Download Unit 5 - Youngstown City Schools

Youngstown City Schools
SCIENCE: PHYSICS
UNIT #5: MOMENTUM- - (4 Weeks) 2013-2014
SYNOPSIS: In this his unit students learn what variables and factors are involved when two objects collide. The also learn 2
types of collisions - - elastic and inelastic - - and the difference between static and kinetic friction in solids vs liquids.
Students will become highway accident investigators and analyze a crash scene to determine who is at fault.
STANDARDS
VII.
MOMENTUM
A. The students will assess the vector nature of momentum and its relation to the mass and velocity of an object.
B. The students will demonstrate their knowledge of momentum, p, is a vector quantity that is directly proportional to the
mass, m, and the velocity, v, of the object. Momentum is in the same direction the object is moving and can be
mathematically represented by the equation, p=mv.
C. The students will demonstrate their understanding of impulse, Δp, is the total momentum transfer into or out of a
system. Any momentum transfer is the result of interactions with objects outside the system and is directly proportional
to both the average net external force acting on the system, Favg, and the time interval of the interaction, Δt. It can
mathematically be represented by Δp = pf – pi = Favg Δt.
D. The students will analyze the factors required to produce a change in momentum.
E. The students will demonstrate their understanding of the conservation of linear momentum that states that the total
(net) momentum before an interaction in a closed system is equal to the total momentum after the interaction. In a
closed system, linear momentum is always conserved for elastic, inelastic and totally inelastic collisions.
F. The students will analyze one-dimensional interactions between objects and recognize that the total momentum is
conserved in both collision and recoil situations.
G. The students will assess real world applications of the impulse and momentum, including but not limited to, sports and
transportation.
H. The students will demonstrate their understanding of vector properties of momentum and impulse as introduced and
used to analyze elastic and inelastic collisions between objects.
I. The students will analyze experimental data collected in laboratory investigations.
VIII. ELASTIC FORCES
A. The students will demonstrate their knowledge of how elastic materials stretch or compress in proportion to the load
they support. The mathematical model for the force that a linearly elastic object exerts on another object is Felastic =
kΔx, where Δx is the displacement of the object from its relaxed position. The direction of the elastic force is always
toward the relaxed position of the elastic object. The constant of proportionality, k, is the same for compression and
extension and depends on the “stiffness” of the elastic object.
IX.
FRICTION FORCES
A. The students will demonstrate their knowledge of the amount of kinetic friction between two objects is dependent on
the electric forces between the atoms of the two surfaces sliding past each other. It also is dependent on the
magnitude of the normal force that pushes the two surfaces together. This can be represented mathematically as Fk =
μkFN, where μk is the coefficient of kinetic friction that depends upon the materials of which the two surfaces are
made.
B. The students will learn that static friction can prevent objects from sliding past each other, even when an external force
is applied parallel to the two surfaces that are in contact.
C. The students will learn that the mathematical equation for static friction is Fs ≤ μsFN.
D. The students will demonstrate their knowledge of the maximum amount of static friction possible depends on the types
of materials that make up the two surfaces and the magnitude of the normal force pushing the objects together, Fsmax
= μsFN.
E. The students will gain an understanding that the external net force exceeds the maximum static friction force for the
object, the objects will move relative to each other and the friction between them will no longer be static friction, but will
be kinetic friction. The students will gain an understanding that liquids have more drag than gases like air.
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LITERACY STANDARDS
RST.5 Analyze how the text structures information or ideas into categories or hierarchies, demonstrating understanding of the
information or ideas.
WHST.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing
on addressing what is most significant for a specific purpose and audience.
MOTIVATION
TEACHER NOTES
1. Teacher uses Newton’s Cradle as intro to unit; students explore with the cradle, and then
hypothesize why they think it works. Teacher lets them know that this is part of what they
will figure out in the unit.
2. Teacher has students recall the Egg Drop Labs in previous unit and hypothesize what an
egg will do if thrown with force into a sheet (make sure that the sheet is slanted so the
eggs will roll down, but not fall to the floor; it may be a good idea to put a plastic drop cloth
on the floor). Students hypothesize if the egg will break and why (if done correctly, the
egg does not break).
3. Students set both personal and academic goals for this Unit.
4. Preview the authentic assessment
TEACHING-LEARNING
TEACHER NOTES
1. Show YouTube video: Understanding Car Crashes: It’s Basic Physics (from the
Insurance Institute for Highway Safety) at http://www.youtube.com/watch?v=LdwnJIPEjFM
(VIIA, VIIB, VIIC, VIID, VIIF, VIIG)
2. Teacher discusses the term momentum, and gives definition. Students take notes and work
sample problems together using p = mv, where P = momentum, m = mass, and v = velocity. Δp
= pf – pi = Favg Δt (VIIB) Holt physics book: pages 84-96; 208-214; 215-221292-294
3. Reinforce the Newton cradle from Motivation #1 to transfer of momentum. See Tim Bakos
for Momentum in Collisions Lab and Impulse and Change in Momentum Lab.
