Course: Physics

I. Grade Level/Unit Number: Physics Unit 4

II: Unit Title: Momentum

III. Unit Length: 7 days (block schedule) or 12 days (traditional schedule)

IV. Major Learning Outcomes:

This unit is focused on the concept of momentum. Students will learn about the relationships between force, time, mass, velocity, and momentum. Specifically students will be able to:

Application of Graphical and Mathematical Tools Momentum – Impulse:

Identify momentum as a vector quantity Recognize the relationship between force and time as it relates to changes

in momentumMomentum – Collisions:

Recognize elastic and inelastic collisions Solve problems using conservation of momentum Design and conduct experiments verifying conservation of momentum

V. Content Objectives Included (with RBT Tags):

COMPETENCY GOAL 1: The learner will develop abilities necessary to do and understand scientific inquiry.

1.01 Identify questions and problems that can be answered through scientific investigations.

(RBT B2, B3, C2, C3)

This goal and these objectives are an integral part of each of the other goals. In order to measure and investigate scientific phenomena, students must be given the opportunity to design and conduct their own investigations in a safe laboratory. The students should use questions and models to formulate the relationship identified in their investigations and then report and share those finding with othersStudents will be able to:

Develop questions for investigation from a given topic or problem.

Physics- Unit 4 DRAFT 1

1.02 Design and conduct scientific investigations to answer questions about the physical world.• Create testable hypotheses.• Identify variables.• Use a control or comparison group when appropriate.• Select and use appropriate measurement tools.• Collect and record data.• Organize data into charts and graphs.• Analyze and interpret data.• Communicate findings.

(RBT C2, C3, C4, C5, C6)

Distinguish and appropriately graph dependent and independent variables.

Discuss the best method of graphing/presenting particular data.

Use technology resources such as graphing calculators and computers to analyze data.

Report and share investigation results with others.

1.03 Formulate and revise scientific explanations and models using logic and evidence to:• Explain observations.• Make inferences and predictions.• Explain the relationship between evidence and explanation.

(RBT B2, B6, C2, C6)

Use questions and models to determine the relationships between variables in investigations.

Use evidence from an investigation to support a hypothesis.

1.04 Apply safety procedures in the laboratory and in field studies:• Recognize and avoid potential hazards.• Safely manipulate materials and equipment needed for scientific investigations.

(RBT B3, C3)

Predict safety concerns for particular experiments

o Electricityo Projectiles

Relate physics concepts to safety applications such as:

o Transportation: seat belts, air bags, speed…

Short circuits, circuit breakers, fire hazards

5.01 Assess the vector nature of momentum and its relation to the mass and velocity of an object. (RBT A1, A2, B2, C3, C5)

Define momentum. Identify that momentum is a vector quantity because velocity

is a vector quantity. Recognize that momentum is proportional to mass and

proportional to velocity. Apply the momentum equation:

Physics- Unit 4 DRAFT 2

5.02 Compare and contrast impulse and momentum.

(RBT A1, A2, B1, C3)

Define impulse. State that impulse is equal to change in momentum:

Recognize that the change in momentum of an object is proportional to the force applied to the object and to the time the force is applied to the object.

5.03 Analyze the factors required to produce a change in momentum.

(RBT B2, B3, C3)

Distinguish between impulse and force. Determine the change in momentum of an object by finding

the area under the “curve” on a force vs. time graph. Show that the larger the mass of an object, the smaller the

change in velocity of an object for a given impulse. Apply the impulse equation in various situations:

5.04 Analyze one-dimensional interactions between objects and recognize that the total momentum is conserved in both collision and recoil situations.

(RBT B4, B5, C3, C6)

Verify that the total momentum before an interaction is equal to the total momentum after an interaction as long as there are no outside forces.

Solve problems using conservation of momentum in the following instances:o two objects initially at rest push each other apart;o a moving object collides with a stationary object and the

two objects stick together;o a moving object collides with a stationary object and the

two objects move off separately;o two moving objects collide and either stick together or

move off separately. Design and conduct investigations verifying the

conservation of momentum in the four situations listed above.

Identify the special case of an elastic collision (recoil) where the objects do not stick together and both momentum and kinetic energy are conserved.

5.05 Assess real world applications of the impulse and momentum, including but not limited to, sports and transportation.

(RBT B1, B5, C3)

Use examples, such as baseball and golf, to explain that “follow through” is a strategy for increasing the impulse on the ball.

Solve collision problems. (Momentum is conserved - assume the system is limited to the colliding objects. Example: car crash.)

Recognize elastic collisions:o ideal gas molecules collide elastically

billiard balls are frequently used as examples of elastic collisions.

Honors Honors topics: collisions in two dimensions

Physics- Unit 4 DRAFT 3

VI. English Language Development Objectives (ELD) Included:NC English Language Proficiency (ELP) Standard 4 (2008) for Limited English Proficiency Students (LEP)- English Language learners communicate information, ideas, and concepts necessary for academic success in the content area of science.

