Download Kinematics Assignment Sheet - Honors

Table of Contents
COURSE SYLLABUS & POLICIES ...................................................................................................1
KINEMATICS.......................................................................................................................................5
Kinematics Assignment Sheet..................................................................................................... 6-7
Graphing Fundamentals with a TI Calculator ..............................................................................8
Constant Speed vs. Constant Acceleration ...................................................................................10
Acceleration Due to Gravity .........................................................................................................15
Vector Field Trip ...........................................................................................................................20
Projectile Motion ...........................................................................................................................22
Projectile Motion at an Angle.......................................................................................................24
Kinematics Review Sheet ........................................................................................................ 25-27
DYNAMICS.........................................................................................................................................35
Dynamics Assignment Sheet..................................................................................................... 36-7
Gravitation Practice Problems......................................................................................................38
Newton’s Second Law ...................................................................................................................39
Newton’s Second Law - Revisited.................................................................................................43
Free Body Diagrams .....................................................................................................................46
Hooke’s Law..................................................................................................................................48
Friction And The Graphing Calculator .......................................................................................51
Torque and Static Equilibrium .....................................................................................................56
Centripetal Force ..........................................................................................................................58
Dynamics Review Sheet .......................................................................................................... 60-61
ENERGY, MOMENTUM, AND RELATIVITY ................................................................................68
Energy And Momentum Assignment Sheet ........................................................................... 69-70
Personal Power .............................................................................................................................71
Work and Energy ..........................................................................................................................73
Conservation of Energy ................................................................................................................77
Conservation of Momentum .........................................................................................................80
Model Rockets ...............................................................................................................................84
Energy, Momentum, and Relativity Review Sheet .......................................................................87
Mousetrap Racecar Project ..........................................................................................................89
APPENDIX A: UNIT CONVERSIONS ............................................................................................97
APPENDIX B: USEFUL INFORMATION ......................................................................................99
APPENDIX C: SECOND SEMESTER EQUATIONS ...................................................................100
Course Syllabus &
Hello! Welcome to physics! This year you will be introduced to the greatest of all the sciences, the
foundation upon which all other sciences are built. You will learn about some of the most influential and
significant ideas developed by humankind, empowering you to have a much better understanding of the
physical universe. In fact, a famous physicist named Ernest Rutherford once said “All science is either
physics or stamp collecting.” Regardless of natural talents in the sciences, or your penchant for art, or
literature, or something else, you will be expected to acquire fundamental knowledge and genuine
fondness of physics.
SYLLABUS
Fall Semester
1. Optics
A. Reflection & Mirrors
B. Refraction & Lenses
C. Optical Phenomena
D. Human Vision
2.
Waves
A. Wave Properties
B. Sound
C. Diffraction & Interference
D. Wave Phenomena
3.
Electricity
A. Static Electricity
B. Current Electricity
C. Electrical Circuits
Spring Semester
4. Kinematics
A. Motion in One Dimension
B. Motion in Two Dimensions
C. Relative Motion (Honors)
5.
Dynamics
A. Newton’s Law of Motion
B. Torque and Rotation
C. Circular Motion
D. Gravitation
6.
Energy, Momentum, and Relativity
A. Work and Energy
B. Impulse and Momentum
C. Conservation Laws
D. Special and General Relativity
PHYSICS LAB BOOK & OTHER MATERIALS
Every day you will need to bring:
• Your lab manual…this is a must…please make it a priority…it doesn’t weigh that much!
• A calculator with trigonometric functions (preferably a TI-84, or a low-cost TI-36)
• On quiz days it is recommended that you bring your textbook for homework review
GRADING
Grading is based on total accumulated points
within weighted categories. The categories
and percentages are as follows:
• Laboratory (25%)
• Homework (15%)
• Quizzes (20%)
• Midterm Exams (20%)
• Final Exam (20%)
The grading scale is shown below
A+
97%
C+
77%
A
93%
C
73%
A90%
C70%
B+
87%
D+
67%
B
83%
D
63%
B80%
D60%
F (0 credits) under 60%
Note: grades are NOT rounded up. For example, 89.5% is NOT rounded to an A-
1
HOMEWORK, QUIZZES, AND UNIT EXAMS
HOMEWORK is due weekly, usually on Tuesdays, from every student for the first unit. After that,
homework will be collected based on the grade leading into the next unit of study (about 6 weeks).
Students with a B (or lower) at the start of a new unit are required to turn in homework each week
for the entire unit. Students with a B+ (or higher) may opt to turn in homework each week, but are
not required to. After each unit this policy is repeated. In Honors Physics, this cutoff grade is an A–.
Homework problems will not be reviewed each day, following each assignment. Some of the
problems will be addressed each week, and additional review will occur the day of a quiz. However,
there will be a homework solution binder available in class to check your work at any time.
10% penalty per day for late homework. Do not make late homework a habit!
QUIZZES are a way to check to see if you have done your homework, including textbook reading
and problem solving, as well as lab analysis and questions. Typically there are about 4-5 multiplechoice problems and 2-3 computational problems to solve, showing all work for credit. Quizzes will
be given every other week and will cover all work from the previous two weeks, and may include
questions related to older topics.
MIDTERM EXAMS will occur at the end of each unit. The last unit of study in the semester will be
covered in a cumulative final exam, not a separate midterm exam. A review sheet will be provided
before each midterm exam. The review sheets are optional, but highly recommended.
All quizzes, midterm exams, and the final exam will be closed notebook, except for equation sheets.
TARDIES AND UNEXCUSED ABSENCES
Tardies and unexcused absences are very disrupting to the class and to a student’s learning. A tardy
is unexcused unless you bring a signed note from the Redwood staff member who caused the tardy.
Please make an effort to be on time and eliminate absences of any kind. Ask your parents to NOT
plan vacation time on school days. Also, college visits should be scheduled around a staff
development day so that students avoid absences.
TARDIES
Poor attendance will result in grade reduction for the semester grade according to the attendance
chart below.
0
1
2
3
4
5
6
7
8
9
10
11
12
0
0
0
0
0
0
0
-1/3
-1/3
-1/3
-2/3
-2/3
-2/3
-1
UNEXCUSED ABSENCES
1
2
3
0
-1/3
-2/3
0
-1/3
-2/3
0
-1/3
-2/3
-1/3
-2/3
-2/3
-1/3
-2/3
-2/3
-1/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-2/3
-1
-1
-1
4
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
5
-1*
-1*
-1*
-1*
-1*
-1*
-1*
-1*
-1*
-1*
-1*
-1*
-1*
* District policy: 5 unexcused absences will also result in loss of 1 credit
2
MAKE UP FOR ABSENCES
LABS: If you miss a lab, you must make it up at lunch, after school, or during office hours, but no
later than SMART period the following week. You cannot just get data from a friend, and expect to
get credit for the lab. In fact, you need to bring a friend in with you so that you have a lab partner to
help explain the procedure and use the equipment to collect data. When the lab is completed, it is
your responsibility to show me the results in order to receive a grade.
QUIZZES: If you miss a quiz your only opportunity to take it will be before the quizzes are returned
to other students, which means you have no more than two days. A quiz given on a Tuesday is
usually returned by Friday. Smart period is often the best time for a quiz makeup.
If you do not make up a quiz, it will be marked as “missing” in the grade book, which will result in
zero points for that grade until the end of the unit, when the midterm exam score for the unit will
replace your missing quiz. This is NOT a good idea, so avoid if possible.
MIDTERM EXAMS: If you miss a midterm exam please email immediately ([email protected]) to
explain your absence and to arrange a make-up exam. There are only two midterms (and a final) per
semester, so missing any one of these days is highly unusual and requires a confirmed and legitimate
excused absence involving a discussion with me and your parents.
Missed work caused by extended absences (more than three school days) for extreme sickness or
trauma will be handled on an individual basis.
Please realize that poor attendance will have a negative effect on your understanding of physics,
and on your semester grade.
BEHAVIOR AND CLASS RULES
In the physics classroom, you should feel comfortable, positive, and enthusiastic. You are expected
to work diligently, conscientiously, and consistently, at all times. A few comments about
student/teacher respect and rules about classroom behavior will soon be discussed during class.
Food and drinks in the classroom are tolerated with three simple rules that apply: 1) it must not be a
distraction to other students, 2) you must clean up and recycle when finished, and 3) if it looks tasty
I get a bite - often called the “Nash tax”!
Bathroom breaks are tolerated with three simple rules that apply: 1) you must ask me first - try to be
subtle and not interrupt the class, 2) you must leave your cell phone behind - bathroom breaks are
not text-messaging breaks! and 3) use of the bathroom must not be excessive, daily occurrence.
Cell phones must be off and away during class. Please turn your cell phone off before you come to
class. Per school policy, the teacher has the right to confiscate your cell phone if it rings in class.
Expect only one warning, and then it will be taken away.
LABORATORY WORK AND LAB ASSESSMENTS
Each week the rubric on the following page will be used for lab assessment. This rubric has four
areas of evaluation. Each area has a value up to five points for a total of 20 points. Generally, each
lab group earns one group grade so choose your lab partners wisely. If a lab partner does
considerably less than the others, that student will receive fewer points.
This lab rubric is designed to minimize the busy work that is sometimes associated with doing labs
in a science class. Physics labs require very little copying of information. Most time is spent
analyzing data - often with a calculator, interpreting results, and answering relevant questions.
It may take some time for you to get used to the way labs are graded, but soon you will be
accustomed to this “real time grading”. You’ll quickly discover that labs are the best way to learn
physics, and also the easiest way to improve your overall class grade. And remember, best of all, you
will not have to turn in any lab reports in this class!
3
LAB REPORT
LAB TECHNIQUES
USE OF TIME
AND CLEANUP
LISTENING TO
INSTRUCTIONS
LAB GRADING RUBRIC
5
4
• Group needs no
supervision after the initial
lab instructions are given.
• Each partner can
articulate the goal of the
lab and can explain the
rationale for the proposed
lab procedure.
• Lab partners ask
coherent and relevant
questions that often lead to
improvements in the lab.
• Group needs minor
clarification after having
moved to the lab area.
• The group, as a whole,
needs minor help
articulating the goal of the
lab and/or explaining the
rationale for the lab
procedure.
• Lab partners sometimes
ask coherent and relevant
questions.
3
• Group needs major
clarification after having
moved to the lab area.
• One or more partners
can articulate the goal of
the lab and explain the
rationale for the lab
procedure, but one or
more partners is slightly
confused.
• Lab partners sometimes
ask illogical or redundant
questions.
• Each partner works
• Some partners work
• One partner does most
equally on the data
harder than others on the
of the work on the lab.
collection and analysis.
lab.
• There is major
• There is no unnecessary • There is minor
socializing within the
socializing within or
unnecessary socializing
group or between groups,
between groups.
within the group, which
which detracts from the
• When finished, each
detracts from the lab
lab experience.
partner is working on
experience.
• When finished, one or
physics until the bell rings. • When finished, each
more partners stop
• All lab areas are clean
partner is working on
working on physics
and all equipment is
physics until the bell rings. before the bell rings.
replaced as directed so that • Not all lab areas are
• Most lab areas are not
it is ready for the next
clean or all equipment not clean and not all
class lab.
replaced.
equipment is replaced.
• All lab stools are put
• Some lab stools are put • Lab stools are not put
back under the lab desks.
back under the lab desks.
back under the lab desks.
• Data collection
• Data collection
• Data collection
techniques by the group
techniques lead to slightly techniques lead to
lead to exceptionally
inaccurate or imprecise
considerably inaccurate
precise and accurate data. data.
or imprecise data.
• Follows all directions
• Follows most directions • Follows most directions
for data collection.
for data collection.
for data collection.
• Always implements
• Makes an effort to avoid • Makes some effort to
techniques to avoid
most experimental error.
avoid experimental error.
experimental error.
• A graphing calculator is • A graphing calculator
• A graphing calculator is used often to minimize
is used occasionally to
used whenever possible to rounding errors.
minimize rounding errors.
minimize rounding errors.
• Presentation is neat,
• Presentation is mostly
• Presentation is
sequential, and clear, using neat, sequential, and clear somewhat neat,
only pencil
using only pencil
sequential, and clear.
• Calculations, and lab
• Calculations, and lab
• Calculations, and lab
analysis, and questions are analysis, and questions are analysis, and questions
all complete and detailed. mostly complete with
are somewhat complete
• All measurements and
most details.
with some details.
results are presented with
• Most measurements and • Some measurements
appropriate variables and
results are presented with and results are presented
units.
appropriate variables and
with appropriate variables
• All data tables, graphs,
units.
and units.
drawings, etc. are
• Data tables, graphs,
• Some data tables,
completed.
drawings, etc. are nearly
graphs, drawings, etc. are
completed.
incomplete.
4
2
• Group needs lab reexplained after having
moved to the lab area.
• One or more partners
can articulate the goal of
the lab and explain the
rationale for the lab
procedure, but one or
more partners has major
confusion.
• Lab partners ask only
illogical or redundant
questions.
• One partner does all of
the work on the lab.
• There is major
socializing within the
group or between groups,
which detracts from the
lab experience.
• When finished, all
partners stop working on
physics before the bell
rings.
• Not all lab areas are
clean and all equipment
is not replaced.
• Lab stools are not put
back under the lab desks.
• Data collection
techniques lead to
drastically inaccurate and
imprecise data.
• Ignores most directions
for data collection.
• Makes little effort to
avoid experimental error.
• A graphing calculator
is used rarely to minimize
rounding errors.
• Presentation is not at
all neat, sequential, and
clear.
• Calculations, and lab
analysis, and questions
are mostly incomplete
with few details.
• Few measurements and
results are presented with
appropriate variables and
units.
• Most data tables,
graphs, drawings, etc. are
incomplete.
Kinematics
“All science is either physics or stamp collecting.”
– ERNEST RUTHERFORD
“Common sense is nothing more than a deposit of prejudices laid
down by the mind before you reach eighteen.”
– ALBERT EINSTEIN
5
Kinematics Assignment Sheet
Online: www.physicsclassroom.com/Physics-Tutorial/1-D-Kinematics (Assignments 1-8)
www.physicsclassroom.com/class/vectors (Assignments 9-15)
No.
Topics
Reading
Homework
1
displacement, speed, average
velocity
40-44
Ch 2: 6,9,11,13
2
instantaneous velocity,
position vs. time graphs
45-47
Ch 2: 2,3,4,10,14
3
average acceleration,
instantaneous acceleration
48-51
Ch 2: 17,19,30,54
4
kinematic equations with constant
acceleration
51-58
Ch 2: 23,24,25,29
5
additional constant acceleration
problem solving
Ch 2: Sec Rev pg 59
1,2,3,4
6
additional constant acceleration
problem solving
Ch 2: 26,28,31,32
7
falling objects,
freefall acceleration
8
more freefall acceleration
problem solving
9
scalars and vectors, properties of
vectors, graphical addition
84-87
Ch 3: 3,7,8,12
10
vector operations, vector
components, analytical addition
88-97
Ch 3: 16,22,23,26,28
11
projectile motion (horizontally
launched projectiles)
98-101
Ch 3: 31,34,36,37
12
projectile motion (projectiles
launched at an angle)
102-104 Ch 3: 35,38,39,41
13
more projectile problem solving
Ch 3: 33,56,58,69
14
projectile review problems
Pg 104: P 1,3
Pg 118-9: P 61,67
15
relative velocity, frames of
reference
60-64
Ch 2: 34,38,39,49
Ch 2: 36,46,48,55
106-109
6
no assignment
Kinematics Assignment Sheet - Honors
Online: www.physicsclassroom.com/Physics-Tutorial/1-D-Kinematics (Assignments 1-8)
www.physicsclassroom.com/class/vectors (Assignments 9-15)
No.
Topics
Reading
Homework
1
displacement, speed, average
velocity
2-1
2-2
Q1
P 5,9,10,11
2
instantaneous velocity,
position vs. time graphs
2-3
2-8
Q 3,4
P 50,51,56abde
3
velocity vs. time graphs, average and
instantaneous acceleration
2-4
Q 5,8
P 17,18,49,55
4
kinematic equations with constant
acceleration
2-5
Q 10
P 19,21,22,26,27
5
additional constant acceleration
problem solving
2-6
Q 11
P 28,63,74,77
6
additional constant acceleration
problem solving
7
falling objects,
freefall acceleration
8
more freefall acceleration problem
solving
9
scalars and vectors, properties of
vectors, graphical addition
3-1
3-2
Q 1,6
P 3,5,13(graphically)
10
vector operations, vector
components, analytical addition
3-3
3-4
Q7
P 1,7,10,12
11
projectile motion (horizontally
launched projectiles)
(to pg 57)
12
projectile motion (projectiles
launched at an angle)
(to pg 61)
3-6
Q 20
P 19,20,24,26
13
more projectile problem solving
3-7
P 62,67,69,70
14
relative velocity, frames of reference
3-8
Q 13
P 37,39,41,42,49
15
review problems
Q9
P 31,32,68,73
2-7
Q 13
P 34,35,37,39
Q 14
P 42,44,45,78,79
3-5&3-6
Q 18
P 18,21,27,31,64
Ch 2: 75,83,85
Ch 3: 53,58,65
7
Graphing Fundamentals with a TI Calculator
PURPOSE
To learn about graphing by hand and also using the TI Graphing Calculator.
To understand the nature of constant speed, average speed, and instantaneous speed.