4. Elastic and Inelastic Collisions. Elastic Collisions (when collision occurs, the two
items that collide, they bounce off each other (e.g., when you hit a car from behind, the
front car is pushed forward and they don’t say together): Use toy cars and demonstrate crash
simulations and students do calculations. Inelastic Collisions (damage during impact with no
bounce back): use ball rolling down a ramp into a box. Give other examples of each type of
collision and have students come up with the critical attributes of Elastic and Inelastic
Collisions. Have students give other examples in sports and games. (VIIB, VIIC, VIID, VIIE,
VIIF, VIIH, VII.I; VIIIA)
5. Conservation of Momentum (attached on page 4); ask students questions from the lab
and discuss the results. (VIIE, VII.I)
6. Teacher asks students questions about Friction: give instances where friction exists (e.g.,
tires on road when you brake; rubbing hands together; walking with friction between feet and
floor; have students come up with a definition of Friction. Prior to lab, teachers explains
variables in the equations and students work problems using the following equations Fk =
μkFN ; Fs ≤ μsFN; Fsmax = μsFN. Do Static and Kinetic Friction Lab - - See Tim Bakos
for this lab. Teacher drops a coin or marble from a set height; then does the same with a coin
or marble into a graduate cylinder of water or oil. Students can see that an object falling
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TEACHING-LEARNING
TEACHER NOTES
through the liquid is slower than falling through the air. (IXA, IXB, IXC, IXD, IXE IXF)
7. Elastic forces: Elastic Lab (attached as pages 5-7). Students conduct lab
TEACHER NOTES
TRADITIONAL ASSESSMENT
1. Unit Test
TEACHER NOTES
TEACHER CLASSROOM ASSESSMENT
1. 2- and 4-Point Questions
2. Lab Reports
TEACHER NOTES
AUTHENTIC ASSESSMENT
1. Students evaluate their goals for the Unit.
2. Traci’s accident thing www.aplusphysics.com/educators/activities/carcrash_home.html#task
Students produce a report from the perspective of an Auto Expert, or a Collision Expert,
or an Investigator Attached as pages 8-13. (RST.5; WHST.5)
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CONSERVATION OF MOMENTUM LAB
Purpose: To demonstrate conservation of momentum by means of the transfer of momentum from one
object to another
Materials:
Two 30 cm (12 inch) metric rulers
One, US Quarter or old British Penny
One, US dime or old European currency of similar size
Procedure:
 Place the ruler horizontally on a flat surface.
 Put the dime (or small coin) face down in contact with
one end of the ruler.
 Slide the quarter (or larger coin) sharply up against the other end of
the ruler.
 Momentum is transferred from the moving quarter to the stationary ruler/dime system.
 Measure how far the dime moves.
 Repeat the process, only this time, keep the larger coin in contact with the ruler and slide the
dime against the other end of the ruler.
 Measure how far the quarter (larger coin) moves
 Measure the mass of the smaller coin and the mass of the larger coin, find their ratio
 Measure the distance the smaller coin traveled and the distance the larger coin traveled, find
the ratio of their distances
Notice that the dime will move much further than the ruler. It should be mentioned here that the
amount of momentum given to the quarter should be approximately equal to the total momentum
transferred to the dime, minus some loss due to friction.
mv (before) = mv (after) for two objects with equal mass
M (quarter) v (quarter = m (dime) V (dime)
Data table
Mass of dime
Mass of quarter
Ratio
(dime/quarter)
Distance dime
traveled
Distance
quarter
traveled
Ratio dime distance/
quarter distance
Wrap up questions:
1. Compare the ratio of the two masses to the ratio of the two distances. Are they close?
2. Multiply the mass of the dime times the distance it traveled. What is your answer?
3. Multiply the mass of the quarter times the distance it traveled. What is your answer?
4. How did this lab demonstrate conservation of momentum?
5. What are your sources of error?
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LAB I: ELASTICITY
Problem: What is the relationship between the force applied to a spring and the stretch of the spring?
NOTE: DO NOT BEGIN YOUR EXPERIMENT UNTIL EACH PERSON IN THE GROUP HAS READ THE
BACKGROUND AND ANSWERED THE BACKGROUND QUESTIONS.
Background and Inquiry: Today you will study some properties of elastic bodies. An elastic body has
the ability to regain its original form after it is stretched. A spring is one example of an elastic body.
Observe the properties of the spring by pulling slowly on the spring and observe the tension in the spring.
DO NOT PULL THE SPRING TO FULL EXTENSION!! If an elastic body is stretched beyond a point
called the elastic limit, it will no longer retain its original properties. By feeling the tension on the spring
discuss with your group how changes in force may the affect the amount of stretch observed.