Suggestions for modified instruction and scaffolding for LEP students and/or students who need additional support are embedded in the unit plan and/or are added at the end of the corresponding section of the lessons. The amount of scaffolding needed will depend on the level of English proficiency of each LEP student. Therefore, novice level students will need more support with the language needed to understand and demonstrate the acquisition of concepts than intermediate or advanced students.

VII. Materials/Equipment Needed: Most of the activities for this unit use inexpensive and simple materials. Those materials can be found here.

Raw eggs Materials for Honors Topic:Sheet Collisions in Two Dimensions

apparatus (1 per group)Bucket or laundry basket (optional- to be used as target)

Carbon Paper

1- spring loaded cart per lab group Tracing paper1- non-spring loaded cart per lab group

String

Meter sticks Tape2- blocks of wood per lab group (books may be used as a substitute)

Washers or other small weights

1- 0.5 kg mass per lab group ClampsRulersProtractors

Physics- Unit 4 DRAFT 4

VII. Detailed Content Description:

Please see the detailed content description for each objective in the biology support document. The link to this downloadable document is in the Physics Standard Course of Study at:

http://www.ncpublicschools.org/curriculum/science/scos/2004/27physics

VIII. Unit Notes:

Overview of Unit Five:This unit is focused on the concept of momentum. Students will learn about the relationships between force, time, mass, velocity, and momentum.

The Unit Guide below contains the activities that are suggested to meet the Standard Course of Study (SCOS) Goals for Unit Three. The guide includes activities, teacher notes on how to implement the activities, and resources relating to the activities which include language objectives for LEP (Limited English Proficient) students. Teachers should also consult the Department of Public Instruction website for English as a Second Language at: http://www.ncpublicschools.org/curriculum/esl/ to find additional resources. If a teacher follows this curriculum (s)he will have addressed the goals and objectives of the SCOS. However, teachers may want to substitute other activities that teach the same concept. Teachers should also provide guided and independent practice from the textbook or other resources.

Physics Support DocumentTeachers should also refer to the support document for Physics at http://www.ncpublicschools.org/curriculum/science/scos/2004/27physics for the detailed content description for each objective to be sure they are emphasizing the specified concepts for each objective.

Reference TablesThe North Carolina Physics Reference Tables were developed to provide essential information that should be used on a regular basis by students, therefore eliminating the need for memorization. It is suggested that a copy be provided to each student on the first day of instruction. A copy of the reference tables can be downloaded at the following URL:

http://www.ncpublicschools.org/docs/curriculum/science/scos/2004/physics/referencetables.pdf

Essential Questions for Unit Five

Essential questions are those questions that lead to student understanding. Students should be able to answer these questions at the end of an activity. Teachers are advised to put these questions up in a prominent place in the classroom. The questions can be answered in a journal format as a closure.

1. How would you define momentum?2. Can you describe what happens to the momentum of an object when

its direction changes? Explain.3. What is the momentum of an object dependent upon?4. Explain the process used to calculate an object’s momentum.5. What is impulse?6. How are impulse and momentum related?7. Compare and contrast force and impulse.8. How would you use a force vs. time graph to determine the change in

an object’s momentum?9. How is an object’s mass connected to its change in velocity for a given

impulse?10.Design an experiment to verify the law of conservation of momentum.11.How do you use conservation of momentum to predict the motion of

objects after a collision or explosion?12.Can you describe a situation where both momentum and kinetic

energy are conserved? Explain.

Modified Activities for LEP StudentsThose activities marked with a have a modified version or notes designed to assist teachers in supporting students who are English language learners. Teachers should also consult the Department of Public Instruction website for English as a Second Language at: http://www.ncpublicschools.org/curriculum/esl/ to find additional resources.

Computer Based ActivitiesSeveral of the recommended activities are computer based and require students to visit various internet sites and view animations of various biological processes. These animations require various players and plug-ins which may or may not already be installed on your computers. Additionally some districts have firewalls that block downloading these types of files. Before assigning these activities to students it is essential for the teacher to try them on the computers that the students will use and to consult with the technology or media specialist if there are issues. These animations also have sound. Teachers may wish to provide headphones if possible.

Web ResourcesThe web resources provided on this page were live links when the unit was designed. Please keep in mind that as individuals make changes to websites, it is possible that the websites may become inactive. These resources are provided to supplement the activities in the unit. Some of the resources can be used as to

supplement your teacher-led discussions by projecting them for the class. Other activities require students to have access to computers.