PROCEDURE
In physics the best way to see patterns and relationships is through graphing the data collected in an
experiment. This is true in the following lab which is designed to help you learn to graph variables,
and help you interpret the meanings of graphs. Follow the directions below in for all graphs.
1. Determine axis variables.
2. Label axes with variable and unit.
3. Title the graph.
4. Establish axis scales (stretch data out.)
5. Plot points in pencil.
6. Draw best fit. Don't "connect the dots"!
DATA & ANALYSIS
1. The table of data below
represents the motion of a toy
car for five seconds of time.
Follow the above steps 1-6 to
create a completed graph.
Toy Car (5 sec)
t (s)
d (cm)
0
0
1.0
190
2.0
395
3.0
605
4.0
810
5.0
1040
2. Enter the data into List
columns in the graphing
calculator by pressing STAT,
then ENTER; put time data
into L1 and distance into L2.
3. Press STAT PLOT (2nd button, then Y= button) and turn Plot 1 on, set to scatter plot, with Xlist
to L1 and Ylist to L2. Press GRAPH, then ZOOM, then 9:ZoomStat to fit data into the display.
4. Press STAT, then move cursor to CALC, then 4: LinReg, then check Xlist:L1, and Ylist:L2, and
Store RegEQ: Y1 (to get Y1 press VARS, then move cursor to Y-VARS, then press 1:Function,
then 1:Y1 and finally ENTER. Press GRAPH to see the curve fit on this equation. (on the TI-83
is has to look like this on the screen – LinReg L1,L2,Y1).
5. Write the equation for the best-fit line below. Use variables for distance (d) and time (t).
6. The toy car moves with nearly constant speed. What is the value, with units, of the speed?
8
7. The table of data below represents
the motion of the same toy car as
before, but now for just the first
half-second of time as it speeds up
from rest. Follow the steps, as
before, to create a graph, including
drawing a best-fit curve.
Toy Car (0.5 sec)
t (s)
d (mm)
0
0
0.10
25
0.20
75
0.30
175
0.40
325
0.50
500
8. Calculate the average speed of the
toy car between 0.1 sec and 0.5
sec. Average speed is distance
traveled divided by time elapsed.
9. Draw with a ruler a line between the data points at 0.1 sec and 0.5 sec. This line is now a secant
line to the best-fit curve. What does the slope of this line tell you?
10. Calculate instantaneous speed of the toy car at 0.25 sec. First draw with a ruler a tangent line to
the best-fit curve at 0.25 sec; then find the slope of the line using two points on the tangent line.
Show work.
11. Now find the instantaneous speed using the graphing calculator. Follow steps 2-4 from the last
page, but this time fit the data with QuadReg since the data nearly fits a quadratic function. Write
this quadratic equation below, with proper variables
12. Next press GRAPH, then DRAW (2nd PRGM) then 5: Tangent. Enter .25 for the time t = 0.25 s.
Press ENTER. The calculator draws the tangent and displays the equation in y = mx + b form,
where m is the slope. Write this linear tangent equation below, with proper variables.
12. Calculate the percent error between the experimental (step 10) and the known (step 11).
9
Constant Speed vs. Constant Acceleration
PURPOSE
To use graphical methods with distance and time data to analyze two types of motion: constant speed
and constant acceleration.
EQUIPMENT
- dynamics track
- dynamics cart
- ticker tape timer
- scotch tape
- meter stick, rulers
- support rod & stand
PROCEDURE
PART A - CONSTANT SPEED
1. Check that the dynamics track is level. If it is not, adjust the leveling screw underneath one end
of the dynamics track and check for level again. See diagram below.
2. Feed one end of a 1-meter long piece of ticker tape through a ticker tape timer. The ticker tape
goes through the metal brackets, over the carbon, and under the metal strike plate.
3. Use scotch tape to attach the end of ticker tape to the back end of a dynamics cart.
4. Set the plunger on the dynamics cart in 2 clicks. It works best if you press it in and slightly
upwards at the same time so the spring is set correctly. Do a “dry run” to see if the cart will make
it across the track with constant speed. Tap the plunger release with the metal block. If the cart
slows down noticeably, set the plunger to 3 clicks and do another trial to check for constant
speed.
5. Now it’s time to collect data! Turn on the ticker tape timer to the 40 Hz setting and then tap the
plunger release lightly with the metal block. This takes a little practice and coordination. Don’t
tap the release until the timer starts ticking.
ticker tape
timer
plunger
plunger
release
dynamics cart
dynamics track
leveling screw
ticker tape
end stop
metal block
DATA & ANALYSIS
1. Remove the ticker tape from the dynamics track and scotch tape it to the lab table. Circle the dot
that represents the starting time (t = 0) where the dots begin uniform spacing. Ignore any dots
before the circled dot. See diagram below.
2. The timer records 40 dots every second. Mark off every four spaces on your tape. These marks
will represent time increments of tenths of seconds. Again, see diagram below.
3. With the meter stick, measure the distances from the circled dot (t = 0) to each of the marks on
your tape. These will represent the total distance covered at the end of each tenth of a second.
Measure each distance to the nearest 0.1 centimeters.
Sample Ticker Tape
d1
d2
10
4. Record the data in the table below. The data may not fit the table exactly.
5. Save the ticker tape. You may need it to check for mistakes.
6. Make a graph of distance vs. time below. Draw with a ruler a best-fit line for the data points.
t (s)
0
d (cm)
0
QUESTIONS & CALCULATIONS
1. Calculate the constant speed of the cart as it moves across the dynamics track. Use the graphing
calculator to do this, and refer to the “Graphing Fundamentals With a TI Calculator” activity.
Write the equation for the best-fit line below. Use variables for distance (d) and time (t).
11
PART B - CONSTANT ACCELERATION
1. In this part you will make the dynamics cart roll down an inclined track. Attach the dynamics
track to the support rod using the metal clamp. Raise the left end of the track so that the bottom
of the track is about 15 cm above the table. See diagram below.
ticker tape
timer
dynamics cart
dynamics track
end stop
ticker tape
2. Feed the ticker tape through tape timer and attach it to dynamics track, as it PART I.
3. Turn on the ticker tape timer to the 40 Hz setting and then immediately release the dynamics
cart. The spring plunger is NOT used here. Don’t start the timer late!
DATA & ANALYSIS
1. Remove the ticker tape from the dynamics track and scotch tape it to the lab table. Circle the dot
that represents the starting time (t = 0) where the dots clearly begin to get further apart. Ignore
any dots before the circled dot. See diagram below.
2. The timer records 40 dots every second. Mark off every four spaces on your tape. These marks
will represent time increments of tenths of seconds.
3. With the meter stick, measure the distances from the circled dot (t = 0) to each of the marks on
your tape. These will represent the total distance covered at the end of each tenth of a second.
d1
d2
4. Record the data in the table below. The data may not fit the table exactly.
5. Save both pieces of ticker tape. You may need them to check for mistakes.
6. Make a graph of distance vs. time. Draw a best-fit curve for the data points.
7. Use the graphing calculator to enter and analyze this new data, referring again to the “Graphing
Fundamentals With a TI Calculator” activity.
12
t (s)
0
d
(cm)
0
Write the best fit quadratic equation below, with appropriate variables for distance and time.
13
QUESTIONS & CALCULATIONS (these refer to the curved graph on previous page)
Show all work and evidence for answers
1. Calculate the average speed of the cart for the entire time it moves down the ramp. On the graph,
lightly draw with a ruler the secant line showing how you determined this average speed.
2. Calculate the average speed of the cart for the final 0.3 seconds of its motion. You do not need to
draw the secant line showing how you determined this average speed.
3. Calculate the experimental instantaneous speed of the cart when it is halfway down the ramp in
terms of time elapsed. That is, if your last recorded time is 1.4 s, then find the instantaneous
speed at 0.7 seconds. On the graph, lightly draw with a ruler the tangent line that shows how you
determined this instantaneous speed.
4. Use the graphing calculator to draw the tangent line for determining the known instantaneous
speed, again referring to the “Graphing Fundamentals With a TI Calculator” activity. Find the
percent error between the known and experimental values.
5. Honors Only: Calculate the instantaneous speed of the cart when it is half the recorded distance
down the ramp (not necessarily the midpoint of the dynamics track). Lightly sketch the tangent
line that shows how you determined this instantaneous speed. (Think about why this question has
a different answer from the previous question.)
14
Acceleration Due to Gravity
PURPOSE
The purpose of this experiment is to investigate the
nature acceleration due to gravity and determine the
position, velocity, and acceleration of an object in
freefall.
EQUIPMENT
- tape timer
- ticker tape
Direction
of motion
Paper tape
(held by hand)
Tape timer
(held by hand)
- meter stick
- scotch tape
- 200 gram mass
PROCEDURE
1. Cut a piece of paper ticker tape about 2 meters
long. Make a loop with one end of the ticker
tape by folding it over and securing it with a
piece of masking tape. Hook the 200 g mass on
the loop end of the paper tape.
PASCO
TAPE
TIMER
40
10
Hooked
mass
2. Thread the other end of the paper ticker tape through the Tape Timer until the mass is at the level
of the Timer.
3. Hold the Tape Timer about 2 meters off the ground by standing on the lab tables. Align the Tape
Timer on its side so the tape passes through the Tape Timer vertically.
4. Hold the paper ticker tape so it can easily thread itself through the Tape Timer. This is best
accomplished by having one partner hold the Tape Timer while the other partner holds the tape
above the timer.
5. Turn on the Tape Timer to 40 Hz and drop the tape, allowing the mass to fall. The 40 Hz setting
means that a dot will be marked on the ticket tape every 40th of a second.
6. Tape the paper ticker tape to a lab table. Identify and circle the first dot where freefall begins,
that is, where zero time has elapsed. If you had very steady hands when performing the freefall
this dot will be the very first one on the ticker tape. If you’re hands were shaky, the first true
freefall dot may not be obvious. Ask for help if needed.
7. Now circle every fourth dot from the first dot. The time elapsed between these circled dots is 0.1
(one-tenth) second. Check for accuracy by noting that the second circled dot is at least 3.5 cm
but no more than 6.5 cm from the first circled dot. (A typical position at time t = 0.1 seconds is
5.0 cm.)
8. Measure the positions of these circled dots to the nearest millimeter and record the data in Table
1. Remember that each dot’s position is measured from the first circled dot. All positions are
negative! (Why?)
15
DATA & ANALYSIS
Position versus Time
1. Make a pencil and paper graph below of position vs. time for the
freefalling mass. This is a graph in the fourth quadrant of an x-y
plane. Why? Draw a best-fit curve for these data points. Don’t
connect the dots. Sketch a curve that represents the data well.
2. Enter position data into a table on the TI Graphing Calculator
First clear existing data in calculator’s List columns by pressing
STAT, then 5:SetUpEditor, and then ENTER. Next enter your new
lab data. Press STAT, then ENTER. The independent variable goes
into the first column L1, the dependent variable into the second
column, L2. The point (0,0) is entered as the first data point.
Table 1
Time
(sec)
Position
(cm)
0
0
3. Graph the data from the table on the TI Graphing Calculator
Press STAT PLOT (2nd button, then Y= button) and turn Plot 1 on,
set to scatter plot, with Xlist to L1 and Ylist to L2. Press ZOOM,
then 9:ZoomStat. This should automatically fit the data onto the
WINDOW and display the graph. What does the data look like?
What function might fit that data?
4. Fit a curve to your graphed data on the TI Graphing Calculator
Press STAT, then move the cursor to CALC, then 5: QuadReg, then check Xlist:L1, and Ylist:L2, and Store
RegEQ: Y1 (to get Y1 press VARS, then move cursor to Y-VARS, then press 1:Function, then 1:Y1 and
finally ENTER. Press GRAPH to see the curve fit on this equation.
(Note: on the TI-83, after 5: QuadReg it has to look like this: LinReg L1,L2,Y1)
5. Write the equation for the best-fit curve on the graph in your lab manual. Use appropriate variables for
vertical position (y) and time (t).
best fit equation:
16
Velocity versus Time
1. Now we must calculate the instantaneous velocity of the freefalling mass at various points in time. Recall
that the slope of a tangent line to the curve on a position graph is the instantaneous velocity at that point
in time. We’ll use the TI graphing calculator to find the slope of a tangent line at each 0.1-second interval.
To avoid rounding errors, record the instantaneous velocities to four significant figures and use all four
significant figures in further steps.
2. Find slopes of tangent lines to your best-fit position curve
While viewing the GRAPH window, press DRAW (2nd PGRM),
then 5: Tangent. Type in 0.1 for the first time t = 0.1 Press ENTER.
The calculator draws the tangent and displays the equation for the
line in y = mx + b form, where m is the slope. Repeat for each 0.1 s
interval and record all instantaneous velocities in Table 2.
3. Make a graph below of velocity vs. time for the freefalling mass.
Use a clear ruler to draw a best-fit line for these data points.
4. Enter velocity data into a table on the TI Graphing Calculator
Press STAT, then ENTER, and put the values for velocities into L3.
Press STAT PLOT and turn on Plot 2, set Xlist to L1 and Ylist to L3.
Repeat the steps you used for position graphing, but now fit a line to
your velocity data using STAT → CALC, 4: LinReg, then L1,L3,Y1.
5. Write the equation for the best-fit line on the graph in your lab
manual. Use appropriate variables for velocity and time.
best fit equation:
17
Table 2
Time
(sec)
Inst. Vel
(cm/s)
0
0
QUESTIONS & CALCULATIONS
1. From your velocity vs. time best fit equation, determine the acceleration of the freefalling 200
gram mass (recall that acceleration is the slope of a velocity vs. time graph.) This acceleration
due to gravity is so special in physics that it is given its own letter, “g”. Write down below your
experimentally determined value for g with units of cm/s2.
2. Convert your value for g to units of m/s2. Show the correct unit analysis.
3. How does your experimental value of g compare with the theoretical (known) value of g?
To compare, find the percent error between the your experimental value with the known value of
-9.80 m/s2. Use the percent error formula shown below to calculate the error.
Known-Experimental
Percent Error =
× 100%
Known
4. Why do students performing this lab typically find an experimental value for the acceleration due
to gravity that is lower (in magnitude) than the accepted (known) value of - 9.8 m/s2? There are
several good reasons that mostly center around one key idea.
5. Honors Only: Velocity graphs can be used to find acceleration (see above), but they can also be
used to find information about position. Recall that the area under a velocity vs. time graph
determines an object’s change in position during that time interval. From your velocity versus
time graph find the area above the line up to the last time measured. How does this compare with
the final position measured from the ticker tape? Show all work.
18
6. Galileo was the first to quantitatively analyze the acceleration due to gravity. Unfortunately, the
only timing devices he had available were things like an hourglass or a simple pendulum. This
made it difficult to measure the position or the velocity of a freefalling object. Do some quick
textbook or internet research and find out how Galileo was able to ingeniously “dilute” or “slow
down” gravity in order to collect lab data. Briefly describe what you learned below.
7. A device that measures acceleration due to gravity (or any other kind of acceleration) is called an
accelerometer. Do some quick textbook or internet research to find out how accelerometers are
used in a practical ways by scientists and engineers. Briefly describe what you learned below.
19
Vector Field Trip
PURPOSE
To add displacement vectors and determine a resultant vector using graphical methods
PROCEDURE
1. In groups of two or three, learn to use a compass to find a bearing.
2. Establish one partner as a walker, and count steps for walking the length of the lunch plaza from
the first square tree planter to the last square tree planter (a total of seven, not the eight near the
building.) Walk this length twice for accuracy. This distance has been carefully measured with a
long tape measure, and it is 140.5 feet. It will be used later to convert steps to meters.
3. From a starting position at the lunch plaza - where the Redwood Tree is painted on the bricks outside the exit doors to the South Lawn, walk in straight displacement vectors, being careful to
take an accurate bearing and count your exact number of steps. You must stay on the asphalt path
around the South Lawn, moving in a counterclockwise direction, ending up at the CEA doors.
4. Take the first vector bearing and walk the first vector length. Record the data in the table.
5. Continue walking straight-line displacement vectors until you reach the double doors of the
CEA, being sure to record the data for each displacement vector.
DATA & ANALYSIS
1. Using a TI Graphing Calculator, press STAT then ENTER. Clear out the first three columns: L1,
L2, and L3. (If columns are missing press STAT 5:SetUpEditor, ENTER.) Type in column L1 the
length, in steps, of your vectors.
2. Using data in Appendix B, calculate the ratio of meters per step in the space below, and then use
this conversion in L2 to convert steps into meters. Record the distances in the table below.
3. Now scale the distance column, so that the vectors can be drawn on a computer to fit on a sheet
of 8.5” X 11” paper. A good scale is 5 meter = 1 centimeters. Convert your vector distance (m)
to a scaled distance (cm) on the calculator, using column L3. Record the scaled distances in the
table below.