Many things in nature have elastic properties. A rubber band is one example. A spring is another. Can
you think of others? Discuss with your group several other examples of elastic bodies.
Take the rubber band and stretch it being careful not to extend it too far. Have each person in the group
observe the properties of the two elastic bodies (spring and rubber band). Discuss any differences in their
properties.
Today you will study the elastic properties of a spring and two different types of rubber band. Your
problem today is to determine the relationship between the force needed to stretch an elastic body and
the length it stretches. For your hypothesis try to predict the type of behavior you expect the spring and
rubber band to follow as you change the amount of force (mass weights) applied to the spring. For
example, would you expect if you double the weight the spring will stretch twice as much? Or three
times? What type of relationship do you predict will occur?
Background Questions:
1) What is an elastic body?
2) Give 4 examples of elastic bodies.
3) Do you think the elastic properties of all elastic bodies are the same? Why?
Hypothesis: State your hypothesis to the problem. Justify your reason. .
Materials: ruler, spring, set of weights, ring stand, two different types of rubber band
Procedure:
1) Copy Table I, Table II, and Table III into your lab notebook.
2) Set up the equipment as shown in in class.
3) Starting with the smallest mass, measure the amount the spring is stretched (difference in length
between spring without mass and with mass). See your class notes on how to measure this difference.
Use additional masses as shown in Table I below. For each mass measure the the stretch. DO NOT
EXCEED 500 GRAMS FOR THE SPRING.
3) Repeat step 3 using the rubber bands, instead of the spring.
Results: Note: To simplify this lab we will only use mass in your tables and graph. See your class notes
for clarification.
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TABLE I SPRING
Mass (g.)
Stretch (cm.)
100
200
300
400
500
TABLE II RUBBER BAND 1 (THIN)
Mass (g.)
100
Stretch (cm.)
200
300
400
500
600
700
800
TABLE III RUBBER BAND 2 (THICK)
Mass (g.)
Stretch (cm.)
100
200
300
400
500
600
700
800
Graph the data from Table I and Table II drawing two graphs, both on the same set of axis. Plot stretch
(cm.) on the y-axis and mass (grams) on the x-axis. Make sure to label each axis, and each plot. Measure
and record the slope of each plot Give the completed set of graphs a title
Discussion:
Be sure to include the following:
1) What type of mathematical relationship is demonstrated in Graph I? Why?
2) Does graph II and III show more than one relationship? For example, does the graph start off linear
then change? If so explain why.
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3) What are the variables in this experiment? Which is the dependent variable, which is the independent
variable?
4) How are the variables changing with relationship to each other?
5) What are some factors that are held constant in this experiment?
6) Can you predict what the stretch would be in Table I if 350 grams were attached to the spring? Why?
7) Can you predict what the stretch would be in Table I if 800 grams were attached? Why? or Why not?
Applications:
How can your graph be used to find the force of an unknown object?
2) Design an experiment to predict if a spring has been over-stretched and is deformed.
3) Research Hooke’s Law; how does it relate to this lab
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Car Crash WebQuest
Introduction
A traffic accident occurred in a 35 km/hr speed limit zone on Millway Street in which a 3000-kg
Cadillac Escalade SUV rear-ended a 2000-kg Subaru Outback Wagon that was stopped at a stop
sign. The entire police investigative division has gone on vacation to Bora Bora to relax, so the
mayor has contracted with you and your team of experts to determine what happened and what
traffic laws were broken.
Task
Your team will provide the mayor with a detailed accident report (including all equations and
work) that includes mass, velocity, and momentum of both vehicles both prior to and after the
collision. Further, the mayor has requested you create a visual demonstration / re-creation of
what happened to assist with the insurance company’s investigation. This may take the form of a
PowerPoint presentation, a 3’x4’ poster, a web site, or an annotated digital video.
The mayor has provided you with the following diagram drawn by police officers at the site of
the accident:
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Process
1. Each group member will choose one of the following roles. The group’s success will
depend upon how well each individual accomplishes their responsibilities.
a. Auto Expert: This individual will research the physics of linear motion and determine,
based upon accident site analysis, how fast the SUV and wagon were moving
immediately following the collision. (See Below)
b. Collision Expert: This individual will research the physics of basic collisions and
determine, based upon data provided by the auto expert, how fast the SUV was initially
moving. (See Below)
c. Investigator: This individual will research elastic and inelastic collisions, then analyze
the accident scene as well as reports from the auto expert and collision expert in order to
determine what type of collision occurred. (See Below)
2. Fulfill your individual roles. Before you can put together a comprehensive picture of
what happened, each individual member of the group must visit several websites and
research their portion of the accident in order to understand what is required and what
steps you must take in order to accomplish your mission. Click on the appropriate link
above to guide you through your role-specific tasks.