WEB RESOURCES FOR UNIT 5—MOMENTUMNice lab from PASCO for honors or AP class covering elastic collisions

http://charmian.sonoma.edu/~bryant/Spring2006/Phys116%20S06/P116/collisionmomentum.doc

Nice demo using “Happy/Sad Balls”

http://serc.carleton.edu/sp/compadre/demonstrations/examples/19119.html(source of Happy/Sad Balls -- http://www.sargentwelch.com/product.asp_Q_pn_E_WL0709_ST_A_Happy+and+Sad+Balls_E_ cost $5.75

Well written site for use in introducing concepts

http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l1b.html

Unit design for momentum complete with quiz links

http://www.physicssource.ca/pgs/3005_momentum.html

Another lab from Pasco using a force sensor and motion detector (adapt for use with Vernier sensors as well)

http://www.pasco.com/resources/experiments/labdownloads/pdfs/explorations/physics/11%20Impulse-Change%20Momentum%20web.pdf

Web site that lists many resources with interactive concept map that should be helpful for organization

http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Momentum/MomentIntro.html

Catchy video from Teacher Tube to introduce

http://www.teachertube.com/view_video.php?viewkey=d0d7498210d63d2d4180http://www.teachertube.com/view_video.php?viewkey=d0d7498210d63d2d4180

From the National Repository of Online Resources: excellent video, study sheet, review problems, self test, assessment and key

http://www.montereyinstitute.org/courses/College%20Preparatory%20Physics%20I/nroc%20prototype%20files/coursestartc.html

Quality site using baseball to teach about momentum. Video and activities included.

http://www.bsu.edu/eft/dev/dm_module/03_momentum.htm

Investigate car crashes with these simulations.

http://www.mrmont.com/games/carcollision.htmlhttp://www.mrmont.com/games/crashtest.html

More advanced topics with car crashes and 2 dimensional motion

http://www.mcasco.com/p1lmc.html

Extensive site with productive ideas for teaching momentum

http://www.learningincontext.com/PiC-Web/chapt07.htm

Two good collision simulations from “Active Physics”

http://www.physicssource.ca/applets/ActivePhysics/pt1a/Media/Momentum/MomentumEnergyChange/Main.html

http://www.physicssource.ca/applets/ActivePhysics/pt1a/Media/Momentum/CarCollisionsTwoDim/Main.html

Some good resources from “Teach the Teachers”

http://tttc.org/find/wpShow.cgi?wpID=1159

X. Global Content: Aligned with 21 st Skills: One of the goals of the unit plans is to provide strategies that will enable educators to develop the 21st Century skills for their students. As much as students need to master the NCSOS goals and objectives, they need to master the skills that develop problem solving strategies, as well as the creativity and innovative thinking skills that have become critical in today’s increasingly interconnected workforce and society. The Partnership for 21st Century Skills website is provided below for more information about the skills and resources related to the 21st Century classroom.

http://www.21stcenturyskills.org/index.php?option=com_content&task=view&id=27&Itemid=120

GLOBAL CONTENT—Goal Five

NC SCS Physics

21st Century Skills Activity

Communication Skills1.01, 5.01,5.02

Conveying thought or opinions effectively

Analysis questions in all labs

5.01, 5.02 When presenting information, distinguishing between relevant and irrelevant information

Data analysis in all labs

5.02, 5.03,5.04

Explaining a concept to others Analysis questions in all labs

5.02, 5.03,5.04

Interviewing others or being interviewed

Comparing data in lab “Momentum Conservation”

Computer Knowledge5.01, 5.02 Using word-processing and database

programsConcept Map

5.01, 5.02 Developing visual aids for presentations

Concept Map

4.02, 4.03 Using a computer for communication Playing “Momentum Jeopardy” 5.02, 5.03,5.04, 5.05

Learning new software programs Concept Map

Employability Skills5.01, 5.02, 5.03, 5.04

Assuming responsibility for own learning

Concept Map and all lab activities

5.01, 5.02, 5.03, 5.04

Persisting until job is completed Concept Map and all lab activities

5.01, 5.02, 5.03, 5.04

Working independently Egg Drop Activity

Developing career interest/goals5.01, 5.02, 5.03, 5.04

Responding to criticism or questions Playing “Momentum Jeopardy”

Information-retrieval Skills5.01, 5.02, 5.03, 5.045.05

Searching for information via the computer

Egg Drop Activity

5.01, 5.02, 5.03, 5.04

Searching for print information Egg Drop Activity

5.01, 5.02, 5.03, 5.04

Searching for information using community, members

Lab: “Momentum Conservation”PPT: “Momentum Jeopardy”

Language Skills- Reading5.01, 5.02, 5.03, 5.04

Following written directions All labs in the unit

5.01, 5.02, 5.03, 5.04

Identifying cause and effect relationships

All labs in the unit

5.01, 5.02, 5.03, 5.04

Summarizing main points after reading Concept Map

5.01, 5.02, 5.03, 5.045.05

Locating and choosing appropriate reference materials

All lab activitiesEgg Drop Activity

5.01, 5.02, 5.03, 5.04. 5.05

Reading for personal learning Concept Map

Language Skills- Writing5.01, 5.02, 5.03, 5.04

Organizing and relating ideas when writing

“Explain” and “Evaluate” sections in all lab activitiesConcept Map

Proofing and Editing5.01, 5.02, 5.03, 5.04

Synthesizing information from several sources

Egg Drop Activity“Momentum Jeopardy”