_____________ steps to walk the lunch plaza, which is 140.5 feet
Bearing (degrees)
Length (# of Steps)
Distance (m)
20
Scaled Distance (cm)
4. Create a scale drawing of your vector walk. Each student must complete their own drawing and
turn it in for grading. You can use Microsoft Word, PowerPoint, or any other software you want,
or you can even do the drawing with pencil and paper. All drawings must have the following:
a. Show the proper axes for bearing angle. This means showing a north-south vertical axis and
an east-west horizontal axis somewhere on the page. (You can import a graphic easily if you
type “compass” or “compass with degrees” into an image search on the computer.)
b. Draw each vector to scale, and show each vector in order of the vector walk, using “head to
tail” addition. If you are using a computer each vector can be drawn as a line with an
arrowhead, usually found as a Shape under the Insert menu. To “nudge” the vectors until
they are head to tail use the cursor arrows, holding Option (Mac) or Ctrl (PC) for precision.
c. Label each vector with magnitude in meters and direction in degrees. For example, your first
vector should be something like this: 18.2 m, 167˚.
d. Show a sample conversion of one of your displacement vectors - from steps to meters, and
then meters to scaled centimeters.
e. Draw the resultant vector, from the tail of the first vector (where you started on the bricks) to
the head of the last vector (where you ended at the CEA doors.) Make this resultant vector in
bold, or a different color, to show it is not just another displacement vector from the data.
f. Determine the magnitude and direction of your resultant vector. This can be measured with a
ruler and protractor, or determined analytically if you used a computer by finding out the
height and width of the resultant vector.
g. Calculate the percent error between your vector’s magnitude and the known magnitude,
which will be given in class. Next, determine the percent error between your vector’s
direction and the known direction, which will be given in class.
5. Print two copies of your vector drawing: one for your lab manual and one to turn in for a grade.
It should look like the drawing below, but with all vectors labeled, conversion and errors shown.
21
Projectile Motion
PURPOSE
To understand the nature of projectile motion and to predict the landing spot for a horizontally
launched object.
EQUIPMENT
- photogate timer with accessory photogate
- steel ball, metal ramp and clamp
- plumb bob
- meter stick
photogates
PROCEDURE
1. Measure the distance between the photogates (centerline to centerline), in meters. It's best to
measure this distance at the bottom of the two photogates, where the ball rolls through. Also,
measure once from each side of the photogates to be sure they are parallel to each other. Record
the distance, in meters, in the table.
2. Measure the height, in meters of the lab table. Record the height in the table.
3. Set the photogate timer to PULSE mode. This will measure the time elapsed as an object passes
between the photogates. This allows the photogate timer to show 4 significant figures instead of
three. The time displayed is in seconds.
4. Roll the steel ball from the top of the ramp, across the lab table, and through the photogates. Do
not let the ball land on the floor. Your peers will catch you if you do!
5. Record the time measured by the photogates in the table below. Repeat four more times, or more
if you have to discard any outliers. Don’t change the photogate locations!
Distance between photogates: ___________
Height of lab table: ___________
time through
photogates
average
time
DATA & ANALYSIS
1. Calculate the average speed of the ball through the photogates. This will determine the horizontal
velocity (vx) of the marble when it leaves the table.
2. Calculate the time of flight (t) for the steel ball. Hint: use an equation for vertical motion.
22
3. Calculate the horizontal displacement (Δx) of the steel ball when it lands on the ground.
4. Use the plumb bob to find the point on the floor that is directly below the launch point. Use a
pencil to mark this point on the floor. Then locate and mark the predicted landing point on the
floor. Draw a large x-y axis at this landing point to align the target sheet.
5. After you have shown me the correct calculations it will be your turn to compete! Score up to 20
points on the total of two tries.
6. Clean up! Erase the pencil marks, turn off and unplug the photogates, and return the steel ball to
the lab table.
QUESTIONS & CALCULATIONS
1. Describe and explain the horizontal and vertical motion of the steel ball while it is in the air. Be
specific and use mathematical expressions.
2. If you are standing near the edge of a cliff how can you determine the height of the cliff using a
rock and a stopwatch?
3. Is the method you described in Question 2 always accurate in a real application? If yes, explain
why. If no, explain the inaccuracy. Be specific.
23
Projectile Motion at an Angle
PURPOSE
To use the equations of motion and the ideas of
projectile motion to predict the range of a steel
marble projected at an angle above the horizontal.
EQUIPMENT
- projectile launcher, marble
- white paper, carbon paper
- plumb bob
- meter sticks
PROCEDURE
1. Set the projectile launcher to zero degrees so
that it is horizontal to the ground.
2. Use the plumb bob to find the point on the floor that is directly below the launch point. Use a
pencil to mark this point on the floor. Circle the point so it is clearly visible.
3. Measure the height, in meters, of the ball at launch point. Measure from the floor to the bottom
of the marble, ignoring the launch position marked on the side of the launcher.
Height of ball at launch (m) ___________
4. Use the ramrod to load the steel marble to the middle setting (2 out of 3 “clicks”). Be sure one
lab partner is in position to “field” the marble after it lands so the marble is not lost.
5. Launch the marble and note carefully where it landed. Look at the tiles on the floor and check to
see that the marble is going straight, and not off to one side. If needed, pivot the projectile
launcher to adjust the aim so it will launch straight, but don’t loosen the clamp.
6. Tape a piece of paper to the floor centered where the marble landed, and then place a half sheet
of carbon paper (dark side down) on top of the paper. (Don’t tape the carbon paper to the floor.)
7. Launch the marble five times onto the carbon paper.
8. Measure the horizontal range, in meters, for each trial and record the results in the table.
Horizontal Range
of Marble, Δx (m)
average:
DATA & ANALYSIS (Show general equations, substitutions, calculations, and units.)
1. Using the height of the launcher, the initial vertical velocity, gravity, and the appropriate
equation of projectile motion, calculate the time of flight for the projectile.
2. Using the time of flight, and the average horizontal range, calculate the launch velocity of the
marble.
24
Now that you know the launch velocity of the marble you can use
this information to launch the marble at any angle and predict the
time of flight and range of the projectile. Use a 70˚ angle.
3. Calculate the horizontal and vertical components of the
marble’s velocity when it is fired at 70˚ above horizontal.
Remember that the launch velocity that you found in the
previous calculation is now the hypotenuse of a right
triangle trigonometry problem.
4. Using the height of the launcher, the initial vertical velocity (not zero now), gravity, and the
appropriate equation of projectile motion, calculate the time of flight for the projectile at a 70˚
angle. This will require using the quadratic formula to solve a quadratic equation.
5. Using the time of flight, and the horizontal velocity component, calculate the range (horizontal
displacement) of the marble.
6. Because air resistance affects path of the projectile, in this lab let’s try to account for it with a
simple approximation. Assume that the actual range is 96% of the theoretical range. Show the
calculation below. Use answer to mark the target clearly on the floor.
7. OK, time to test your physics! After you have shown me the correct calculations it will be your
turn to compete! Score up to 20 points on the total of two tries.
8. Clean up: set the launcher back to 0 degrees, place the ramrod and marble on the launcher,
replace the paper, recycle used paper, set the plumb bob on the carbon/paper.
25
QUESTIONS & CALCULATIONS
1. Continuing with the data from the lab, calculate the time it takes for the projectile to achieve
maximum altitude, when launched at a 70˚ angle.
2. Calculate the maximum altitude above the floor for the projectile, when launched at a 70˚ angle.
3. Calculate the horizontal distance to where the projectile’s altitude is at a maximum, when
launched at a 70˚ angle.
4. What accounts for the errors in this lab? Why are the results of this lab less accurate and less
precise than in the last lab?
26
Kinematics Review Sheet
Multiple choice. Circle the best answer.
1. Consider the position vs.
time graph on the right. At
which lettered point or
points is the object a)
moving the fastest?
b) moving to the left?
c) speeding up? d) slowing
down? e) turning around?
2.
3.
4.
5.
10. A penny is dropped near the surface of the earth and
freefalls without any air resistance. After 1 second the
displacement and the velocity of the penny are
(A) -4.9 m, -4.9 m/s
(C) -4.9 m, -9.8 m/s
(B) -9.8 m, -4.9 m/s
(D) -9.8 m, -9.8 m/s
11. A rock falls from rest 0.72 m down near the surface of a
planet in 0.63 s. The planet’s acceleration due to gravity
is
(A) -1.1 m/ s2
(C) -3.6 m/s2
2
(B) -2.3 m/s
(D) -9.8 m/s2
Consider the
velocity vs. time
graph on the right.
During which
segment(s) is the
object a) moving
with constant
velocity?
b) speeding up? c)
slowing down? d)
standing still? e) moving to the right
12. Two vectors having magnitudes of 5 and 8 cannot have a
resultant with a magnitude of
(A) 3
(C) 13
(B) 7
(D) 15
On a highway, a car is driven 80 km/h during the first 1.0
hour of travel, 50 km/h during the next 0.5 hour, and 40
km/h in the final 0.5 hour. What is the car’s average
speed for the entire trip?
(A) 45 km/h
(C) 85 km/h
(B) 62.5 km/h
(D) 170 km/h
As a car is driven south in a straight line with decreasing
speed, the acceleration of the car must be
(A) directed northward
(C) zero
(B) directed southward
(D) constant, but not zero
A race car starting from rest accelerates uniformly at a
rate of 4.9 m/s2. What is the car’s speed after it has
traveled 200 m?
(A) 1960 m/s
(C) 44.3 m/s
(B) 62.6 m/s
(D) 31.3 m/s
.
6.
Velocity is to speed as displacement is to
(A) acceleration
(C) momentum
(B) time
(D) distance
For the next three questions consider the graph
below, which shows the motion of three cars.
Car A
v(m/s)
15
Car B
10
Car C
5
10
20
30
40
t(s)
7.
(Honors only) From 0 s to 20 s, which car has
been displaced the most?
(A) car A
(B) car B
(C) car C
8.
At 30 s which car has the most velocity?
(A) car A
(B) car B
(C) car C
9.
At 40 s which car has the most acceleration?
(A) car A
(B) car B
(C) car C
13. When a softball, thrown vertically upwards, gets to the
top of its path, it has
(A) velocity = 0 m/s; acceleration = 0 m/s2
(B) velocity = -9.8 m/s; acceleration = 0 m/s2
(C) velocity = 0 m/s; acceleration = -9.8 m/s
(D) velocity = -9.8 m/s; acceleration = -9.8 m/s
2
2
14. Starting from rest a coconut falls from a tree. Its average
speed during 8 s of freefall is
(A) 19.6 m/s
(C) 39.2 m/s
(B) 9.8 m/s2
(D) 9.8 m/s
15. A golfer putts the ball 5.0 m due east, then 2.1 m due
north, and then finally 0.5 m due west, into the hole.
What is the magnitude and direction of the resultant
vector for the three putts?
(A) 5.89 m, at 69.0˚ from north
(B) 5.89 m, at 21.0˚ from north
(C) 4.97 m, at 65.0˚ from north
(D) 4.97 m, at 25.0˚ from north
16. A ball thrown horizontally from a 20 m high building
strikes the ground 5.0 m from the base of the building.
With what velocity was the ball thrown?
(A) 4.9 m/s
(C) 3.0 m/s
(B) 3.3 m/s
(D) 2.5 m/s
17. A cannon,
elevated at
40˚ is fired
at a wall 300
m away on
level
ground, as
shown. The
initial speed of the cannonball is 89 m/s
How long does it take for the ball to hit the wall?
(A) 1.3 s
(B) 3.3 s
(C) 4.4 s
(D) 6.8 s
18. Referring to the previous question, at what height h does
the ball hit the wall?
(A) 39 m
(B) 47 m
(C) 137 m (D) 157 m
27
Kinematics Review Sheet
Problem solving. On separate paper, show all your work,
(general equation, substitutions, calculations, and units).
19. A car accelerates from rest at 4.50 m/s2.
a. What is its velocity after it’s been displaced 100 m?
b. If the car now brakes and comes to rest after 6 s of
braking, how far did it travel in total from its start?
c. How much time elapsed from start to stop?
28. A racecar completes one lap around a track at 200 miles
per hour, and the second lap at 220 miles per hour. What
is the average speed of the racecar? (Hint: you don’t
know the length of one lap, but show how that distance d
cancels in the solution. By the way, the answer is called a
harmonic average, and it’s not the arithmetic average!)
20. A hot air balloon descends vertically at a constant speed
of 2 m/s. When it is 40 m above the ground, a rock is
dropped from the balloon and freefalls to the ground.
a. What is the rock’s velocity when it strikes ground?
b. What is the balloon’s height above the ground when
the rock hits the ground?
29. A motorist is driving at 20 m/s when she sees that a
traffic light 200 m ahead has just turned red. She knows
that this light stays red for 15 s, and she wants to reach
the light just as it turns green again. It takes her 1.0 s to
step on the brakes and begins slowing at a constant
acceleration. What is her speed as she reaches the light at
the instant it turns green?
21. During a fireworks display, a rocket is launched with an
initial velocity of 35 m/s at an angle of 75° above ground.
a. What is the rocket’s height when it explodes in 2.0 s?
b. What is angle (from horizontal) of the rocket’s
velocity just before the explosion occurred?
22. A baseball is thrown at an unknown angle, from 2.0 m
above the ground, and it lands at a horizontal distance of
90, away. If the baseball takes 3.5 s to hit the ground:
a. What is the horizontal component of the ball's
velocity when it leaves the hand?
b. What is the vertical component of the ball's velocity
when it leaves the hand?
c. What is the resultant velocity of the ball when it
leaves your hand?
23. Draw a head-to-tail addition of the four vectors below,
and show the resultant vector. Then draw them in reverse
order. Tracing is the best method.
A
D
B
C
24. A football is kicked from the ground at an angle of 40˚
and a speed of 23 m/s. To score a field goal, the football
has to clear a 3.05 m high crossbar. How far away can the
kick be made to for the football to just clear the crossbar
(on its way downward)?
25. A rocket is fired straight up and accelerates from rest at
30 m/s2 for 5 s, and then it runs out of fuel. Assuming no
air friction, a) What is the rocket’s maximum altitude?
b) How long in total does it take the rocket to return to
the ground? (Hint: it free falls up, then down to the
ground)
Questions 26-33 are Honors only
26. A hiker walks vectors (θ in bearing) 20 m, 60˚; 30 m, 0˚;
40 m, 270˚; 20 m, 135˚. Find the resultant (θ in bearing.)
27. On the Apollo 14 mission to the moon, astronaut Alan
Shepard hit a golf ball that went 330 m on level ground.
The balls left the “club” at 25 m/s. The free fall
acceleration on the moon is about 1/6 of its value on
Earth. At what angle was the golf ball hit? (Do this
problem without using the “range equation”.)
30. A boat that can travel at 9.0 km/hr in still water is used to
cross a river flowing at a speed of 4.0 km/hr.
a. At what angle must the boat head so that its motion
is straight across the river?
b. Find the resultant speed relative to shore.
31. A stunt car rolls down a 24˚ incline, starting from rest,
accelerating at 4.0 m/s2, for 50 m. It then rolls off the
incline and freefalls into water, which is 30 m below the
incline. How far forward (range) does the stunt car land?
32. A stone is thrown downward at 8 m/s from a height of 22
m. At the same time, a stone is thrown upward from 2 m
the ground with a speed of 17 m/s.
a. At what point in time do their paths intersect?
b. At what height do their paths intersect?
33. Extra Challenge: In a 100-m race, a sprinter accelerates
from rest at 2.68 m/s2. After reaching a top speed, he runs
the rest of the race at constant speed, finishing the race in
12 s total.
a. For how much time does the runner accelerate? (time
to reach max. speed)
b. How far does he run during while maintaining
constant speed?
Answers
1. a) D b) C,D,E c) C d) A,E e) B
2. a) A,D b) C c) B,E d) F e) A,B
3. B
4. A
5. C
6. D
7. C
8. A
9. B
10. C
11. C
12. D
13. C
14. C
15. C
16. D
17. C
18. D
19. a. 30.0 m/s b. 190 m c. 12.67 s
20. a. -28.1 m/s b. 34.7 m
21. a. 48.0 m b. 57.5˚
22. a. 25.7 m/s b. 16.6 m/s
c. 30.6 m/s at 32.8˚ from horizontal
23. see solutions page for vector drawings
24. 49.2 m 25. a. 1523 m b. 37.9 s
26. 27.2 m, 341.3˚ 27. 29.8˚ 28. 209.5 km/h
29. 5.71 m/s 30. a. 63.6˚ from river b. 8.06 km/hr
31. 32.5 m 32. a. 0.8 s b. 12.5 m
33. a. 3.67 s b. 81.9 m
28
Notes
29
Notes
30
Notes
31
Notes
32
Notes
33
Notes
34
Dynamics
“If I have seen farther than others, it has been by
standing on the shoulders of giants.”
– SIR ISAAC NEWTON
“The most incomprehensible thing about the universe is
that it is comprehensible.”
– ALBERT EINSTEIN
35
Dynamics Assignment Sheet
Online: www.physicsclassroom.com/Physics-Tutorial/Newton-s-Laws (Assignments 1-6)
www.physicsclassroom.com/class/vectors (Assignments 9-11)
www.physicsclassroom.com/class/circles (Assignments 12-15)
No.
