06/13/12
page 16 of 17
Physics
HS/Science
Unit: 03 Lesson: 01
Instructional Procedures
Notes for Teacher
their project in an order determined by a
random draw is a possibility. Each
group could be given the target range
for their projectile and the materials. The
groups would be given 10–15 minutes
to perform calculations and prepare
their set up. Following this preparation
time, no further calculations or
adjustments would be allowed without
some penalty. The groups then perform
in rotation.
Suggestions for assigning range
distances and other elements of the
project are discussed in the Hit the Cup
Teacher Guide document.
©2012, TESCCC
06/13/12
page 17 of 17