Documenting sources5.01, 5.02, 5.03, 5.04

Developing an outline Concept Map

5.01, 5.02, 5.03, 5.04

Writing an outline Concept Map

5.01, 5.02, 5.03, 5.04

Writing to persuade or justify a position All lab activities and “Momentum Jeopardy”

Creating memos, letters, other forms of correspondence

Teamwork5.01, 5.02, 5.03, 5.04

Taking initiative All lab activities and “Momentum Jeopardy”

5.01, 5.02, 5.03, 5.04

Working on a team All lab activities and “Momentum Jeopardy”

Thinking/Problem-Solving Skills5.01, 5.02, 5.03, 5.04

Identifying key problems or questions All lab activities and “Momentum Jeopardy”

5.01, 5.02, 5.03, 5.04

Evaluating results All lab activities and “Momentum Jeopardy”

TEACHER NOTES for CONCEPT MAPS for IMPULSE & MOMENTUM

ENGAGE:Show the idea of how a concept map works for physics by projecting the URL listed below.http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#mechconThen hand out the Concept Map for Impulse & Momentum as an exercise to be completed. This should be as part of a reading assignment on momentum and impulse from the textbook that you use. The two links below discuss the use of concept maps.http://www.learnnc.org/lp/pages/757http://go.hrw.com/resources/go_sc/ssp/HK1BSW05.PDF

EXPLORE:Tell students that the Concept Map is a map for exploring relationships and connections.

EXPLAIN: Students are asked to explain various items about which they read.

ELABORATE:Encourage students to add any frames that help with organization.

EVALUATE:Check the maps to see how students used the idea and ask them to write a paragraph on the back of the sheet evaluating how helpful this organization might be in understanding the reading. For future maps students should create their own organization.

Language (ELP) Objective for LEP Students: Describe in paragraph form the Impulse/Momentum Theorem referring

to key terms such as impulse, momentum, force that were used in the completed concept map.

In paragraph form, explain how student would conduct a similar experiment using other materials which could be found in the physics classroom.

Discuss verbally or in paragraph form real life examples of the

CONCEPT MAPS for IMPULSE AND MOMENTUM

Egg Drop Teacher’s Guide

This activity is designed to be used as a quick, fun competition to aid in the study of impulse and momentum. One quick way to increase the difficulty level of the project is to include a target for the eggs to be dropped on.

Engage: An excellent way to introduce this activity is to do the “Demonstration for Applying Impulse” from the NC DPI Physics Support Documents. During this demonstration, an egg is thrown at a sagging sheet. Because of the sheet’s ability to “give”, the stopping time is increased, and the egg doesn’t break. Have students try throwing the egg, and then have the group discuss why the egg doesn’t break.

Explore: Students use household materials to design a contraption that will prevent an egg from breaking when it is dropped from a high point.

Explain: Upon completion of the lab, students are asked to write a paper explaining the relationships between force, time, and change in momentum. In this paper, they have to analyze their design, explain why they did it that particular way, and discuss possible improvements.

Elaborate: Students should be asked to analyze the designs of other groups and suggest improvements.

Evaluate: The written portion of this activity provides a structure in which students can evaluate their own projects as well as the work of others in the class.

Language (ELP) Objectives for LEP Students: Describe in own words written or verbally The Egg Drop lab activity and

how it relates to the concept of momentum. Think pair-share explanation of the Egg Drop activity with a partner and/ or

the class. Verbally or in written form, explain how the Egg Drop activity relates to the

Impulse/ Momentum Theorem.

Egg Drop Competition

Mission objective: to design the most efficient contraption to safely transport an uncooked egg from the top of the stadium to the ground

Available materials: any common household items your group would like to use. However, keep in mind that the goal is to be the most efficient…the less materials you use, the more likely you are to win!

Rules: The outside container must be a cardboard box (shoebox or some other

small box) no larger than 10” x 10” x 10”. This box may have small items attached to its outer surface, however, it

may NOT be completed covered with something else. No more than 2 square inches of the outside surface may be covered.

The container should be fully assembled when you come to class on competition day. You will have no more than 2 minutes to insert the egg into the container.

The container must be reusable. Any decorations on the surface of the container must be in good taste and

appropriate for school. Containers with inappropriate materials will be immediately disqualified.

The egg must be whole, dry, and clean (no materials stuck to it) for a container to be successful. Cracked eggs are considered broken.

Judging:The containers will be judged based on two criteria: efficiency and

creativity. Efficiency for this project refers to the amount of material used. Less material = more efficient. Creativity refers to the types of materials used and the application of physics principles in construction, NOT to the “prettiness” of the outer surface!

Analysis:Upon completion of this project, you are expected to submit a written

analysis of the competition. This should include the following: Discussion of the physics principles involved Analysis of your container: what did you use, why did you use it, how

would you improve it if we did this again

Analysis of 3 other containers: why were they or weren’t they successful? What improvements would you suggest?

How do the principles at work in this project relate to real life? Why is this concept important?