Topics
Reading
Homework
1
Newton’s First Law of Motion
“The Law of Inertia”
130-135
Ch 4: 1,2,3,4,6
2
Newton’s Second Law of Motion
“The Law of Acceleration”
136-138
Ch 4: 14,19,20,21
3
Newton’s Third Law
“The Law of Action-Reaction”
138-140
Ch 4: 13,17,18,33
4
definition and units of force,
free-body diagrams
124-125
Ch 4: 7,8,9,10,11
5
common forces: weight, normal,
friction, tension
141-142
Ch 4: 15,26,45,47,49
6
more on common forces: weight,
normal, friction, tension
7
static and kinetic friction;
coefficients of friction
8
more problems on Second Law
of Motion with force of friction
Ch 4: 36,53,63ab,64a
9
more problems on Second Law
of Motion
Ch 4: 35,50,51,67
10
torque, force, lever arm, and
rotational motion
278-282
Ch 8: 1,8,9,39
11
rotational equilibrium
286-288
Ch 8: 18,20,45,48
12
circular motion and centripetal
acceleration
257-259
Ch 7: 16,26,47a,50
13
centripetal forces that cause
circular motion
260-262
Ch 7: 19,43,47b,48
14
Newton’s Law of Universal
Gravitation
263-265
Ch 7: 29,35,39,40,49
15
supplemental problems on
gravitation
In the lab
book
Practice problems
2,3,4,7,8,9
Ch 4: 25,56,57,58
FBDs in lab manual
143-148
36
Ch 4: 34,37,44,52
Dynamics Assignment Sheet - Honors
Online: www.physicsclassroom.com/Physics-Tutorial/Newton-s-Laws (Assignments 1-6)
www.physicsclassroom.com/class/vectors (Assignments 9-11)
www.physicsclassroom.com/class/circles (Assignments 12-15)
No.
Topics
Reading
Homework
1
Force; Newton’s First Law of
Motion: “The Law of Inertia”
4-1
4-2
Q 1,2,3,9,18
2
Mass; Newton’s Second Law of
Motion: “The Law of Acceleration”
4-3
4-4
Q 4,10
P 3,6,9,11
3
Newton’s Third Law:
“The Law of Action-Reaction”
4-5
Q 6,7,15,16,17
4
Force of gravity (weight);
Normal force
4-6
Q 14
P 4,5,13,15,20
5
Free body diagrams; solving
problems with Newton’s laws
4-7
P 24,25,29,31
6
More problem solving with
Newton’s laws
7
Static and kinetic friction;
coefficients of friction
8
More problem solving with friction
and inclined planes
P 41,42,45,56,60
9
Newton’s law review problems
Q 13
P 67,69,76,86,87
10
Torque and rotational motion
8-4
Q6
P 22,23,24,26
11
Rotational equilibrium
9-1
9-2
Q8
P 6,7,16,20,21
12
Uniform circular motion and
centripetal acceleration
5-1
Q6
P 2,5,6,72
13
Centripetal forces; banked and
unbanked curves
5-2
5-3
Q 1,8
P 7,9,11,14
14
Newton’s law of universal
gravitation
5-6
5-7
Q 11
P 28,30,33,39,70
15
Satellite motion; weightlessness;
Kepler’s laws
5-8
5-9
Q 20
P 43,48,58,83,90
FBDs in lab manual
P 23,26,32,33,35
4-8
37
P 37,39,46,48,61
Gravitation Practice Problems
1. The mass of Pluto was not accurately known until a satellite of the planet was discovered. Explain
why? What law helps answer this question?
2. Respond carefully to the question, "What keeps a satellite up?"
3. Mimas, a moon of Saturn, has an orbital radius of 1.87 × 108 m and an orbital period of about 23
hours. Use Newton's variation of Kepler's third law to find the mass of Saturn.
4. A geosynchronous satellite appears to remain over one spot on Earth. Such a satellite has an orbital
radius of 4.23 × 107 m.
a. Calculate its period in hours (the answer explains why the satellite’s orbit is “geosynchronous”)
b. Calculate its orbital speed.
5. Jupiter has about 300 times the mass of Earth and about 10 times earth's radius. Estimate the size of
g on the surface of Jupiter.
6. On July 19, 1969, Apollo 11's orbit around the moon had an average altitude of 111 km above the
moon. The moon’s radius is 1785 km and the moon’s mass is 7.3 × 1022 kg.
a. How many minutes did it take to orbit once?
b. At what velocity did it orbit the moon?
7. If the space shuttle goes into a higher orbit, what happens to the shuttle’s period?
8. If a mass located in Earth's gravitational field is doubled, what happens to the force exerted by the
field upon this mass? Is the Earth’s field constant at such a location?
9
Yesterday, Sally had a mass of 50.0 kg. This morning she stepped on the scale and found that she
gained weight.
a. What happened if anything to Sally's mass?
b. What happened, if anything, to the ratio of Sally's weight to her mass?
10. Earth's gravitational field is 7.83 N/kg at the altitude of the space shuttle. What is the size of the
force of attraction between a student, mass of 45.0 kg, and Earth?
Answers:
3. 5.65 × 1026 kg
4. a) 24 hours (86,400 s) b) 3070 m/s
5. about 3 times g on Earth
6. a) 124 minutes b) 1600 m/s
10. 352 N
38
Newton’s Second Law
PURPOSE
The purpose is to investigate the relationship between force and acceleration, on a fixed (constant)
mass.
EQUIPMENT
- dynamics track and cart
- photogate timer and accessory photogate
- mass set and hanger
- meter stick
plastic
flag
end
stop
dynamics cart
with block photogate timer
m1
accessory
photogate
pulley
mass hanger
with mass
m2
PROCEDURE
1. Place two 100 g, a 50 g, a 20 g, and a 10 g masses in the cart. Place a 5 g and a 10 g mass on the
mass hanger. The hanger itself is 5.0 g. The cart has a mass of 500 g, and the black metal block
in the cart also has a mass of 500 g. The clear plastic “flag” with the black tape is 17 g. Calculate
the total known mass of the system, in kilograms, and record this value in your lab book above
the data table.
2. Record the hanging mass, in kilograms, in the mass column of the data table. Remember that the
hanger itself has a mass of 5.0 g so initially the total hanging mass is 20.0 g. There should only
be a small acceleration as the 20.0 g is nearly balanced by the force of friction. (You will
calculate force later.)
3. Pull the cart back until it touches the rubber bumper on the dynamics track. This will be the
release point for the cart for the entire lab. Move the photogate timer back so that the flag on the
cart will immediately trigger the timer when the cart is released. The initial velocity of the cart
will now be zero. Place the other photogate 70.0 cm away from the photogate timer. Record the
distance, in meters, in your lab book above the data table.
4. Turn the photogate timer to Pulse Mode, which measures the time between gates. With the cart
against the rubber bumper, release the cart and then catch it before it hits the end stop. Repeat
three more times. Record the times across the first row in your data table. Ignore obvious outliers
and take additional time trials if necessary. Watch carefully for masses that may fall off the
hanger onto the floor. Also be sure to check that the end stop doesn’t interfere with the string.
5. Now move one 10 g mass out of the cart and place it on the mass hanger. The mass of the system
has not changed, but the hanging mass (and therefore the net force) has changed. Record this
new 30 g mass, in kilograms, in the mass column of the data table. Measure and record four new
time trials in the next row of the data table
6. Keep adding to the hanging mass in increments of 10 g until 100 g of mass are moved. Think
about it! You have a 50 g, a 20 g, two 10 g, and two 5 g masses so increments of 10 g is certainly
possible. Measure and record four new time trials for each new hanging mass value.
39
DATA & ANALYSIS
1. Press STAT, then 5:SetUpEditor, then ENTER to reset the Lists in your calculator. Then press
STAT, then ENTER to view the Lists. If there is any data in Lists L1 through L6 delete the data
by moving the cursor to the top of the list and pressing CLEAR, ENTER.
2. Enter the time trials into your graphing calculator in Lists L1 through L4. Then calculate the
average times for the four time trials by moving the cursor to the top of L5 (in the column
heading) and type (L1+L2+L3+L4)/4, then ENTER. Record these average times in the table in
your lab book.
3. Enter the hanging mass data into List L6 in your calculator. Then create a new List column by
going to the column heading of List L6 and move the cursor one space to the right. Name this
new column “F” for force using the F key on the calculator.
4. Calculate the force acting on the system for each set of trials. To convert hanging mass into a
force (its weight) in newtons use:
force (N) = hanging mass (kg) × 9.8
( )
N
kg
In the top of the “F” List write L6 × 9.8, then ENTER. Record the forces in the data table.
5. Create another new column in your calculator and name the List “A” for acceleration. Since the
cart started from rest, and you measured the time it takes to travel a known distance, you can use
an appropriate kinematics equation to determine the acceleration. Solve the equation for
acceleration, and then write the equation in the top of List “A”. Record the accelerations in the
table in your lab book.
6. Create a graph of acceleration versus force in your lab book. Make sure that the independent
variable is on the x-axis. Ask yourself: “does the cart’s acceleration depend on the force applied
or does the force applied depend on the cart’s acceleration?”
7. Graph the acceleration vs. force on the calculator by turning on a STAT PLOT and adjusting the
Xlist to “F” and the Ylist to “A”. To access a List, use the LIST menu (2nd STAT) and then
move the cursor down to the appropriate list.
8. Looking at your force and acceleration data, use the WINDOW menu to determine the Xmin,
Xmax, Xscl, Ymin, Ymax, Yscl so the graph can be viewed clearly. Or, just press ZoomStat to
automatically fit the data onto the graph.
9. To find the best-fit line, press STAT, then move the cursor over to CALC and use
4:LinReg(ax+b). Then adjust the menu to read Xlist:A, and Ylist:F, and Store RegEQ: Y1. (To get
“A” and “F” press 2nd STAT for Lists and cursor down; to get Y1 press VARS, then move cursor
to Y-VARS, then press 1:Function, then 1:Y1 and finally ENTER)
Note: on the TI-83 this should appear on screen as: LinReg(ax+b) LF, LA, Y1 then press ENTER.
10. Draw the best-fit line on your graph. Write the equation of the best-fit line on the graph in your
lab book. Use appropriate variables in the equation. DON’T use y and x!
40
Photogate distance (in meters): __________
t1 (s)
(L1)
t2 (s)
(L2)
t3 (s)
(L3)
Known system mass (in kg): __________
t4 (s)
(L4)
tav (s)
(L5)
best fit equation:
41
hanging
mass (kg)
(L6)
force (N)
(F)
acc
(m/s2)
(A)
QUESTIONS & CALCULATIONS
1. a) From your equation for the best-fit line, predict what force is needed to accelerate the cart at a
rate of 2.0 m/s2?
b) How many grams (not kilograms!) of hanging mass are necessary to do this?
2. The line of best fit should cross the positive x-axis. This x-intercept has a very real physical
significance in the lab. What is the significance of the x-intercept on your graph?
3. The slope of your graph should be a straight line. What does this imply about the relationship
between acceleration and the force that causes it?
4
If acceleration is proportional to force and inversely proportional to mass then we could propose
that a = mF . That could also be expressed as a = m1 ⋅ F . That means that the experimental mass of
the system is the reciprocal of the slope of the graph of a vs. F. Calculate the experimental
system mass.
5. Find the percent error between the experimental system mass and the known system mass.
42
Newton's Second Law - Revisited
(Honors Physics only)
PURPOSE
The purpose is to investigate the relationship between mass and acceleration using a constant net force.
EQUIPMENT
- dynamics track and cart
- photogate timer and accessory photogate
- mass set and hanger
- meter stick
plastic
flag
end
stop
dynamics cart
with block photogate timer
m1
accessory
photogate
pulley
mass hanger
with mass
m2
PROCEDURE
1. Place three 100 g and two 50 g masses in the cart. The cart has a mass of 500 g and the black
metal block in the cart also has a mass of 500 g. The clear plastic “flag” with the black tape is 17
g. Calculate the total cart mass in kilograms, not grams.
2. Place two 20 g and a 5 g mass on the mass hanger. Remember that the plastic mass hanger is 5 g.
Record the total hanging mass (in kilograms) in the data table. Then record the system mass (in
kilograms) in the first row of the data table.
3. Pull the cart back until it touches the rubber bumper on the dynamics track. This will be the
release point for the cart for the entire lab. Move the photogate timer back to the cart so that the
flag on the cart will immediately trigger the timer when the cart is released. The initial velocity
of the cart will now be zero. Place the other photogate about 70.0 cm away from the photogate
timer, Record the distance, in meters, in your lab book above the data table.
4. Turn the photogate timer to Pulse Mode, which measures the time between gates. Release the
cart, but catch it before it hits the end. Record the time in your lab book. Repeat three more
times. Ignore obvious outliers.
5. Now remove 100 g from the cart, and record the new system mass in the table. The hanging mass
remains at 50 g. Remember, you are not changing the hanging mass, only the cart mass, so put
the 100 g mass that came out of the cart back in the mass set box.
6. Repeat steps 3 & 4. Record these four new times in the second row of the data table.
7. Keep removing 100 g at a time until the cart is completely unloaded, including the block. Repeat
steps 3 & 4 again and record new times for each new cart mass value. WATCH FOR MASSES
THAT MAY JUMP OFF!
43
DATA AND ANALYSIS
1. Press STAT, then 5:SetUpEditor, then ENTER to reset the Lists in your calculator. Then press
STAT, then ENTER to view the Lists. If there is any data in Lists L1 through L6 delete the data
by moving the cursor to the top of the list and pressing CLEAR, ENTER.
2. Enter the time trials into your graphing calculator in Lists L1 through L4. Then calculate the
average times for the four time trials by moving the cursor to the top of L5, type
(L1+L2+L3+L4)/4, then ENTER. Record these average times in the table in your lab book.
3. Enter the system mass data (sum of cart mass and hanging mass) in kilograms into List L6 in
your calculator.
4. Then create a new List column by going to the top of List L6 and move the cursor one space to
the right. Name this new column “INM” for inverse of mass.
5. Calculate the inverse mass of the system for each set of trials. To convert mass into an inverse
mass, go to the top of the “INM” List and write L6-1, then ENTER. Record the inverse mass in
the data table.
6. Create another new column in your calculator and name the List “A” for acceleration. Since the
cart started from rest, and you measured the time it takes to travel a known distance, you can use
an appropriate kinematics equation to determine the acceleration. Solve the equation for
acceleration, and then write the equation in the top of List “A”. Record the accelerations in the
table in your lab book.
7. Create a graph of acceleration versus inverse mass in your lab book. Make sure that the
independent variable is on the x-axis. Ask yourself: “does the cart’s acceleration depend on the
mass or does the mass depend on the cart’s acceleration?”
8. Graph the acceleration vs. inverse mass on the calculator by turning on a STAT PLOT and
adjusting the Xlist to “INM” and the Ylist to “A”. To access a List, use the LIST menu (2nd
STAT) and then move the cursor down to the appropriate list.
9. Looking at your force and acceleration data, use the WINDOW menu to determine the Xmin,
Xmax, Xscl, Ymin, Ymax, Yscl so the graph can be viewed clearly. Or, just press ZoomStat to
automatically fit the data onto the graph.
10. To find the best-fit line, press STAT, then move the cursor over to CALC and use
4:LinReg(ax+b). Then adjust the menu to read Xlist:INM, and Ylist:A, and Store RegEQ: Y2. (To
get “INM” and “A” press 2nd STAT for Lists and cursor down; to get Y2 press VARS, then move
cursor to Y-VARS, then press 2:Function, then 2:Y2 and finally ENTER)
Note: on the TI-83 this appear on screen as: LinReg(ax+b) LINM, LA, Y2 then press ENTER.
11. Draw the best-fit line on your graph. Write the equation of the best-fit line on the graph in your
lab book. Use appropriate variables in the equation. DON’T use y and x!
12. Calculate the known value of the net force acting on the system by converting the hanging mass
into a force (its weight) in newtons. Use:
force (N) = hanging mass (kg) × 9.8
( )
N
kg
13. Convince yourself that the slope for the graph a vs. 1/m yields the experimental value for the net
force on the system. Compare this with the known value for the net force on the system from the
last step. Calculate percent error below.
44
Photogate Distance (in meters): ____________
t1 (s)
(L1)
t2 (s)
(L2)
t3 (s)
(L3)
Hanging Mass (in kg): ____________
t4 (s)
(L4)
tav (s)
(L5)
best fit equation:
45
system mass-1 (kg-1) acc (m/s2)
mass (kg)
(INM)
(A)
(L6)
Free Body Diagrams
This lesson is designed to help students apply Newton’s 2nd Law
to solve problems, which is the central theme within the study of
dynamics. Thus, the need to identify, draw, and label a variety of
forces is essential.
Read through the list of forces on the right. Details about these
forces, like the difference between static and kinetic friction, will
be described later. For now, you are only drawing and labeling
forces.
Follow these rules: 1) Draw forces on the dot, to the right of each
picture. 2) Draw forces with a ruler, and put an arrow on each, to
show direction. 3) Draw forces that are proportionally correct.
That is, if you intend to show equilibrium, then forces are
balanced. If not, then the net force must be in the direction of
acceleration.
4) Label each force according to the list shown to the right.
5) Draw an acceleration arrow nearby (unless it’s zero)
1
2
3
4
5
6
46
Common Forces
Fg = force of gravity (weight)
Fn = normal force (support)
Fr = air resistance (drag)
Fs = static friction
Fk = kinetic friction
FT = tension
Fsp = spring force
7
8
9
10
11
12
13
The next four are Honors Physics only
14
15
16
47
Hooke's Law
.
PURPOSE
To investigate Hooke's Law, the relationship
between spring force and displacement for a
stretched spring; to investigate how multiple
springs behave in different arrangements.
SET UP
Δx
series
parallel
single
PROCEDURE
Do NOT exceed the elastic limit of any spring by
overloading it past a maximum stretch of 50 cm!
PART A - SINGLE SPRING
1. Hang a single spring from the support. Use
an upright (vertical) meter stick, with the
100 cm mark on the lab table, to measure the
initial position of the lowest loop on the
spring. Record this initial position.
