AP PHYSICS 1(SECONDARY)

ESSENTIAL UNIT 3 (E03)

(Dynamics: Newton’s Laws of Motion)(Giancoli chapter 4)

(July 2015)

Unit Statement: Units 1 and 2 are dedicated to the effects of motions (kinematics), but in this unit students will study the causes of motion (dynamics). Dynamics is a branch of physics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to its causes. In addition, Isaac Newton established the undergirding physical laws which govern dynamics in physics. By studying his system of mechanics, in particular Newton’s second law of motion, dynamics can be understood. (Estimated class time four weeks)

Essential Outcomes: (must be assessed for mastery)

1. The Student Will explain that forces exerted on an object are always due to the interaction of that object with another object, including the ideas that:

a. An object cannot exert a force on itself. b. Even though an object is at rest, there may be forces exerted on that object by

other objects. c. The acceleration of an object, but not necessarily its velocity, is always in the

direction of the net force exerted on the object by other objects. (EK 3.A.3)

2. TSW challenge a claim that an object can exert a force on itself. (LO 3.A.3.2, SP 6.1)

3. TSW justify if one object exerts a force on a second object, the second object always exerts a force of equal magnitude on the first object in the opposite direction. (EK 3.A.4)

4. TSW represent forces in free body diagrams using appropriately labeled vectors with magnitude, direction, and units during the analysis of a situation. (EK 3.B.2)

5. TSW calculate net force and predict motion of objects interacting with each other. (EK 3.B.1)

6. TSW identify contact forces result from the interaction of one object touching another, and they arise from the interatomic electric forces. These forces include tension, friction, normal and spring. (EK 3.C.4)

7. TSW articulate situations when the gravitational force is the dominant force and when the electromagnetic, weak, and strong forces can be ignored. (LO 3.G.1.1, SP 7.1)

8. TSW examine the relationship between gravitational field, g, an object with mass, m. (EK2.B.1)

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9. TSW describe linear motion of a system by the displacement, velocity, and acceleration of its center of mass. (EK 4.A.1)

10. TSW justify that acceleration is equal to the rate of change of velocity with time, and velocity is equal to the rate of change of position with time. Including the ideas that:

a. The acceleration of the center of mass of a system is directly proportional to the net force exerted on it by all objects interacting with the system and inversely proportional to the mass of the system.

b. Force and acceleration are both vectors, with acceleration in the same direction as the net force. (EK 4.A.2)

11. TSW validate in a lab setting (virtual or practical) the forces that systems exert on each other are due to interactions between objects in the systems. If the interacting objects are parts of the same system, there will be no change in the center-of-mass velocity of that system. (EK 4.A.3)

12. TSW solve problems in which application of Newton’s laws leads to two or three simultaneous linear equations involving unknown forces or accelerations.

Guided or Essential Questions: How can you utilize Newton’s laws of motion to predict the behavior of objects? Do action-reaction force pairs (Newton’s third law) have a cause-and-effect

relationship? Why or why not? How can free-body diagrams be utilized in the analysis of physical interactions between

objects? Why can’t an object exert a force on itself? How can the forces acting on an object be

represented? How can a free-body diagram be used to create a mathematical representation of the

forces acting on an object? How do Newton’s laws apply to interactions between objects at rest and in motion?

How does the presence of a net force determine the acceleration of an object? What is the nature of friction and how does it factor into an object’s acceleration? How can an Atwood’s machine be used to calculate the acceleration of gravity? What are action-reaction force pairs? And do they cancel each other? What considerations must be made when a system is composed of two or more objects? Why is the Atwood machine an exemplar for systems of masses? How can you utilize Newton’s laws of motion to predict the behavior of objects?

