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.
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 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
TRADITIONAL ASSESSMENT / TEACHER NOTES
1. Unit Test
TEACHER CLASSROOM ASSESSMENT / TEACHER NOTES
1. 2- and 4-Point Questions
2. Lab Reports
AUTHENTIC ASSESSMENT / TEACHER NOTES /
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)
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:
Ø Place the ruler horizontally on a flat surface.
Ø Put the dime (or small coin) face down in contact with one end of the ruler.
Ø Slide the quarter (or larger coin) sharply up against the other end of the ruler.
Ø Momentum is transferred from the moving quarter to the stationary ruler/dime system.
Ø Measure how far the dime moves.
Ø 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.
Ø Measure how far the quarter (larger coin) moves
Ø Measure the mass of the smaller coin and the mass of the larger coin, find their ratio
Ø 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 quarter / Distance quarter traveled
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?
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.
TABLE I SPRING
Mass (g.) / Stretch (cm.)100
200
300
400
500
TABLE II RUBBER BAND 1 (THIN)
Mass (g.) / Stretch (cm.)100
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