Teacher Key—Physics of Sports Project

ENGAGE:Show one of the Exploratorium links:

http://www.exploratorium.edu/skateboarding/trick03.htmlThis is a good place to start. Ask questions such as “Does the physics of impulse/momentum apply to sports? How does it apply?”

EXPLORE:Students will explore resources to discover the connection to sports and physics.

EXPLAIN:Students will explain what they have discovered about momentum/impulse and the connection to sports on the poster that they create.

ELABORATE:Students create a poster featuring the relationship between physics and their favorite sport. This activity allows them to explore the real world connections between physics and athletics.

EVALUATE:Students use the rubric provided to evaluate their achievement.

Language (ELP) Objectives for LEP Students: Describe in several paragraphs you favorite sport and the importance of

impulse and momentum in this particular sport.

Explain verbally or in written form how you would design a poster that would relate the concepts of physics related to your favorite sport.

Think-pair–share your poster with a partner or the whole class.

PHYSICS OF SPORTS PROJECTYour challenge is to research a favorite sport and discover how impulse and momentum are important to the sport you choose. Next, you must design and create a poster that illustrates the application of these physics concepts to the sport you chose. Some links below are listed to help you get started. Please document ALL your sources on a paper that should be taped to the back of your poster. You should use at least 6 different sources.http://www.exploratorium.edu/sports/http://www.newtonsapple.tv/TeacherGuides_physicsSports.phphttp://mb-soft.com/public2/sports.htmlhttp://home.nc.rr.com/enloephysics/sports.htmYour grading rubric is included. List your sources below:1.

2.

3.

4.

5.

6.

7.

Making A Poster : Physics of Sports

Teacher Name: ______________________________________Student Name:     ________________________________________

CATEGORY 4 _____ 3 ______ 2 ______ 1 _______Graphics – Relevance

Total Points =

_____________

All graphics are related to the topic and make it easier to understand. All borrowed graphics have a source citation.

All graphics are related to the topic and most make it easier to understand. All borrowed graphics have a source citation.

All graphics relate to the topic. Most borrowed graphics have a source citation.

Graphics do not relate to the topic OR several borrowed graphics do not have a source citation.

Content – AccuracyTotal Points =

At least 7 accurate facts are displayed on the

5-6 accurate facts are displayed on

3-4 accurate facts are displayed on

Less than 3 accurate facts are displayed.

____________ poster. the poster. the poster.Knowledge Gained

Total Points =

_____________

Student can accurately answer all questions related to facts in the poster and processes used to create the poster.

Student can accurately answer most questions related to facts in the poster and processes used to create the poster.

Student can accurately answer about 75% of questions related to facts in the poster and processes used to create the poster.

Student appears to have insufficient knowledge about the facts or processes used in the poster.

AttractivenessTotal Points =

_____________

The poster is exceptionally attractive in terms of design, layout, and neatness.

The poster is attractive in terms of design, layout and neatness.

The poster is acceptably attractive though it may be a bit messy.

The poster is distractingly messy or very poorly designed. It is not pleasing.

MechanicsTotal Points =

_____________

Capitalization and punctuation are correct throughout the poster.

There is 1 error in capitalization or punctuation.

There are 2 errors in capitalization or punctuation.

There are more than 2 errors in capitalization or punctuation.

Graphics – Relevance

Total Points =

_____________

All graphics are related to the topic and make it easier to understand. All borrowed graphics have a source citation.

All graphics are related to the topic and most make it easier to understand. All borrowed graphics have a source citation.

All graphics relate to the topic. Most borrowed graphics have a source citation.

Graphics do not relate to the topic OR several borrowed graphics do not have a source citation.

Grammar

Total Points =

_____________

There are no grammatical mistakes on the poster.

There is 1 grammatical mistake on the poster.

There are 2 grammatical mistakes on the poster.

There are more than 2 grammatical mistakes on the poster.

Student Comments:Teacher Comments:Final Grade: ____________________

Lab-Momentum Conservation in an Explosion--Teacher NotesLanguage (ELP) Objectives for LEP Students:

Explain verbally or in written form in own words the concept of an explosion and give examples of an explosion. Use terms such as momentum, velocity, mass, and force.

Explain verbally or in written form the basketball/tennis drop demo and write a summary of the results of this activity.

Answers to Lab Questions:1. Both carts are at rest so the total momentum is zero (m1 x 0 + m2 x 0).

2. Absolute error is the absolute value of the difference between the actual value and the experimental value. Relative error is the ratio of the absolute error to the actual value. (Percent error is relative error x 100).

3. Student answers will vary in the form of 0 0.02 kg m/s

4. Momentum has the same direction as the velocity vector because momentum is a positive scalar (mass) multiplied by a vector which has direction unchanged by the positive scalar.