2. Attach the 5.0 g mass hanger to the bottom of the spring. Add 35 more grams of mass for a total
of 40 grams on the spring. Measure the final position of the bottom of the lowest coil on the
spring (the one that’s turned vertically). Subtract initial position from final position to find the
displacement of the masses. Record this displacement in the lab table.
3. Place another 20 grams of mass on the mass hanger for a total of 60 grams. Again, measure final
position, calculate displacement, and record the data in the table. Add more mass in 20-gram
increments up to a maximum of 140 grams and record all collected data.
PART B – SERIES SPRINGS
4. Now hang a second spring from the bottom of the first one, an arrangement called "series."
Again start with 40 grams of initial total mass, and add masses in 20-gram increments, up to a
maximum of 140 grams. You may need to raise the support rod to allow for a greater maximum
displacement. Check it with the 140-gram load to be sure. Measure final position, calculate
displacement, and record the data in the table.
PART C – PARALLEL SPRINGS
5. Now hang the second spring on the mass hanger next to the first one, an arrangement called
"parallel." Use a small paper clip, bent into a triangle, to connect both springs. Again start with
40 grams of initial total mass, and add masses in 20-gram increments, up to a maximum of 140
grams. Measure final position, calculate displacement, and record the data in the table.
DATA & ANALYSIS
1. Complete the data table of mass (in kilograms), displacement (in meters), and force (in newtons)
for each part of the lab. Remember, to calculate force (weight), multiply the mass by g = 9.8
N/kg.
2. Graph the data for force vs. displacement for each part of the lab on the same graph, making sure
to determine dependent and independent variables. Be sure to consider the maximum
displacement and maximum force to set the graph scale so the graph is filled.
3. Enter the data into the TI Graphing Calculator using the Lists (L1 through L5) according to the
columns in the data table.
4. Use the TI Graphing Calculator to find the equation for each best-fit line, and include the
equations below the graph. Use appropriate variables - DON’T use y and x!
5. From the best-fit equation, determine the spring constant (in units of N/m) for each part of the
lab. Label each best-fit line on the graph with this spring constant. Use k for the single spring,
kseries for the series springs, and kparallel for the parallel springs.
48
Single Spring
m (kg)
(L1)
F (N)
(L2)
Series Springs
Δx (m)
(L3)
initial position (m) ________
Equations:
single spring
m (kg)
(L1)
F (N)
(L2)
Parallel Springs
Δx (m)
(L4)
initial position (m) ________
springs in series
49
m (kg)
(L1)
F (N)
(L2)
Δx (m)
(L5)
initial position (m) ________
springs in parallel
QUESTIONS & CALCULATIONS
1. The results from Part B confirm that for two identical springs in series, the spring constant is
kseries = 12 ksingle . Now rearrange the equation and solve for the single spring constant, ksingle . Then
find the percent difference (not percent error) between this value and the value for ksingle that you
found from data on the single spring. Look up percent difference in the back of the lab manual.
2. The results from Part C confirm that for two identical springs in parallel, the spring constant is
kparallel = 2ksingle . Now rearrange the equation and solve for the single spring constant, ksingle . Then
find the percent difference (not percent error) between this value and the value for ksingle that you
found from data on the single spring.
3. What is the physical significance of the x-intercept of the graphs you created?
4. Why does the spring constant get smaller when two springs are added together in series? Why
does the spring constant get larger when two springs are added together in parallel?
5. A spring is cut exactly in half. What happens to the spring constant of the two equal-sized pieces
compared with the spring constant of the original full-sized spring? (Hint: think about your
answer to the previous question about series springs.)
50
Friction & The Graphing Calculator
PURPOSE
To measure the coefficient of static friction (µs) between a TI Graphing Calculator and a Dynamics
Track, using a level plane and an inclined plane.
EQUIPMENT
- dynamics track
- mass set and hanger
- meter stick
- calculator
- cardboard
PROCEDURE
PART A - LEVEL PLANE
m1
TI graphing
calculator
mass hanger
m2
1. Measure the mass of the calculator on the electronic balance, and record the mass, in kilograms,
in the data table.
2. Put cardboard on the floor below the hanging mass to ease the impact, especially when a lot of
hanging mass is used. Attach the string to the calculator using the method shown in class.
3. In this part of the lab, you will test the coefficient of friction between the TI Graphing Calculator
and a level Dynamics Track. Start with the calculator resting on the four friction pads of the
calculator cover. Make sure the friction pads are not on the groves in the track.
4. While one lab partner pushes down lightly on the calculator (to give it more normal force)
another lab partner loads mass on the mass hanger. Then the person pushing down on the
calculator releases it to see if the calculator moves. Your job is to put enough mass on the hanger
so the calculator just starts to move along the track. Trial and error is necessary. Record the
hanging mass, in kilograms, for this first trial in the table below.
5. Repeat step 4 three more times with the calculator placed on a different section of the track.
Record the data in the table. DO NOT let the hanging mass slam onto the floor!
6. Now repeat steps 4 and 5 with the calculator placed on its keyboard side. Record all data.
mass of calculator, m1 (in kg) = ____________
m2 - trial #1
(kg)
m2 - trial #2
(kg)
calculator on
4 friction pads
calculator on
keyboard
51
m2 - trial #3
(kg)
m2 - trial #4
(kg)
m2 - average
(kg)
DATA & ANALYSIS
1. Carefully draw free body diagrams below for the calculator (m1) and the hanging mass (m2).
Check that the forces are drawn qualitatively to scale, and are labeled properly.
2
Calculate the weight of the calculator, and the weight of the average hanging mass for both trials.
3. Look at the free body diagrams above. Determine the normal force on the calculator. To do this,
recognize that the forces must keep the calculator’s mass in equilibrium.
4. Look at the free body diagrams above. Determine the static friction force on the calculator on the
friction pad side and keyboard side. Again, recognize the forces keep the mass in equilibrium.
friction pad:
keyboard:
5. Calculate the coefficient of static friction for the friction pad side and the keyboard side.
friction pad:
keyboard:
52
PROCEDURE
PART B - INCLINED PLANE
meterstick
m1
h
L
TI graphing
calculator
θ
1. Take the pulley off the end of the Dynamics Track and leave it on the table. Put the calculator on
the track, with the calculator resting on the four friction pads of the case. Make sure the friction
pads are not on the groves in the track.
2. Lift the bumper end of the track up slowly until the calculator just starts to slide down the track.
Trial and error is necessary. (Be sure to use the same calculator from Part I.)
3. Use the meter stick to measure the height of the track. Be sure you are measuring the under side
of the track not the top. Record the height, in meters, in the table below.
4. Repeat steps 2 and 3 three more times with the calculator placed on a different section of the
track. Record the data in the table.
5. Now repeat steps 2 and 3 with the calculator placed on its keyboard side. Record all data.
6. Determine the angle θ from the height (opposite) and length (hypotenuse) of the track. Show one
sample calculation for finding the angle, θ, using one height average.
mass of calculator, m1 (in kg) = __________
h - trial #1
(m)
h - trial #2
(m)
length of track, L (in meters) = __________
h - trial #3
(m)
calculator on
4 friction pads
calculator on
keyboard
53
h - trial #4
(m)
h – average
(m)
angle, θ
DATA & ANALYSIS
1 Honors: Draw a free body diagram for the calculator in Part II. Be sure to check that the forces
are drawn qualitatively to scale, and are labeled properly.
2
Honors: Use Newton’s 2nd Law to show that forces in the direction parallel to the inclined plane
on the calculator are balanced.
3
Honors: Use Newton’s 2nd Law to show that forces in the direction perpendicular to the inclined
plane on the calculator are balanced.
4
Honors: Combine the 2nd Law equations from the last step to prove that µ s = tan θ .
5. Using the result, µ s = tan θ , for the calculator on the inclined plane, calculate the coefficient of
static friction for both the friction pad side and the keyboard side.
friction pad:
keyboard:
54
QUESTIONS & CALCULATIONS
1. Calculate the percent difference (not percent error) for the coefficient of static friction for the
friction pad side in Part A versus Part B. Look up percent difference in the lab manual. Then
calculate the percent difference for the keyboard side.
friction pad:
keyboard:
2. Some people just fidget a lot. They can’t help it. They tap their pencils on the desk, they twirl
their hair, and they peel things off that should stay put, like the rubber feet on the bottom of their
graphing calculator. Use data from the lab to describe why this is a bad habit for the calculator.
3. The TI Graphing Calculator only uses four small friction pads on the cover, but they effectively
work about as well as a calculator that has the entire case covered with a large friction pad.
Explain why these small pads work so well; that is, why surface area of contact appears to have
little effect on frictional force.
4. The backside of the TI-83 has only two friction pads, and the backside of the TI-84 has three
friction pads, while the case has four. Why the difference? (There are several good reasons, and
only Texas Instruments can tell us for sure!)
55
Torque & Static Equilibrium
PURPOSE
To investigate the torques responsible for creating a system with rotational equilibrium and to
calculate an unknown torque if all other torques in the system are known.
d2
d1
m2
m1
dcm
center of mass
support stand
PROCEDURE
1. Insert a meter stick into a balance clamp and place onto the support stand Adjust the position of
the clamp until the meter stick balances level on the metal support stand. Record the center of
mass for the meter stick exactly to the nearest millimeter.
2. Now move the clamp 10 cm to one side. The meter stick will no longer balance if supported at
the clamp, but if weight is added to the light side, a balance can once again be achieved. Add two
sets of “hanging masses” to the light side until the meter stick is balanced again. Note that the
mass hangers have a mass of 5 grams. Record both masses.
3. Measure and record the distances from the point of rotation to each of the hanging masses and to
the center of mass of the meter stick.
4. Measure and record the meter stick’s mass (without the clamp) using an electronic balance.
DATA & ANALYSIS
meter stick center of mass
_______ (m)
distance to center of mass, dcm ________ (m)
hanging mass #1
_______ (kg)
distance to first mass, d1
________ (m)
hanging mass #2
_______ (kg)
distance to second mass, d2
________ (m)
meter stick mass
_______ (kg)
1. There are now three torques creating rotational equilibrium. On the one side of the point of
rotation there are two torques due to the weights (gravitational forces) of the hanging masses. On
the other side, the torque comes from the weight of the meter stick. This meter stick weight can
be considered to be concentrated at the center of mass. Using the relationship Fg = mg, convert
the hanging masses into weights measured in newtons.
56
QUESTIONS & CALCULATIONS
1. Now calculate the torques produced by the hanging masses. Express these in newton-meters
(N⋅m).
2. Using the sum of torques law, write an equation to determine the torque on the other side
produced by the meter stick’s center of mass.
3. Calculate the mass of the meter stick.
4. Calculate the percent error between the experimental meter stick mass and the known mass.
5. Using a torque equation, calculate the normal force that the support stand exerts on the meter
stick (while it is loaded with masses m1 and m2). Check your answer using a force equation.
6. Calculate the unknown mass and distance in the diagram of
the mobile to the right so that it will balance properly in
static equilibrium.
0.2 m
0.6 m
?m
0.1 m
? kg
2 kg
57
5 kg
PURPOSE
Centripetal Force
To use the ideas of uniform circular motion to calculate the centripetal force acting on a rubber
4π 2 mr
stopper moving in a circle using the equation Fc =
.
T2
PROCEDURE (PART 1)
1. Set up your apparatus as shown to the right.
2. Choose and measure a convenient radius “R” at which to swing the
rubber stopper. Measure the radius to the center of the stopper.
- Use a piece of tape on the string a bit below the plastic tube to help
keep the radius constant (but don’t let it touch the bottom of the tube).
- Don’t let any part of your body touch the string or the tape.
3. Use a stopwatch to measure the time for the stopper to go through 10
revolutions. Do this five times with both partners taking turns swinging
the stopper.
DATA
Hanging mass: ___________ kg
Radius: ___________ m
Time for 10
revolutions (s)
Average time for 10 revolutions: ___________
Period: ___________
QUESTIONS/CALCULATIONS (Show all work)
1. Calculate the weight of the hanging mass.
2. The weight you calculated in the last question provides the centripetal force to move the rubber
stopper in a circle. Use this idea to calculate the mass, in grams, of the rubber stopper.
Predicted Mass: __________
Actual Mass: __________
58
Percent Error: __________
PROCEDURE (PART 2)
Obtain a mystery mass from me with which to replace the hanging mass. Use the space below to
provide data and calculations that determines the mystery mass (in grams).
Predicted Mass: __________
Actual Mass: __________
QUESTIONS (PART 2)
Complete the following free body diagrams for objects in circular motion
A
D
B
E
C
F
59
Percent Error: __________
Dynamics Review Sheet
Match the Free Body Diagram with the correct description.
1. Book at rest on a level table
2. Freefalling body (no air friction)
FT
Fr
3. Person on elevator accelerating up
4. Car skidding to rest (no airndfriction)
5. Mass #2 from Newton’s 2 Law Lab
Fg
Fg
6. Skydiver falling at terminal velocity
7. Mass at rest on incline, held by friction
8. Football at peak of path (with air friction) A
B
Fs
Fn
Fk
Fg
C
Fn
Fn
Fg
Fg
E
D
Fr
Fn
Fg
Fg
Fg
F
G
H
Multiple choice. Circle the best answer.
9. A 60-kilogram skydiver is falling at constant speed near
the surface of Earth. The magnitude of the force of air
friction acting on the skydiver is
A. 0 N
C. 58.8 N
B. 5.88 N
D. 588 N
14. If the sum of all the forces acting on a moving object is
zero, the object will
A. slow down and stop
B. change the direction of its motion
C. accelerate uniformly
D. continue moving with constant velocity
10. Two masses exert a gravitational force F on each other.
If the mass of each is doubled and the distance between
them is tripled, the force between them is:
15. As a ball falls, the action force is the pull of the earth’s
mass on the ball. The reaction force is the
A. air resistance acting against the ball.
B. acceleration of the ball.
C. pull of the ball’s mass on the earth.
D. non-existent in this case.
A. 12F
B.
4
9
F
3
4
4
3
F
D. F
C.
11. A child is riding on a merry-go-round. As the speed of
the merry-go-round is doubled, the magnitude of the
centripetal force acting on the child
A. remains the same
C. is halved
B. is doubled
D. is quadrupled
16. A net force of 10 newtons accelerates an object at 5
meters per second squared. What net force would be
required to accelerate the same object at 1.0 meters per
second squared?
A. 1.0 N
C. 5.0 N
B. 2.0 N
D. 50.0 N
12. A 1,200-kilogram car traveling at 10 meters per second
hits a tree that is brought to rest in 0.10 second. What is
the magnitude of the net force acting on the car to bring
it to rest?
A. 120 N
C. 12,000 N
B. 1200 N
D. 120,000 N
17. (HONORS ONLY) A force applied to a 100-kilogram
rocket gives it an upward acceleration 15 meters per
second squared. The magnitude of the applied force is
equal to:
A. 520 N
C. 2480 N
B. 1500 N
D. 14700 N
13. A satellite is observed to move in a circle about the earth
at a constant speed. This means that the force acting
upon it is:
A. zero
B. opposite of the satellite’s velocity
C. perpendicular to the satellite’s velocity
D. parallel to the satellite’s velocity
18. (HONORS ONLY) If a net force is applied to a 1000kilogram car traveling at 38 meters per second, the car is
brought to rest in 100 meters. If the braking force is
doubled, what maximum speed can the car have and still
come to rest in 100 meters?
A. 53.7 m/s
C. 26.9 m/s
B. 76.0 m/s
D. 19 m/s
Problem solving. Show all your work including general equation, substitutions, calculations & units.
19. An advertisement claims that a certain 1060-kilogram car 21. The gravitational field strength on the surface of the
can be accelerated from rest to 80 kilometers per hour in
moon is 1.63 N/kg. An astronaut weighs 960 N on earth.
9.4 seconds. How large a net force must act on the car to
(a) What is the astronaut’s mass? (b) What does the
give it this acceleration?
astronaut weigh on the moon? (c) What is the astronaut’s
mass on the moon?
20. A rope pulls upward on a bucket weighing 54 newtons.
The bucket is accelerating upward at 0.77 m/s2. What is
the tension in the rope?
22. Two identical spherical balls are placed so their centers
are 2.1 m apart. The force between them is 3.4 x 10-11 N.
What is the mass of each ball?
60
23. A 6-kg block is pushed with an force F of 75 N, as
shown in the drawings to the right. The coefficient of
kinetic friction between the block and the surface is 0.22.
What is the force of friction in each case, and what is the
acceleration in each case?
53˚
F
F
F
27. Our solar system is in the Milky Way galaxy. The
nearest galaxy is Andromeda, a distance of 2 x 1022 m
away. The masses of the Milky Way and Andromeda
galaxies are 7 x 1041 kg and 6 x 1041 kg, respectively.
Treat the galaxies as particles and find the magnitude of
the gravitational force exerted on the Milky Way by the
Andromeda galaxy.
37˚
HONORS
ONLY
HONORS
ONLY
28. Titan, a moon of Saturn, has on orbital period of 15.95
days and an orbital radius of 1.22 x 109 m. From this
data, determine the mass of Saturn.
24. The tension in the rope used to pull the two blocks
shown in the drawing to the right is 58 N. (a) Find the
acceleration of the blocks if there is no surface friction.
(b) Find the acceleration of the blocks if the coefficient
of kinetic friction between the blocks and the surface is
0.33. (c) HONORS ONLY: Find the tension in the rope
between the blocks, using the case of friction and no
friction.