3. Design your written accident report. This should include a one-paragraph introduction, a
written step-by-step summary of what you believe occurred (including any appropriate
diagrams), any assumptions you made during the analysis, and a listing of what traffic
laws were broken, and by whom. Include a final paragraph describing why you would or
would not be interested in a career in accident investigation.
4. Design your final presentation, which visually and verbally explains to a non-technical
audience in a professional manner what your group believes occurred at each step of the
accident.
5. As a team, fill out a self evaluation for this project. Not only will you be assessing your
final result, but also your group with respect to each team member’s work ethic and
dedication. You will be evaluated based on the same criteria by your instructor.
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Evaluation
Work will be evaluated based on the attached rubric. Each group will self-assess based on
criteria. Self-assessments will be combined with the instructor's assessment for a total of 40
possible points.
Conclusion
Once the project is completed, students should have a solid understanding of momentum,
conservation of momentum, and inelastic and elastic collisions. Further, students will have
connected previous kinematics work with the newer topics of collisions and energy. Finally,
students will have been introduced to careers in accident investigation.
Teacher Notes
Teacher Notes
This activity was designed as a guided inquiry activity for Regents Physics students in groups of
three.
Prior to beginning this activity, students should be proficient in application of basic onedimensional kinematic equations, as well as basic metric conversions. It is expected that this
entire activity can be completed in the space of four class periods.
Although a full computer lab is recommended, this activity may be undertaken with one
computer per group (with students in groups fulfilling the individual roles). This activity can be
easily modified for more advanced classes by removing a given item or two, requiring the
students to work through simultaneous equations using both conservation of linear momentum
and the definition of a specific type of collision involving kinetic energy.
Related Curriculum Standards
1. Using the relationships of velocity, acceleration and displacement, students will describe
different forms of motion quantitatively, qualitatively, and graphically.
2. Students will explain how to calculate the change in an object's momentum.
3. Students will prove the Law of Conservation of Momentum.
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Auto Expert
Responsibilities
As the team expert in automobile kinematics and performance, it is your job to analyze the
accident site and determine the velocities of both the SUV and the wagon immediately following
the collision.
1. Review the kinematic equations for one-dimensional motion
o Link to APlusPhysics 1D Kinematics Page
o Physics Classroom Kinematic Equations
o PhysicsLab Online Kinematics
2. Analyze the diagram of the collision scene below. Note that the acceleration of a Subaru
Outback Wagon with the brakes locked is -3 m/s2, and the acceleration of a Cadillac
Escalade SUV with the brakes locked is -2 m/s2.
3. Using the information provided, and looking at just the time period AFTER the collision,
find the initial velocities of both the SUV and the wagon prior to their deceleration to
rest. Give this information to your team members.
4. Create a one-page type-written report (including appropriate diagrams and equations)
explaining your work and showing your derivations.
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Collision Expert
Responsibilities
As the team expert in collisions, it is your job to research the principles of conservation of
momentum. You will use this knowledge, along with data provided by the auto expert, to
determine the initial velocity of the SUV prior to the collision.
1. Research the qualitative and quantitative definitions of momentum, as well as the law of
conservation of momentum.
o Link to APlusPhysics Momentum Page
o Physics Classroom Momentum Page
o PhysicsLab Momentum Page
2. Read through a sample analysis of a similar collision in one dimension: Collisions in One
Dimension.
3. Using the information provided by the auto expert, calculate the total momentum of the
wagon/SUV system AFTER the collision. How does this compare to the total
momentum of the system BEFORE the collision?
4. Knowing the total momentum of the system BEFORE the collision, calculate the initial
velocity of the SUV (Hint: What is the initial velocity of the wagon? What is its initial
momentum?)
Create a one-page type-written report (including appropriate diagrams and equations) explaining
your work and showing your derivations.
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Investigator
Responsibilities
As the team coordinator and head investigator, it is your job to research elastic and inelastic
collisions and, using reports from the auto expert and collision expert, determine whether this
collision was elastic or inelastic in nature. Further, you are responsible for coordinating the work
of the entire team to insure that each team member is providing the appropriate information to
put together a comprehensive picture of what happened during the accident.
1. Research the qualitative and quantitative definitions of kinetic energy, as well as what
differences exist between elastic and inelastic collisions both qualitatively and
quantitatively.
o APlusPhysics Kinetic Energy
o APlusPhysics Collisions
o Physics Classroom Kinetic Energy
o PhysicsLab Kinetic Energy
2. Using the information provided by the auto expert and collision expert, determine
whether the accident you are investigating is elastic or inelastic. Examples of similar
situations may be used for reference:
o Physics Classroom Collisions
o Elastic and Inelastic Collisions
Create a one-page type-written report (including appropriate diagrams and equations) explaining
your work and showing your derivations.
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