Engage:Ask students to remember the most impressive “explosion” they witnessed. Most will remember some type of fireworks. Ask several students to give their definition of the word “explosion”. A good physics use of the term indicates that objects that are together (whether at rest or moving) separate from each other over a very short time interval. Perform the basketball/tennis ball drop demo (“double ball bounce”) as shown at this URL. http://www.wfu.edu/physics/demolabs/demos/avimov/byalpha/cdvideos.html#DoubleBallBounce

5. Student answer. You, the teacher, should walk around the room as data is collected to spot places where procedural errors are occurring.6. No, as the time is the same for both carts. It is simply a way to reinforce the concept of momentum as mass multiplied by velocity.7. “In a closed system, total momentum before interaction of masses equals total momentum after interaction” or similar words such as this. Please discuss the meaning of “closed system” in a post-lab discussion.8. Student answers will vary in the form of 0 0.02 kg m/s9. Student answer. You, the teacher, should walk around the room as data is collected to spot places where procedural errors are occurring.

Lab--Momentum Conservation in an ExplosionName: Period:Background: Sir Isaac Newton wrote his Second Law of Forces not as F = ma but as F t = m v. (Note that a = v/t). The expression F t is known as “Impulse” and m v is known as “change in momentum”. Momentum is represented by the letter “p” and equals “m v” where “m” is the mass of an object in kilograms and “v” is the velocity of the object in meters/second. Challenge:Your lab team will investigate to see if momentum is conserved in an “explosion”. You will need a spring loaded cart and another cart that is not spring loaded. You will also need two blocks of wood or 2 stacks of books to serve as bumpers, a meter stick and a 0.500 kilogram mass. Procedure:1. Place the blocks or stacks of books one meter apart (or less) on a table as shown below. The blocks/books are your bumpers. Both carts must hit the bumpers so move the bumpers close enough to the carts to make sure this happens.

2. Measure the mass of each of the two carts and record the values on the next page.3. Load the spring cart by pressing the spring into a locked position. Place the spring cart on the table between the bumpers. Place the other cart on the table so that it just touches the spring mechanism of the other cart. (An overhead view looking down on the table top is shown below.)

4. To release the loaded spring mechanism, tap the mechanism with a ruler.

d 1 meter

Lab table top

1 meter or less

5. Listen for the noise each cart makes upon striking the bumpers. Your challenge is to place the carts in such a position so that they both strike each bumper at the same time after the spring is released. Keep moving the carts as a pair until you are satisfied that they take the same time to reach the bumpers. Record the time (the same for both carts) and x1 and x2. See the figure below. (Mark the end of the carts on the table with chalk to measure x1 and x2.)

6. Repeat the process 2 more times with the same carts and the same bumper placement. Make sure the carts hit at the same time. Record your results and find the average velocity for each cart. Remember that velocity is a vector. A velocity to the right is positive and to the left is negative. DATA

Mass of spring cart

(kg)

Mass of cart without spring

(kg)

x1 (m) x2 (m) Time of motion (s)

v1 (m/s) v2 (m/s)

CALCULATIONSTotal momentum before explosion (kg-m/s)

Momentum of spring cart after explosion (kg-m/s)

Momentum of cart without spring after explosion (kg-m/s)

Total momentum after explosion (kg-m/s)

ANALYSIS:1. How did you calculate the total momentum before explosion? Explain.

2. What is the difference between absolute error and relative error? Check out this reference. http://canu.ucalgary.ca/map/content/erroranalysis/absrel/explain/index.html

1 m (or less)

X1 X2

Table Top

3. What is your absolute error between your total average momentum before explosion (actual value of zero) and your total average momentum after explosion (your data value)?

4. Does momentum have the same vector direction as velocity? Explain your answer.

5. Does your data convince you that momentum is conserved? Why or why not? Compare your data with other lab groups.

6. Was it absolutely necessary to time the distance traveled (other than to enforce the concept that momentum = mass x velocity)? Why or why not?

7. State in your own words a “Conservation of Momentum” theory.

ELABORATE:Place a 0.500 kilogram mass on one of the carts and repeat the experiment. Once again, the carts must be placed so that both carts hit the bumper at the same time. DATA FOR EXPLORATION

Mass of spring cart

(kg)

Mass of cart without spring

(kg)

x1 (m) x2 (m) Time of motion (s)

v1 (m/s) v2 (m/s)

CALCULATIONS FOR EXPLORATIONTotal momentum before explosion (kg-m/s)

Momentum of spring cart after explosion (kg-m/s)

Momentum of cart without spring after explosion (kg-m/s)

Total momentum after explosion (kg-m/s)

8. What was your absolute error?

9. Were you satisfied that momentum was conserved in this part of your exploration? Explain:

Momentum in Two Dimensions Teacher’s Guide

This activity is designed to be used as an honors extension in the study of momentum. To be able to complete the calculations, students will need to review the algebraic method of vector addition.

The Collision in Two Dimensions apparatus can be found at several vendors including:

Fisher Science Education (search for 2-D Collision) http://www.hometrainingtools.com/product_categories/164/

products/3349-collision-in-2-dimensions-kit

Engage: Have students discuss collisions they have seen in person, on television, or in the movies. Most will list car crashes or other large scale collisions, and they should recognize that these collisions occur in more than one dimension.