3 kg
8 kg
29. A device called Atwood’s Machine,
shown in the drawing to the right, can be
used to determine g, the gravitation field
strength. Mass A = 5.1 kg, mass B = 2.7
kg, and the pulley C is massless. If a
student measures the acceleration of the
system as 3.0 m/s2, what is the student’s
measured value for g?
FT
25. A 500 kg racecar travels at a constant speed around a
circular track whose radius is 1.6 km. (a) If the car
travels once around the track in 2.0 minutes, what is the
magnitude of the centripetal acceleration of the car? (b)
If the force of static friction from the road on the tires is
1200 N, how fast can the car travel around the track
without slipping?
26. A lunch tray is being
held in one hand, as
shown. The mass of
the tray itself is 0.28
kg, and its center of
gravity is located at
its geometrical
center. On the tray is
a 1.0-kg plate of food
and a 0.295-kg cup of coffee. Find the force T exerted by
the thumb and the force F exerted by the four fingers.
30. HONORS ONLY: A 1220 N
uniform beam is attached to a
vertical wall at one end and is
supported by a cable at the
other end. A 1960 N crate
hangs from the far end of the
beam. Use the data shown in
the drawing to the right. (a)
Find the magnitude of the
tension in the wire. (b) Find the
magnitude of the horizontal and
vertical components of the
force that the wall exerts on the
left end of the beam.
Answers
1 E
2 F
3 H
4 D
5 B
6 G
7 C
8 A
9 D
10 B 11 D 12 D 13 C 14 D
15 C 16 B 17 C 18 A 19 2506 N 20 58.2 N 21 (a) 98 kg (b) 160 N (c) 98 kg 22 1.50 kg 23 (a) 12.9 N,
2
2
2
10.3 m/s right (b) 26.1 N, 3.17 m/s right (c) 10.3 N, 4.88 m/s up 24 (a) 5.27 m/s2 (b) 2.04 m/s2 (c) 15.8 N for both
25 (a) 4.39 m/s2 (b) 62.0 m/s 26 76.8 N, 61.4 N 27 7.0 x 1028 N 28 5.66 x 1026 kg 29 9.75 m/s2 30 2260, 1453, 1449 N
61
Notes
62
Notes
63
Notes
64
Notes
65
Notes
66
Notes
67
Energy, Momentum, and Relativity
“For those who want some proof that physicists are
human, the proof is in the idiocy of all the different
units which they use for measuring energy”
– RICHARD FEYNMAN
“A new scientific truth does not triumph by convincing
its opponents and making them see the light, but
rather because its opponents eventually die, and a new
generation grows up that is familiar with it.”
– MAX PLANCK
68
Energy, Momentum, Relativity Assignment Sheet
Online: www.physicsclassroom.com/class/energy (Assignments 1-6)
www.physicsclassroom.com/class/momentum (Assignments 7-11)
No.
Topics
Reading
Homework
1
work and energy, work done by a
constant force
168-171
Ch 5: 1,7,9,10a
2
kinetic energy; work-energy
theorem
172-175
Ch 5: 12,14,15,19,20
3
potential energy: gravitational
and elastic
177-179
Ch 5: 13,23,24,25
4
conservation of mechanical
energy, conservative forces
181-184
Ch 5: 28,33,37,39,43
5
conservation of total energy,
non-conservative forces
185-186
Ch 5: 41,47,48,49
6
power versus energy
187-189
Ch 5: pg 189: SR 1-3
page 195, #35
7
linear momentum, impulse, and
the impulse-momentum theorem
208-214
Ch 6: 5,7,13,15,16
8
more problems on impulse and
momentum
9
conservation of momentum in
one dimension
215-220
Ch 6: 17,23,24a,25,
10
collisions in one dimension:
inelastic collisions
222-225
Ch 6: 31,35,48,49
11
collisions in one dimension:
elastic collisions
226-230
Ch 6: 28,29,36,38,39
12
space-time, postulates of
relativity, time dilation
282-289
Q 2,6
P 2,3b,d,f,11
13
twin paradox, space and time
travel, length contraction,
correspondence principle
290-295
Q 8,10
P 1,4,8
14
relativistic inertia & momentum,
mass/energy equivalence,
correspondence principle
302-308
Q 13,15
P 15,18,20,22
15
general relativity,
gravity/space/time/geometry, test
of general theory of relativity
308-316
Q 16,17,18,19,20
Ch 6: 6,10,12,14,56
69
Energy, Momentum, Relativity Assignment Sheet - Honors
Online: www.physicsclassroom.com/class/energy (Assignments 1-6)
www.physicsclassroom.com/class/momentum (Assignments 7-11)
No.
Topics
Reading
Homework
1
work and energy, work done by a
constant force
6-1
Q2
P 2,3,4,9,10
2
kinetic energy; work-energy
principle
6-3
Q 19
P 15,18,20,22,25
3
potential energy: gravitational and
elastic
6-4
Q 14
P 26,28,30,31,32
4
conservation of mechanical energy,
conservative forces
6-5 to
6-7
Q 10
P 36,37,39,40,43
5
conservation of total energy, nonconservative forces
6-8
6-9
Q 15
P 48,49,52,53,55
6
power vs. energy
6-10
P 58,59,66,67,69
7
linear momentum, impulse, and the
impulse-momentum theorem
7-1
7-3
Q6
P 2,3,15,17,19
8
conservation of momentum in one
dimension
7-2
7-4
Q8
P 4,6,7,8,12
9
collisions in one dimension: inelastic
collisions
7-6
Q 11
P 31,32,34,35,36
10
collisions in one dimension: elastic
collisions
7-5
P 22,24,27,28
11
conservation of momentum in two
dimensions
7-7
P 40,41,42,43
12
space-time, postulates of relativity,
time dilation
26-1 to
26-4
13
twin paradox, space and time travel,
length contraction, correspondence
principle
26-5
26-6
14
relativistic inertia & momentum,
mass/energy equivalence,
correspondence principle
26-7 to
26-9
Q 14,15
P 15,17,22,24
15
general relativity,
gravity/space/time/geometry, test of
general theory of relativity
online:
308-316
Q 16,17,18,19,20
70
Q 2,6
P 3a,c,e,5,11,12
Q 8,9
P 1,4,7
Personal Power
PURPOSE
To measure your personal power while performing three exercises.
EQUIPMENT
- stopwatch
- meter stick
- various weights
PROCEDURE
1. There are three exercises each person must do:
A. Stair climb. Use the stairs by the Little
Theater or towards the math classrooms.
B. Sit ups. Use the carpet and pillow for
comfort. Do 10 sit-ups.
C. Arm curls. Use the 5, 7, or 10 pound
weights at a lab table. Do 10 arm curls.
d
2. Work in groups of two or three, but record data
for each person so that everyone calculates
their own personal power.
3. Use a meter stick to measure the displacement
over which work is done. Measure only the
displacement in the direction of the force so
that work can be calculated as W = Fd.
d
d
• Stair climb: measure the vertical displacement (the height of all stairs you climb).
• Sit up: the vertical displacement of your armpit from start to finish
• Arm curl: the vertical displacement of the mass (from elbow to fist)
4. Use a stopwatch to time the exercise. If you want, repeat trials for your personal best!
DATA & ANALYSIS
1. Calculate the force used in the exercise. Use the conversion:
1 pound = 4.45 newtons
• Stair climb: the force is your weight
• Sit up: the force is half your weight
• Arm curl: the force is the weight you lifted, plus 2% of your body weight to account for lifting
your own forearm!
2. Calculate the TOTAL vertical displacement for each exercise. If the exercise requires and up and
down motion (sit ups and arm curl), technically the net displacement is zero, so instead calculate
the absolute value of all the displacements to get a non-zero answer. For example, since you do
10 arm curl repetitions, this total vertical displacement is 20 times the length of your forearm,
from fist to elbow.
3. Calculate the TOTAL work done in each exercise.
4. Calculate your personal power for each exercise in watts.
5. Convert personal power for each exercise into horsepower using the conversion
1 horsepower = 746 watts
6. Show calculations (below the table) for the arm curl showing how you calculated the total
displacement, force, work, power in watts, and power in horsepower.
71
type of
work
TOTAL
force
displacement
(newtons)
(meters)
time
(seconds)
work
(joules)
power
(watts)
power
(hp)
stair climb
xsit up
arm curl
QUESTIONS & CALCULATIONS
1. Show calculations below for the arm curl, showing how you calculated the total displacement,
force, work, power in watts, and power in horsepower.
2. A rock climber wears a 7.5 kg backpack while scaling a cliff. After 30 minutes, the climber is 8.2
m above the starting point.
a. How much work does the climber do on the backpack?
b. If the climber weighs 645 newtons, how much work does she do lifting herself and the
backpack?
c. What is the average power developed by the climber?
3. You have an after school job carrying cartons of new copy paper up a flight of stairs, and then
carrying recycled paper back down the stairs. The mass of the paper does not change. Your
physics teacher says that you do not work all day, so you should not be paid. In what sense is the
physics teacher correct? What arrangement of payments might you make to ensure that you are
properly compensated?
72
Work and Energy
PURPOSE
The purpose of this activity is to compare the work done on a cart to the change in kinetic energy of
the cart. Determine the relationship of work done to the change in energy.
EQUIPMENT
- PASPORT Xplorer GL
- Dynamics Track
- Mass Set
- PASPORT Motion Sensor
- Dynamics Car
- String
- PASPORT Force Sensor
- Super Pulley with Clamp
BACKGROUND
For an object with mass m that experiences a net force Fnet over a distance d that
W = Fnet d
is parallel to the net force, the equation on the right shows the work done, W.
If the work changes the object's vertical position, the object's gravitational potential energy changes.
However, if the work changes only the object's speed, the
object's kinetic energy, KE, changes as shown in the next W = ΔKE = KE − KE = 1 mv 2 − 1 mv 2
f
i
f
i
equation where W is the work, vf is the final speed of the
2
2
object and vi is the initial speed of the object.
PREVIEW
Use a Force Sensor to measure the force applied to a cart by a string attached to a descending mass.
Use the Motion Sensor to measure the movement of the cart as it is pulled by the string. Use the
Xplorer GLX to record and display the force and the motion. Determine the work done on the
system and the final kinetic energy of the system. Compare the work done to the final kinetic energy.
PREDICTION (record answers to questions in the Questions & Calculations section)
1. As work is done to accelerate a cart, what will happen to its kinetic energy?
2. How would the work done on the cart compare to its final kinetic energy?
PROCEDURE
GLX Setup
1. Turn on the GLX ( ) and open the GLX setup file labeled work
energy. To open a specific GLX file, go to the Home Screen
( ). In the Home Screen, select Data Files and press
to
activate your choice. In the Data Files screen, use the arrow keys
to navigate to the file you want. Press
to open the file. Press
the Home button to return to the Home Screen. Press
to open
the Graph.
• The file is set up to measure force 50 times per second (50 Hz)
and to measure motion 20 times per second (20 Hz). The Graph
screen opens with a graph (Graph 1) of Position (m) and Time (s). The file also has a second
graph (Graph 2) of Force (N) versus Position (m). (go to
to switch between graphs).
2. Connect the Motion Sensor to sensor port 1 on the GLX and connect the Force Sensor to sensor
port 2. Be sure the pins are aligned properly, and then press firmly.
3. Set the range selection switch on top of the Motion Sensor to the ‘near’ (cart) setting, as shown
in Fig 1.
4. Check that the Dynamics Track is level and adjust the leveling screw on the left side as needed.
5. Be sure the Super Pulley with Clamp at the right end of the track is secure, and the Motion
Sensor at the left end of the track is aimed directly at the pulley.
73
6. Add two 100 g of mass to the cart. The cart is 500 g. The Force Sensor is 100 g of mass.
7. Press the ZERO button on the Force Sensor to reset the sensor
8. Attach a string to the cart and put the string over the pulley. Adjust the length of the string so that
when the cart is almost to the pulley, the end of the string almost reaches the floor.
(Note: if you ZERO the sensor again later, be sure you remove the string first so there is no
force!)
9. Put a 50 g mass on the end of the string. The mass hanger is another 5 g. Adjust the pulley up or
down so the string is parallel to the track.
10. The kinetic energy of the system depends on all the mass that is in motion. Add up the total mass
(cart & mass, sensor, hanger & mass) and record in the Lab Report.
Fig. 2: Equipment setup
•
NOTE: The procedure is easier if one person handles the cart and a second person handles the
Xplorer GLX.
11. Pull the cart away from the pulley until the cart is about 15 cm from the Motion Sensor. (The
sensor doesn’t work well with a distance less than 15 cm).
12. Support the Force Sensor’s cable so the cart can move freely.
13. Press Start
14. Press
•
•
to start recording data. Release the cart so it moves toward the pulley.
to stop data recording just before the cart reaches the pulley.
NOTE: Catch the cart before it hits the end stop on the track.
NOTE: You may need to try several Runs before you get good data. Be sure to look at the
correct Run (see Fig 3 and information below).
DATA & ANALYSIS
Use the Graph screen to examine the Position versus Time and the Velocity
versus Time data. Use the second graph (Graph 2) to examine the Force
versus Position.
1. To change the Graph screen to show a specific run of data, press
to
activate the vertical axis menu. Press the arrow keys (
) to move to
‘Run #_’ in the upper left hand corner. Press
to open the
menu, select the data run in the menu, and press
to
activate your choice.
2. Change the Graph screen to show Velocity versus Time. Press
to activate the vertical axis. Press
to open the
vertical axis menu. Use the arrow keys to select ‘Velocity’
and press
again to activate your choice.
3. Move the cursor to the maximum value of velocity and record
the value in the Data Table.
74
Fig. 3: Select data run
Fig. 4: Select ‘Velocity’
4. Switch to Graph 2. Press F4 (
activate your choice.
) to open the ‘Graphs’ menu. Select ‘Graph 2’ and press
to
5. Find the area under the curve. Move the cursor to the beginning of the data. Press F3 (
) to
open the ‘Tools’ menu. Select ‘Area Tool’ and press
to activate your choice.
6. The area under the curve is shown above the X-axis. Record the value as the work done.
7. Use the maximum velocity and the mass of the system (cart, sensor, string, hanging mass) to
calculate the final kinetic energy of the system.
8. Please Delete All Runs when you are finished with the lab so the next class starts with No Data.
QUESTIONS & CALCULATIONS
Prediction
1. As work is done to accelerate a cart, what will happen to its kinetic energy?
2. How would the work done on the cart compare to its final kinetic energy?
Data
Sketch a graph of velocity versus time and a graph of force versus position for one run of data.
Include units and labels for your axes.
75
Data Table
Item
Value
Mass of system, total
Velocity, maximum
Work done
Kinetic energy, final
Percent difference
Calculations
Use the mass of the system and the final (maximum) velocity to calculate the final kinetic energy of
1
the system. Kinetic energy is KE = mv 2 where m is the mass and v is the velocity.
2
Calculate the percent difference between the work done (area under force-position curve) and the
final kinetic energy.
%diff =
W − KE
× 100% .
W + KE
2
Questions
1. What happens to the kinetic energy as work is done on the system?
2. How does the final kinetic energy compare to the work done? Refer to the calculation for the
percent difference between the work done and the final kinetic energy.
3. The kinetic energy is measured in joules and the work done is measured in newton•meters (N m).
What is the relationship between a joule and a newton•meter?
4. Do your results support your predictions? What sources of error account for the difference
between work and energy?
76
Conservation of Energy
PURPOSE
To use the principle of conservation of mechanical energy (elastic potential, gravitation potential,
and kinetic energy), comparing the initial and final energy of a system.
EQUIPMENT
- dynamics carts
- mass set and hanger
- block mass
- pulley & string
- photogate timers
- meter stick & ruler
PROCEDURE
PART A – ELASTIC (SPRING) POTENTIAL TO KINETIC ENERGY
dynamics cart with
block and flag
m1
end
stop
photogate timer
1. Begin by using the dynamics cart with the built-in plunger to store elastic potential energy. The
cart is 500 grams, the block is 500 grams and the flag is 17 grams. Record the mass m1 in
kilograms below.
2. Measure the depth of the plunger; that is, measure how far the plunger protrudes from the surface
of the dynamics cart, in meters. This is the amount of spring displacement, x.
3. Now measure the width of the black flag on the cart, in meters. This distance will be used to
calculate the velocity of the cart.
4. Push the plunger in (and slightly up) until it is even with the end of the cart. Do not push it any
farther in or it will jam. Set the cart on the dynamics track until the plunger lightly touches the
rubber bumper. Move the photogate timer back so that the plastic flag on the cart will trigger the
timer just after the released plunger loses contact with the bumper.
5. Turn the photogate timer to Gate Mode, which measures the time for the plastic flag to pass
through the gate. Release the plunger by tapping it with another black block. Record the time in
the table below. Repeat four more times. Ignore obvious outliers.
DATA &ANALYSIS
mass of cart w/ flag (m1): ________ plunger depth (x): ________ black flag width (d): _________
t1 (s)
t2 (s)
t3 (s)
t4 (s)
t5 (s)
tave (s)
1. Calculate the cart’s velocity, in meters per second, by dividing the black flag width by the
average time.
77
2. Set the elastic potential energy equal to the kinetic energy, and solve for the spring constant of
the plunger.
PROCEDURE
PART B – GRAVITATIONAL POTENTIAL TO KINETIC ENERGY
dynamics cart with
block and flag
m1
end stop
pulley
accessory
photogate
photogate timer
mass hanger
m2
1. Attach the string to the dynamics cart and the mass hanger as shown above. Use the method
shown in class to make it easier to take the string off at the end of the lab.