Explore: Students explore the ideas of momentum as a vector and conservation of momentum using simple lab apparatus.

Explain: Upon completion of the lab, students are asked to determine whether momentum was conserved in this lab. They are then asked to explain any errors that might have affected their results.

Elaborate: Students should be asked to share their findings with other lab groups. As an extension, they could be asked to use their knowledge of horizontal projectiles to determine the velocity of each ball or to explain the conversions of energy that occur during this lab.

Evaluate: A post lab discussion should be used to evaluate student understanding of the key concepts. Any misconceptions should be cleared up at this time.

Language (ELP) Objectives for LEP Students: In written or verbal form discuss the concept of collisions and

real life examples collisions. Think-pair-share examples of real life collisions with a partner of

the whole class. Describe why collisions occur in more than one dimension why

you need to use the algebraic method of vector addition.

Answer KeyAnalysis Questions1. Students should use trigonometry to break each incident and target vector

into its components, and then add those components to find a resultant vector. If you don’t want to review vector addition, this could also be done graphically, but that would increase the amount of error. For example, if the incident vector was 16 cm at 40° left of center, and the target vector was 18 cm at 25° right of center, the following process would be used to find the resultant:

Resolve incident vector.

cos 40° = yincident/16yincident = 12 cm

x incident2 + 122 = 162

x incident = -10.6 cm (left = negative)

Resolve target vector.

cos 25° = ytarget/18ytarget = 16 cm

xtarget2 + 162 = 182

xtarget = 8 cm

Add components of incident and target.

xincident + xtarget = xtotal

-10.6 + 8 = -2.6 cm

Yincident + ytarget = ytotal

12 + 16 = 28 cm

Use trigonometry to find the resultant.

-2.62 + 282 = c2

-2.6 c = 28 28 θ 28 tan-1 (-2.6/28) = θ

θ = -5.3°

2. Students should compare the resultant values for each of their trials to the value of the single ball, and use that data to determine whether momentum was conserved.

3. Answers will vary, but will probably include: placement of the incident ball is inconsistent, incident ball could be hitting the screw at the bottom, and extra marks from the bounce interfere with data. Some students may recognize that the sound produced during the collision represents a loss of energy, thus a loss of momentum.

Momentum in Two Dimensions

Materials: 4-6 sheets of carbon paper4-6 sheets of tracing paper (or printer paper)StringTapePlumb bob (any small weight will work)

Collisions in two dimensions apparatusClampRulerProtractor

ProcedureSet up

1. Use the clamp to attach the collision apparatus to the lab bench.2. Cut a piece of string long enough to reach from the collision apparatus to the

floor. Tie the plumb bob to the string, then tie the string to the base of the collision apparatus.

3. Tape 4 pieces of carbon paper together in a rectangular shape. Tape the tracing paper together in the same way.

4. Place the carbon paper on the floor just in front of the plumb bob, carbon side up, and then tape the tracing paper on top of it. The plumb bob should mark the edge of the paper directly beneath the collision apparatus. Make a mark on the paper directly below the plumb bob.

5. Choose a starting location on the apparatus. If this location is not the top of the ramp, then mark it with masking tape. It will be very important that you start from the same spot each time.

Data Collection: Single ball6. Take one of the balls from the kit, place it at the starting point, and release it.

Be sure that the screw at the base of the apparatus is low enough that the ball does not hit it. If it is too high, adjust and start over.

7. Once you’ve gotten a clear run, repeat this 9 times. On the tracing paper, circle the area where the ball landed. Mark this area “single”.

8. Using your ruler, draw the initial momentum vector from the point directly below the plumb bob to the center of the area labeled “single”. Measure that

Physics- Unit 5 DRAFT

Lab Bench or desk

Ball

BallCollision apparatus

String

Plumb bob

Carbon paper covered by tracing paper

27

distance, and record it as the “incident” in the table. Since there is no collision, there is no target value for this trial. The angle for this vector should be either 0° or 90°, depending on whether you measure from the edge of the paper under the lab bench, or the imaginary line extending straight out from the plumb bob.

Data Collection: Collision at ≈ 30°9. Now take the second ball and place it on the support post at the bottom of the

ramp. Turn the post so that it makes an approximately 30° angle with the original position. The ball on this post will be called the “target”.

10. Release the first ball from the original starting position. This is the “incident” ball. After the collision, both balls should hit the floor at the same time. If they don’t, you need to adjust the apparatus so that the incident ball does not hit the screw.

11. Label the new marks on the paper “incident” and “target”, respectively.12. Repeat this procedure 9 more times.13. On the tracing paper, circle the areas where the incident and target balls

landed. Label them accordingly, and measure the distance and angle from the starting point to the center of each circle. Be sure to use the same reference point for each angle (If you are measuring one of them from the edge of the paper, you must measure the other the same way.) Record your data in the table.

Data Collection: Collision at ≈ 45°14. Now change the angle between the post and the original direction to

approximately 45° and repeat steps 9-12. You will probably need to use new pieces of tracing paper.

15. On the tracing paper, circle the areas where the incident and target balls landed. Label them accordingly, and measure the distance and angle from the starting point to the center of each circle. Record your data in the table.

Clean up16. Save the tracing paper as a reference to use during the analysis. The carbon

paper may be used again, so turn it in with the rest of the lab materials.17. All lab equipment should be put away before you begin the analysis.

Data Table

Incident ball Target ball ResultantSingle Ball

At ° At °

Collision at ≈ 30° At ° At ° At °

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Collision at ≈ 45° At ° At ° At °

Analysis1. Using the algebraic method, add the incident and target vectors for each trial.

Show your work!! Record your answers in the table.

2. According to your data, was momentum conserved in this lab? Explain your answer.

3. What are some possible sources of error in this lab? How could you reduce them?

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Physics Jeopardy

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Assessment- Impulse and MomentumName: Period:

_____________1. Rank the following in order from smallest momentum to largest momentum. a. b.

c. d.

2. The position, time graph is shown for a 2.0 kg object. Please draw the matching momentum, time graph from 0 to 4 s.

3. Two girls on ice skates are standing at rest on the ice with hands placed together as shown. The girls push hard against each other. If girl A (mass of 38 kg) moves to the left with a speed of 1.4 m/s then how fast and in what direction will girl B (mass of 45 kg) move?

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0.5 m/s

4 kg

1.5 m/s

4 kg

Girl A Girl B

1.5 m/s2 kg

5.0 m/s2 kg

4. Answer the following using the Law of Conservation of Momentum. Two objects of identical mass, one at rest and the other moving, collide. a. Is it possible for both to be at rest after the collision? Explain your answer.

b. Is it possible for one of the objects to remain at rest after the collision? Explain your answer.

5. A 3.0 kg object is moving to the left with a speed of 2 m/s when it experiences the force pushing to the right as shown below. Find the velocity of the object after the force is delivered.

6. A 3.0 kg moving to the right at 4.2 m/s collides with a 2.0 kg mass moving to the left with a speed of 1.5 m/s in a head-on collision. After the collision, the 3.0 kg mass moves to the right with a speed of 1.0 m/s. What is the speed and direction of the 2.0 kg mass after the collision?

7. Revisit problem six. Is the collision an elastic one? Show your calculations to support your answer.

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F (N)

t(s) 0 1 2 3

4

2

8. A 10.0 g bullet moving at 120 m/s hits a wooden 2.20 kg block at rest on a table at the very edge as shown. How far from the edge will the block land if the bullet embeds in the block? The table is 0.8 m high.

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X=?

TEACHER KEY—Assessment for Momentum and Impulse1. The calculated momentum for each is a. 4 kg x .5 m/s = 2 kg m/s b. 2 kg x 1.5 m/s = 3 kg m/s c. 2 kg x 5 m/s = 10 kg m/s d. 4 kg x 1.5 m/s = 6 kg m/s so the ranking is a<b<d<c.2. The slope of position, time produces velocity and momentum = mass x velocity.

3. Total momentum before = total momentum after 0 + 0 = (-38)(1.4) + (45)(v2) so v2= 1.2 m/s to the right (as v2 is positive)4. a. No, it is not possible because momentum is not conserved. Total momentum before collision is not zero so total momentum after collision cannot be zero. b. yes, it is possible according to the conservation of momentum. The objects just trade momentum where the object originally moving stops and the object originally at rest gains momentum.5. The area under the curve gives impulse which equals 2 N x 2 s = 4 N-s. Impulse= m v so 4 = 3 [v2 - (-2)]. 4 = 3v2 + 2 or v2=2/3 m/s.6. Using conservation of momentum: 3(4.2) + 2(-1.5) = 3(1.0) + 2v2 so that v2=3.3 m/s.7. A 3.0 kg moving to the right at 4.2 m/s collides with a 2.0 kg mass moving to the left with a speed of 1.5 m/s in a head-on collision. After the collision, the 3.0 kg mass moves to the right with a speed of 1.0 m/s. What is the speed and direction of the 2.0 kg mass after the collision? No, because kinetic energy is not conserved. The following calculations prove that kinetic energy is not conserved. ½ (3) (4.2)2 + ½ (2)(-1.5)2 ½ (3)(1.0)2 + ½ (2)(3.3)2 or 38.2 kg m2/s2 15.8 kg m2/s2

8. Using conservation of momentum: (0.010)(120) + (2.20)(0)= (0.010+2.20)v so that v= 0.54 m/s.Now we have a projectile problem where the initial velocity of launch is 0.54 m/s at 0 degrees. To find the time in the air use y = vo(y)t - 4.9t2. -0.8 = 0 - 4.9 t2 yields t = 1.28 s. Use this time in x = vo(x) t so that x= (0.54)(1.28)= 2.78 m.

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