2. Place 45 grams of mass on the 5-gram mass hanger. Recall that the dynamics cart is 500 grams,
the block is 500 grams, and the photogate flag is 17 grams. Record the cart/block/flag mass m1
and the hanger/mass m2 in kilograms, in the space below.
3. Pull the cart back until it touches the rubber bumper on the dynamics track. This will be the
release point for the cart for the entire lab. Move the photogate timer back so that the flag on the
cart will immediately trigger the timer when the cart is released. The initial velocity of the cart
will now be zero. Place the other photogate about 0.70 m away from the photogate timer. With a
meter stick, carefully measure the distance between the photogates. Record the distance, in
meters below.
4. Turn the photogate timer to Pulse Mode, which measures the time between gates. Also set it to
the 1 ms setting. Release the cart with someone ready to catch it after it passes through the
second photogate. Record the time in your lab book below. Repeat four more times. Ignore
obvious outliers.
DATA &ANALYSIS
Distance between photogates (Δx): ____________ m1: ____________
t1 (s)
t2 (s)
t3 (s)
t4 (s)
t5 (s)
m2: ____________
tave (s)
1. Use an appropriate kinematic equation to calculate the final speed of the system.
78
2. Calculate the final kinetic energy of the system. Remember to include both masses.
3. Calculate the initial potential energy of the system. Careful! Which mass has a change in
gravitational potential energy? (Recognize that the change in vertical position of the hanging
mass is equal to the photogate distance measured earlier.)
4. Calculate the percent difference (not error) between the initial and final energy of the system.
difference % =
QUESTIONS & CALCULATIONS (Show all work and evidence for answer)
1. There is some error in this lab that comes from not investigating all possible energies of the
system. What energies did we ignore?
2. Why is it generally easier to investigate mechanics using energy conservation than to use
Newton’s laws?
3. Honors only: If the dynamics track is set at an angle of 15˚ to the horizontal, how far up the
track would the cart go if it is launched using the spring plunger from Part I?
79
Conservation of Momentum
PURPOSE
To investigate the principle of conservation of momentum in separations (explosions), elastic
collisions, and perfectly inelastic collisions.
EQUIPMENT
- dynamics track
- photogate timer with accessory photogate
- dynamics carts and flags
- meter stick
d
negative
direction
photogate
flag
positive
direction
cart 2
accessory
photogate
photogate timer
PROCEDURE
1. You will be measuring photogate times which allows you to calculate cart velocity and
momentum (remember, both are vectors so +/- direction is important.) Each cart has a mass of
500 g, and the photogate flags are 17 g.
2. Begin by using the dynamics cart with the built-in plunger to generate an explosion between
carts. Push the plunger in and slightly up until it is even with the end of the cart. Do not push it
any farther in or it will jam. Place the carts face-to-face on the track.
3. Place the carts together between the photogate timers, but off to the left side so that the left gate
triggers before the right gate triggers. You will measure the velocity of each cart with the timer
in GATE mode, by calculating v = d/t where d is the flag width (measured to the tenth of a
millimeter!).
flag width, d, (in meters): _____________
4. You will use one photogate system to measure two times by setting the MEMORY on. Only the
first time displays on the timer. To get the second time, toggle to READ, and then subtract the
first time from the READ time. For example if the first time displays 0.0685 s and the READ
time is 0.136 s, then the second time is 0.136 - 0.0685 = 0.0675 s.
6. Be sure that one photogate is triggered on and off before the other is triggered on. The proper
placement of both photogates is very important for collecting good data with little error!
7. Use a metal block to tap and release the plunger. Don't let the carts rebound & retrigger the
timers. Make three trials and record the times in the tables. Repeat each trial from the same
position on the track and leave the photogates in the same position.
8. Place a 500 g block in cart 2, repeat three trials, and record all data in the table.
DATA & ANALYSIS
1. Complete the data tables, which include calculating initial and final velocities, initial and final
momentum, and initial and final kinetic energy of each cart in the system.
80
PART A - CARTS SEPARATING
plunger
catch
cart
here
cart 1
cart 2
accessory
photogate
photogate timer
mass
(kg)
time #1
(s)
time #2
(s)
time #3 time ave
(s)
(s)
catch
cart
here
vi
(m/s)
vf
(m/s)
pi
(kgm/s)
pf
(kgm/s)
KEi
(J)
cart 1
0
0
0
cart 2
0
0
0
mass
(kg)
time #1
(s)
time #2
(s)
time #3 time ave
(s)
(s)
vi
(m/s)
vf
(m/s)
pi
(kgm/s)
pf
(kgm/s)
KEi
(J)
cart 1
0
0
0
cart 2
+500g
0
0
0
KEf
(J)
KEf
(J)
QUESTIONS & CALCULATIONS
1. For part A, calculate the percent difference between the magnitude (absolute value) of the final
momentum of one cart with the other cart. Do this for the equal mass trials, and then again for
the unequal mass trials.
equal mass
unequal mass
2. In each separation of the carts, where did the kinetic energy come from?
3. In the second set of trials, why does the smaller mass (cart 1) have more kinetic energy than the
larger mass (cart 2 + 500 g)?
81
PART B - PERFECTLY INELASTIC COLLISION
plunger
velcro
cart 1
end stop
cart 2
photogate timer
accessory
photogate
PROCEDURE
1. Arrange the carts with the Velcro tabs aligned so that the carts will stick together after the
collision. The stationary cart must have the side with no magnets facing the plunger cart.
2. Set up the photogate timers so that the velocity of one cart before the collision and the velocity of
both carts after the collision can be measured, as shown above. Triggering should occur as soon
as possible for best results. (Note: it’s important that cart 2 is set up beyond both photogates
initially, as shown in the diagram.
3. Use the plunger for launching, set at the second click in, not all the way. Send the plunger cart
into the stationary cart, so that they stick together and pass through the second photogate. Record
the times in the table below. Remember to subtract from read times!
4. Place a 500 g block on the stationary cart and repeat. Record all times in the table.
mass
(kg)
time #1
(s)
time #2
(s)
time #3 time ave
(s)
(s)
vi
(m/s)
vf
(m/s)
pi
(kgm/s)
pf
(kgm/s)
KEi
(J)
KEf
(J)
cart 1
cart 2
0
mass
(kg)
time #1
(s)
time #2
(s)
time #3 time ave
(s)
(s)
vi
(m/s)
0
vf
(m/s)
pi
(kgm/s)
0
pf
(kgm/s)
KEi
(J)
KEf
(J)
cart 1
cart 2
+500g
0
0
0
QUESTIONS & CALCULATIONS
1. For part B, calculate the percent difference between the initial momentum of the system and the
final momentum of the system. Do this for the equal mass trials, and then again for the unequal
mass trials.
equal mass
unequal mass
2. For these perfectly inelastic collisions, why isn’t kinetic energy conserved?
82
PART C - ELASTIC COLLISION
plunger
magnets
end stop
cart 1
cart 2
photogate timer
photogate timer
PROCEDURE
1. Turn the stationary cart around so the repelling magnets in both carts face each other to create an
elastic collision. Put the photogate flag back in the stationary cart.
2. Again use the plunger for launching, set at the second click in, not all the way. Send the plunger
cart into the stationary cart. With equal masses the carts will switch velocities (why?) so only
one final velocity is measured. Record all times in the table below.
3. Place a 500 g block in the stationary cart and repeat the elastic collision. This time the plunger
cart will rebound, so a third time must be measured. This is not possible with one photogate and
its accessory gate, so join another lab group and use two photogate timers without the accessory
gates. Record all times in the table below. (Initial time for cart 1 goes above the dotted line, final
time for cart 1 goes below the dotted line.)
mass
(kg)
time #1
(s)
time #2
(s)
time #3 time ave
(s)
(s)
vi
(m/s)
cart 1
vf
(m/s)
pi
(kgm/s)
0
cart 2
0
mass
(kg)
time #1
(s)
time #2
(s)
time #3 time ave
(s)
(s)
vi
(m/s)
pf
(kgm/s)
0
0
vf
(m/s)
KEi
(J)
pi
(kgm/s)
KEf
(J)
0
0
pf
(kgm/s)
KEi
(J)
KEf
(J)
cart 1
cart 2
+500g
0
0
0
QUESTIONS & CALCULATIONS
1. For part C, calculate the percent difference between the initial momentum of the system and the
final momentum of the system. Do this for the equal mass trials, and then again for the unequal
mass trials.
equal mass
unequal mass
2. Has kinetic energy been conserved for these elastic collision? Calculate the ratio of KEfinal to
KEinitial to best answer this question.
83
Model Rockets
PURPOSE
To investigate the principles of rocket flight. To build and launch a toy rocket, and to apply laws of
mechanics to analyze the vertical motion of the launched rocket.
DATA
Rocket model: ____________________
Rocket mass (in kg) with recovery wadding, but without the engine: ____________________
The table below includes data that is common to all groups, plus your group’s angles for launch:
Air Resistance on rocket
when using A8-3 engine
Engine Masses
Engine Stage Mass (kg)
Initial
0.0163
End Thrust
0.0131
End Coast
0.0105
Rocket Type
Awesome
Alpha
Wizard
Viking
Air Resist. (N)
0.44
0.47
0.54
0.56
Angle
Measurements
Angle a
1.
2.
3.
Angle b
4.
5.
6.
DATA & ANALYSIS
MAXIMUM MEASURED ALTITUDE
1. Calculate the rocket’s measured altitude using the data collected during the launch and the
equation shown below. Be sure to show all data and average angle calculations.
h
A
a
b
h=
B
ABsin(a)sin(b)
sin(a + b)
ROCKET MASS
2. Calculate the rocket’s mass at each engine stage listed above: Average Thrust Stage m1, End
Thrust Stage m2, and Average Coast Stage m3.
84
THRUST STAGE
3. Calculate the impulse from each of the forces (lift from engine, gravity, air resistance) acting on
the rocket during the Thrust Stage.
4. Use the impulse-momentum theorem to calculate the rocket’s velocity at the end of the Thrust
Stage.
5. Use an appropriate kinematic equation to calculate the upward vertical displacement of the
rocket during the Thrust Stage.
COAST STAGE
6. Calculate the rocket’s kinetic energy at the beginning of the Coast Stage (this is the same as the
end of the Thrust Stage.)
7. Use the conservation of energy equation to calculate the rocket’s vertical displacement during
the Coast Stage. Set the zero level for potential energy at the height where the Coast Stage
begins.
MAXIMUM PREDICTED ALTITUDE
8. Add the Thrust Stage and the Coast Stage displacements to determine the maximum predicted
altitude of the rocket above the ground level where it was launched.
85
QUESTIONS & CALCULATIONS
1. Calculate the percent difference between the maximum measured altitude and the maximum
predicted altitude.
2. Give a detailed account for any discrepancy between the actual and predicted altitudes.
3. Use a kinematic equation to calculate the rocket’s acceleration during the thrust stage.
4. Use a kinematic equation to calculate the rocket’s acceleration during the coast stage.
5. Calculate what the maximum altitude would be without air resistance. Use separate paper to
show all your work for this problem.
6. Use your altitude from the previous question to calculate the speed of the rocket as it hit the
ground if there were no air resistance. Use separate paper to show all your work for this problem.
7. Honors only: Calculate the actual drag force for the rocket. Show that this answer is accurate by
recalculating the predicted altitude and comparing to the actual altitude. Use separate paper to
show all your work for this problem.
86
Energy, Momentum, and Relativity Review
Multiple choice. Circle the best answer.
1 A librarian picks a 2.0-kilogram book up 1.5 meters
from the floor. She then carries it 15 meters to a
bookshelf. Raising it an additional 0.5-meter, she
places it on the bookshelf. How much work has she
done on the book?
(A) 3.92 J
(C) 39.2 J
(B) 30 J
(D) 333 J
8 A 3-gram bullet traveling horizontally at 400 m/s hits a
3-kilogram wooden block, which is initially at rest on a
frictionless horizontal table. The bullet buries itself in
the block without passing through. The speed of the
block after the collision is
(A) 1.33 m/s
(C) 12.0 m/s
(B) 0.40 m/s
(D) 40.0 m/s
2 A spring has a spring constant of 120 newtons per
meter. How much potential energy is stored in the
spring as it is stretched 0.20 meter?
(A) 2.4 J
(C) 12 J
(B) 4.8 J
(D) 24 J
9 The diagram below shows two carts on a horizontal,
frictionless surface being pushed apart when a
compressed spring attached to one of the carts is
released Cart A has a mass of 3.0 kilograms and cart B
has a mass of 5.0 kilograms. The speed of cart A is 0.33
meters per second after the spring is released.
3 A 10-newton force is required to move a 3.0-kilogram
box at constant speed. How much power is required to
move the box 8.0 meters in 2.0 seconds?
(A) 40 W
(C) 15 W
(B) 20 W
(D) 12 W
4 A bullet traveling at 5.0 × 102 meters per second is
brought to rest by an impulse of 50 newton-seconds.
What is the mass of the bullet?
(A) 2.5 × 104 kg
(C) 1.0 × 10-1 kg
(B) 1.0 × 101 kg
(D) 1.0 × 10-2 kg
If the carts are initially at rest, what is the approximate
speed of cart B after the spring is released?
(A) 0.12 m/s
(C) 0.33 m/s
(B) 0.20 m/s
(D) 0.55 m/s
10 A 2.5-kilogram stone is released from rest and falls
toward the Earth. After 4.0 seconds, its momentum is
(A) 98 kg·m/s
(C) 39 kg·m/s
(B) 78 kg·m/s
(D) 24 kg·m/s
5 A box weighing 1.0 × 102 newtons is dragged to the
top of an incline, as shown below.
The gravitational potential energy of the box at the top
of the incline is approximately
(A) 1.0 × 102 J
(C) 8.0 × 102 J
(B) 6.0 × 102 J
(D) 1.0 × 103 J
6 A cart of mass M on a frictionless track starts from
rest at the top of a hill having height h1, as shown in
the diagram below.
Mg(h1 − h2 )
12 A 2-kilogram mass moving with a speed of 5 meters
per second to the right strikes a wall. It rebounds,
moving with a speed of 3 meters per second to the left.
The magnitude of the change in the momentum of the
mass is:
(A) 4 kg·m/s
(C) 16 kg·m/s
(B) 8 kg·m/s
(D) 32 kg·m/s
13 A student drops two eggs of equal mass simultaneously
from the same height. Egg A lands on the tile floor and
breaks. Egg B lands intact, without bouncing, on a
foam pad lying on the floor. Compared to the
magnitude of the impulse on egg A as it lands, the
magnitude of the impulse on egg B as it lands is
(A) less
(B) greater
(C) the same
What is the kinetic energy of the cart when it reaches
the top of the next hill, having height h2?
(A) Mgh1
(C) Mg(h2 − h3 )
(B)
11 A cart is moving at 4.0 meters per second at the top of a
hill 6 meter high. It rolls down the hill and up an
adjoining hill 5 meters high. What is the cart’s speed
when it reaches the top of the second hill? (Assume
there is no friction.
(A) 2 m/s
(C) 6 m/s
(B) 4 m/s
(D) 8 m/s
14 A horizontal force of 500 newtons is applied to a 200kilogram cart for a distance of 10 meters. The kinetic
energy gained by the cart is
(A) 25 J
(C) 5000 J
(B) 2000 J
(D) 10000 J
(D) 0
7 A cart of mass m traveling at speed v has kinetic
energy KE. If the mass of the cart is doubled and its
speed is halved, the kinetic energy of the cart will be
(A) halved
(C) quartered
(B) doubled
(D) quadrupled
87
15 If the speed of a moving object is doubled, which
quantity must also double?
(A) momentum
(C) acceleration
(B) kinetic energy
(D) potential energy
HONORS ONLY – QUESTIONS #27-#32
27 The unstretched spring in the diagram below has a
length of 0.40 meter and spring constant k.
A weight is hung from the spring, causing it to
stretch to a length of 0.60 meter.
16 In an elastic collision between two particles
(A) neither particle loses any of its kinetic energy
(B) neither particle loses any of its momentum
(C) the velocity gained by one particle is equal to
that lost by the other
(D) the total kinetic energy before and after the
collision remains constant
17 A 5-newton force causes a spring to stretch 0.2 meter.
What is the potential energy stored in the stretched
spring?
(A) 1 J
(B) 0.5 J
(C) 0.2 J
(D) 0.1 J
18 An object of mass 1.0 kilogram is whirled in a
horizontal circle of radius 0.5 meter at a constant
speed of 2 meters per second. The work done on the
object during one revolution is
(A) 0 J
(B) 2.0 J
(C) 4.0 J
(D) 8.0 J
19 A postulate of Einstein’s theory of relativity is:
(A) moving clocks appear to run slower than when
at rest
(B) moving rods appear longer than when at rest
(C) light has both wave and particle properties
(D) the laws of physics must be the same for
observers moving with uniform velocity relative
to each other.
20 Repeat previous question, but replace the word
“postulate” with the word “consequence”.
How many joules of elastic potential energy are
stored in this stretched spring?
(A) 0.020 × k
(C) 0.18 × k
(B) 0.080 × k
(D) 2.0 × k
28 Block A has mass 2 kg and moves to the right at 10
m/s, block B has mass 3 kg and moves to the left at 5
m/s. After they collide head-on elastically their
velocities are, respectively: (use relative velocity!)
(A) -10 m/s, +5 m/s
(C) -8 m/s, +7 m/s
(B) -9 m/s, +6 m/s
(D) -5 m/s, +10 m/s
29 Camping equipment weighing 6000 newtons is pulled
across a frozen lake by means of a horizontal rope.
The coefficient of kinetic friction is 0.05. The work
done by the campers in pulling the equipment 1000
meters at constant velocity is
(A) 1.5 × 105 J
(C) 6.0 × 105 J
5
(B) 3.0 × 10 J
(D) 6.0 × 106 J
30 A man pushes an 80-newton crate a distance of 5.0
meters upward along a frictionless slope at an angle
of 30˚ above horizontal. The force he exerts is
parallel to the slope. If the speed of the crate is
constant, then the work done by the man is
(A) -200 J
(C) 200 J
(B) 140 J
(D) 260 J
21 A millionaire was told in 1992 that he had exactly 15
years to live. However, if he travels away from the
Earth at 0.8c and then returns at the same speed, he
will live until the year
(A) 2001 (B) 2007 (C) 2010 (D) 2017
22 An observer notices a moving clock runs slow by a
factor of exactly 10. The speed of the clock is
(A) 0.995c (B) 0.900c (C) 0.990c (D) 0.100c
31 A 0.3 kg puck, initially at rest, is struck by a 0.2 kg
puck moving along the x-axis at 2 m/s. After the
collision, the 0.2 kg puck has a speed of 1 m/s at an
angle of 53˚ above the x-axis. After the collision, the
velocity of the 0.3 kg puck is now:
(A) 0.896 m/s, -26.6˚
(C) 0.269 m/s, 63.4˚
(B) 0.067 m/s, 3.81˚
(D) 1.07 m/s, -29.7˚
23 A meter stick moves at 0.95c in the direction of its
length through a laboratory. According to the
measurements taken in the laboratory, its length is
(A) 0.098 m (B) 0.31 m (C) 3.2 m (D) 1.0 m
32 According to relativity theory a particle of mass m
with a momentum of 2mc has a speed of
(A) 2c
(B) 4c
(C) c
(D) 0.89c
24 A particle with rest mass m moves with speed 0.6c.
Its kinetic energy is
(A) mc2 (B) 0.18mc2 (C) 0.25mc2 (D) 1.25mc2
25 A 3-gram bullet is fired horizontally into a 2kilogram block of wood suspended by a rope from the
ceiling. The block swings in an arc, rising 3
millimeters above its lowest position. The kinetic
energy of the block at the bottom of its swing is
(A) 0.0589 J
(C) 589 J
(B) 0.147 J
(D) 147 J
26 Referring to the previous question, the velocity of the
bullet before it struck the block was
(A) 0.242 m/s
(C) 242 m/s
(B) 0.162 m/s
(D) 162 m/s
88
ANSWERS
1 C
7
2 A
8
3 A
9
4 C
10
5 B
11
6 B
12
A
B
B
A
C
C
13
14
15
16
17
18
C
C
A
D
B
A
19
20
21
22
23
24
D
A
D
A
B
C
25
26
27
28
29
30
A
D
A
C
B
C
31 D
32 D
Mousetrap Racecar Project
OBJECTIVE
Build a vehicle powered solely by the energy of one standard sized mousetrap that will travel the
greatest linear distance.
RULES
1. The car must be powered by a single mouse trap (size is about 1 3/4" × 3 7/8"). This is not a rat trap!
2. The mousetrap cannot be physically altered except for the following:
a. holes can be drilled in the wood base to mount the mousetrap to the car frame.
b. the spring can have a lever arm attached to it.
Note: the spring from cannot be altered in any other way (like adding more coils).
3. The device cannot have any additional potential or kinetic energy at the start other than what can be
stored in the mousetrap's spring itself. No extra springs, rubber bands, elastic, ramps, etc. are
allowed.
4. The mousetrap must be contained in the car and must propel the car by means of a wheel or wheels
in contact with the ground. A launcher or device that pushes the car from a stationary object is
prohibited.
5. The spring cannot be wound more than its normal rotation angle of 180 degrees.
6. The car must be started from a standstill by releasing the mousetrap spring in a manner that imparts
no additional energy to the vehicle (i.e., the vehicle may not be given a push start in the forward
direction or side direction.).
7. The trigger on the mousetrap can be, but doesn’t have to be, used to release the mousetrap.
8. No purchased mousetrap car kits will be accepted.
9. No use of Legos or K-nex, or any part designed specifically for the purpose of making a car part.
CONTEST
1. The racetrack will be on the smooth hallway floor (or in the gym if available).
2. Each group will have two attempts. The winner will be that car that has obtained the greatest
distance on any one of the two attempts. Any ties will be decided by a single run off between the
groups that tied.
3. Distance measurements will be determined by the forward displacement of the racecar. Distance will
be measured from the front of the tape at the starting line to the front of the car when it comes to
rest.
4. If the car curves to one side, only the forward distance at the point will be measured.
GRADING
See next page for grading rubric.
89
Mousetrap Racecar Grading Rubric
Checkpoint
Innovation
Craftsmanship Assembly
Competitio
n
Rank
Disassembly
Construction
Materials
Rules
Design
Energy
Progress
Each category will be graded on a 5-point rubric. Competition results count double.
5
4
3
2
• checkpoint includes
all details: group
names, racecar name,
1 photo and 1 movie,
3 or more results, and
written summary.
• race car uses spring
energy very efficiently
and completely.
• checkpoint missing
small details: group
names, racecar name,
1 photo and 1 movie,
3 or more results, and
written summary.
• race car uses spring
energy mostly
efficiently and
completely.
• checkpoint missing
some details: group
names, racecar name,
1 photo and 1 movie,
3 or more results, and
written summary.
• race car uses spring
energy somewhat
efficiently and
completely.
• checkpoint missing
most details: group
names, racecar name,
photo (or movie),
results (3 or more) and
written summary.
• race car uses spring
energy not efficiently
and completely.
• race car design uses • race car design uses • race car design uses • race car design does
very creative and
mostly creative and
somewhat creative and not use creative and
unique techniques.
unique techniques.
unique techniques.
unique techniques.
• race car design
complies with all rules
of competition.
• race car design has
minor issue that
doesn’t comply with
all rules.
• race car design has
major issue that
doesn’t comply with
all rules. (0 points)
• race car made from
very high quality
materials with great
• race car made from
mostly high quality
materials
• race car made from
mid quality materials
• race car made from
low quality materials
• race car very well
assembled and can
perform many races.
• race car fairly well
assembled and can
perform many races.
• race car fairly well
assembled and may
perform some races.
• race car poorly
assembled and won’t
perform many races.
• race car is built with • race car is built with • race car is built with • race car is built with
great skill and great good skill and good
fair skill and fair
poor skill and poor
attention to detail.
attention to detail.
attention to detail.
attention to detail.
• groups disassembles
the race car after the
competition,
recovering as much of
the materials as
possible.
• groups disassembles
the race car after the
competition,
recovering most of the
materials as possible.
• groups disassembles
the race car after the
competition,
recovering some of
the materials as
possible.
• groups does not
disassembles the race
car after the
competition.
• ranks in the 95th
percentile compared
with all groups in all
classes.
• ranks in the 75th
percentile compared
with all groups in all
classes.
• ranks in the 55th
percentile compared
with all groups in all
classes.
• ranks in the 35th
percentile compared
with all groups in all
classes.
90
Notes
91
Notes
92
Notes
93
Notes
94
Notes
95
Notes
96
Appendix A: Unit Conversion, the Right Way
A few years ago NASA launched a spacecraft called the Climate Orbiter designed to help relay
information about the possibility of past life on Mars. Ten months after leaving Earth, the spacecraft
began maneuvering into orbit around the Red Planet. Unfortunately the orbiter flew too close to the
Martian atmosphere, and to the shock and great disappointment of many NASA engineers, it burned into
pieces. The hopes and dreams of the mission were lost in an instant.
A week after the disaster, NASA reported that the $125 million Climate Orbiter was lost because the
engineering team that manufactured the spacecraft in Colorado used metric units while the mission
navigation team in California used English units. They simply forgot to check for unit conversion.
That’s a small mistake that wasted a large amount of taxpayers’ money.
In physics, we often need to convert units either from one system to another, as in English to metric
units, or even just from one power of ten to another, as in millimeters into meters. Surprisingly, many
physics students do not know how to convert units, or have poor habits in attempting to convert units.
Enough is enough - you should all get this straightened out immediately! A teacher might say “If I had a
nickel for every time a student made a simple unit conversion mistake...” Well, this teacher wouldn’t
retire early, but it’d be a lot of money.
So let’s practice this technique. First, let’s look at a conversion from metric to English. For example,
there are 1609 meters in a mile, so how many miles are there in a 10,000-meter race? (Common
conversions and prefixes are listed in the back of the textbook and the lab manual.)
1 mile
10, 000 meters ×
= 6.215 miles
1609 meters
Easy, right? Notice a few things. First, the fractions are written vertically. Never write fractions that
slant (for example, 1 mile/1609 meters). Also note that the unit of meter cancels properly, like numbers
in fractions do, because it appears in numerator of one fraction and the denominator of the other (10,000
meters doesn’t appear as a fraction, but division by 1 is implied).
Now, let’s try a harder one. Let’s convert 65 miles per hour into meters per second.
65
miles 1609 meters
1 hour
1 minute
m
×
×
×
= 29.05
s
hour
1 mile
60 minutes 60 seconds
Notice that the conversion between miles and meters is used again, but this time the fraction is
reciprocated so that proper cancellation occurs. Also, if you remember that there are 3600 (60 squared)
seconds in an hour you can simplify this. And, if you look up the direct conversion from miles per hour
to meters per second, this would simplify the calculation even more.
Next, what about conversions that involve powers of ten, where prefixes are used to denote specific
powers of ten? For example, let’s convert 10,000 kilometers into millimeters. Recall that kilo- means
103 and milli- means 10-3.
10 3 meters 1 millimeter
10, 000 kilometers ×
× −3
= 1010 millimeters
1 kilometer 10 meters
Be aware that a prefix describes a particular power of ten. A mistake is often made with conversions that
are usually well understood, like 100 centimeters in a meter. Yes, that is a true statement, but you might
mistakenly think that centi- means 102 - it does not! The power of ten may then be changed incorrectly
when fractions are done mentally, without care. It’s better to be careful and actually write out the unit
analysis, than to just try to do it in your head. For example the length wavelength of red light is 660
nanometers (nm), so when converting to centimeters, set up the unit analysis as follows:
660 nanometer ×
10 −9 meter
1 centimeter
× −2
= 6.60 × 10 −5 centimeters
1 nanometer 10 meter
97
Practice Problems
Show all work by setting up the proper fraction for each conversion, show cancellations, and then
determine the final result. Express answers in scientific notation with 3 significant figures. Use the
prefix table conversions table in the back of the textbook or lab manual as a reference.
1. Convert 2600 feet into meters.
2. Convert 1300 kilometers into inches.
3. Convert 220 centigrams into kilograms.
4. Convert 55 miles per hour into feet per second.
5. Convert 42.3 centimeters into nanometers.
6. Convert 350 megabytes into terabytes.
7. Convert 5 x 107 gigajoules into picojoules.
8. Convert 8.30 kilopounds into newtons.
2
7
-3
1
Answers: 1. 7.92 × 10 meters 2. 5.12 × 10 inches 3. 2.20 × 10 kilograms 4. 8.07 × 10 ft/sec
5. 4.23 × 108 nanometers 6. 3.50 × 10-4 terabytes 7. 5.00 × 1028 picojoules 8. 3.69 × 104 newtons
98
Appendix B: Useful Information
1024
1021
1018
1015
1012
109
106
103
102
101
Prefixes
yotta (Y)
10-1
zetta (Z)
10-2
exa (E)
10-3
peta (P)
10-6
tera (T)
10-9
giga (G)
10-12
mega (M)
10-15
kilo (k)
10-18
hecto (h)
10-21
deca (da)
10-24
English - Metric Conversion Factors
1 inch = 2.54 centimeters
1 foot = 30.48 centimeters
1 yard = 91.44 centimeters
1 mile = 5280 feet = 1609 meters
1 meter = 39.37 inches = 3.281 feet
1 pound = 4.448 newtons
1 horsepower = 745.7 watts
1 gallon = 3.785 liters
1 calorie = 4.187 joules
1 btu = 1055 joules
deci (d)
centi (c)
milli (m)
micro (µ)
nano (n)
pico (p)
femto (f)
atto (a)
zepto (z)
yocto (y)
Trigonometry
r
Constants
mass of earth
Me
5.97 × 1024 kg
mass of sun
Ms
1.99 × 1030 kg
mass of moon
Mm 7.36 × 1022 kg
radius of earth
Re
6.37 × 106 m
radius of moon
Rm
1.74 × 106 m
radius of sun
Rs
6.96 × 108 m
Earth-moon distance
3.84 × 108 m
Earth-sun distance
1.496 × 1011 m
speed of light
c
3.0 × 108 m/s
grav. constant
G
6.67 × 10-11 Nm2/kg2
Coulomb constant k
9.0 × 109 Nm2/C2
–
electron charge
e
–1.60 × 10-19 C
+
proton charge
e
+1.60 × 10-19 C
electron rest mass me 9.11 × 10-31 kg
proton rest mass
mp 1.673 × 10-27 kg
neutron rest mass mn
1.675 × 10-27 kg
y
θ
x
sin θ =
y
r
cosθ =
r = x 2 + y2
x
r
tan θ =
y
x
⎛ y⎞
θ = tan −1 ⎜ ⎟
⎝ x⎠
International System of Units (Metric)
Base Units
Physical quantity
Name of Unit Symbol
length
meter
m
mass
kilogram
kg
time
second
s
electric current
ampere
A
temperature
Kelvin
K
amount of substance mole
mol
luminous intensity
candela
cd
International System of Units (Metric)
Derived Units
Physical quantity
Name of Unit Symbol
frequency
hertz
Hz
energy
joule
J
force
newton
N
power
watt
W
electric charge
coulomb
C
electric potential
volt
V
electric resistance
ohm
Ω
Percent Error
Percent Difference
Percent error is calculated to compare an
experimental value to a known value.
Percent Error =
Percent difference is calculated to compare
two experimental values to each other.
Known - Experimental
× 100%
Known
99
Percent Diff. =
Exp1 - Exp 2
× 100%
( Exp1 + Exp 2 ) / 2
Appendix C: Second Semester Equations
Kinematics
savg = average speed
vavg = average velocity
aavg = ave. acceleration
t = time
d = distance
Δx, Δy = displacement
Dynamics
ΣF = resultant (net) force
m, M = mass
Fg = force of gravity (weight)
Energy and Momentum
W = work
d = displacement
t = time
g = 9.8
P = power
N
kg
= grav. field strength
⎫
⎪
v f 2 = vi 2 + 2aΔx ⎬ OR Δy
⎪
Δx = 12 (vi + v f )t ⎭
Projectile motion
k = spring constant
Fn = normal force
Fr = air resistance (drag)
Fs = static friction force
Fk = kinetic friction force
µ s = coefficient of static friction
µ k = coefficient of kinetic friction
FT = tension
Fsp = spring force

ΣF = 0 (1st Law)


ΣF = ma (2nd Law)


F1,2 = − F2,1 (3rd Law)
t = time
Δx = horiz. displacement
Δy = vert. displacement
g = acceleration of gravity
Fs = µ s Fn
Fk = µ k Fn
Circular Motion & Gravitation
ac = centripetal acceleration
a = inst. acceleration
vi = initial velocity
v f = final velocity
d
Δx
Δv
vavg =
aavg =
t
t
t
v f = vi + at
savg =
Δx = vi t + 12 at 2
v = velocity
vx = horizontal velocity
vyi = initial vertical velocity
vyf = final vertical velocity
Components/Resultant:
vx = v cosθ v = vx 2 + vy 2
vy = vsin θ
θ = tan −1 (vy / vx )
Horizontal motion (ax = 0)
Δx = vx t
Vertical motion (g = −9.8
vyf = vyi + gt
Δy = vyi t + 12 gt 2
vyf 2 = vyi 2 + 2gΔy
Δy = 12 (vyi + vyf )t
m
s2
)
Fg = mg
Fsp = kΔx
Fc = centripetal force
Fg = gravitational force
vt = tangential speed
T = period
r, R = distance, orbital radius
vt2 4π 2 r
ac =
= 2
r
T
2π r
vt =
T
mv 2 4π 2 mr
Fc = t =
r
T2
Gm1m2
4π 2 R 3
2
Fg =
T =
r2
GM
Torque
τ = Fd sin θ = F⊥ d
Στ = 0 (equilibrium)
100
KE = kinetic energy
GPE = grav. potential energy
EPE = elastic potential energy
TE = thermal energy (heat)
Fk = kinetic friction force
I = impulse
p = momentum
W = Fd cosθ
W
P=
= Fv
t
KE = 12 mv 2
GPE = mgh
EPE = 12 kx 2
TE = Fk d
W + KEi + PEi = KE f + PE f + TE
I = Ft
Ft = mΔv
p = mv
m1v1i + m2 v2i = m1v1 f + m2 v2 f
Relativity
γ = Lorentz factor
v = relative velocity
c = speed of light
t 0 = time in observer's frame
t = time in another frame
L0 = length in observer's frame
L = length in another frame
v2
γ = 1/ 1− 2
c
t = γ t0
E = γ mc 2
L=
L0
γ
p = γ mv
KE = (γ − 1)mc 2