Key Concepts: Force Vector nature Weight Normal Force Dynamic Equilibrium Free Body Diagrams Net Force Factors of Acceleration Friction String Tension

Mass Inertial Noninertial Newton’s 1st Law Static Equilibrium Apparent Weight Gravitational Mass Inertial Mass Incline Atwood Machines

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Two Mass Systems Newton’s 3rd Law

Action- Reaction

Common Equations for this Unit:

F = F1+ F2+ F3+ F4+. . . = 0 First Condition of Equilibrium

Newton’s Second Law

W= mg Weight formula where g= 9.8ms-2

T = W + ma Tension if the body is moving upwardFriction Formula

T = W – ma Tension if the body is moving downwardFGP= -FPG Newton’s Third Law

Good to Know Mathematical Equations - from Trigonometry

Components of a vector a in the xy-plane: ax = a cos(θ), ay = a sin(θ) , tan(θ) = ay/ax

Schedule of suggested laboratory experiments (guided inquiry format is suggested for labs shaded in gray)

Lab # Name of Laboratory Description of Lab Associated Science Practices

11 Y Spring and Free Body Diagrams

This is an introduction to vector nature. Students suspend unknown masses between two spring scales, forming a y-shape. White paper is taped behind the suspended apparatus. Students then stretch the forces and show calculations. After the free body diagram is drawn with calculated angles and spring forces, students can determine the weight of the unknown mass.

Puri and friends

1.1, 1.4, 2.1, 2.2,

3.1, 4.1, 4.2, 4.3,

5.1, 5.3, 6.1, 6.4, 7.2

12 Drawing Free Body Diagrams This is a follow-up to lab #11. After lab 11, discuss free body diagrams and proper vocabulary. Then set up different stations around the room in which students must draw the proper free diagram.

Puri and Friends

1.1, 1.4, 2.1, 2.2,

3.1, 4.1, 4.2, 4.3,

5.1, 5.3, 6.1, 6.4, 7.2

13 Inertia Mini Labs Inquiry Lab- different material such as cups, pipes, eggs, pennies, string are set out for student use. Students must design a mini experiment that shows the law of inertia. Students must be able to describe the motion and forces of the objects.

Link of video to help with supplies https://www.youtube.com/watch?v=3TpXlMO5fGE

1.4, 2.1, 2.2, 3.1,

4.1, 4.2, 4.3, 5.3,

6.1, 6.4, 7.2

14 Bowling Grand Prix The activity gives students a kinesthetic feel for the inertia concept. It helps provide students with an experience that can be very thoroughly discussed and analyzed. (Students must push a bowling ball through an obstacle course with a broom) Found online- http://slapt.org/resources/labs/bowlingprix.html

1.1, 1.4, 1.5, 2.1,

2.2, 3.1, 4.1, 4.2,

4.3, 5.3, 6.1, 6.4, 7.2

15 Coffee Filter Drop Using motion detectors students drop different numbers of basket-like coffee filters. The graphs are printed and analyzed detailing each segment of the graph.

Vernier

1.4, 2.1, 2.2, 3.1,

4.1, 4.2, 4.3, 5.3,

6.1, 6.4, 7.2

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16 AP Physics 1 Sample Lab # 1: Newton’s Second Law What Factors Affect the Acceleration of a System?

In this lab the students will investigate the relationship among the net force exerted on an object, its inertial mass, and its acceleration. Students should have already completed the study of kinematics and Newton’s First Law.

AP College Board or Value @AmritaIf equipment is not available- http://amrita.vlab.co.in/index.php?sub=1&brch=74&sim=207&cnt=4 virtual lab (must register- free)

1.4, 2.1, 2.2, 3.1,

4.1, 4.2, 4.3, 5.3,

6.1, 6.4, 7.2

17 Inertial vs Gravitational Mass Inertial mass and gravitational mass are appearing in two independent Newton's laws. This lab will help show how the two types of masses are related.

Link is listed in technology link

1.4, 2.1, 2.2, 3.1,

4.1, 4.2, 4.3, 5.3,

6.1, 6.4, 7.2

18 Bungee Jump Accelerations In this experiment, students will investigate the accelerations that occur during a bungee jump. Students will generate an acceleration vs. time graph for an actual bungee jump, where the jumper jumped straight upward, then fell vertically downward.

Vernier

1.4, 2.1, 2.2, 3.1,

4.1, 4.2, 4.3, 5.3,

6.1, 6.4, 7.2

19 AP Physics Sample Lab #1 –Newton’s Second Law

In this lab the students will investigate the relationship among the net force exerted on an object, its inertial mass, and its acceleration. Students should have already completed the study of kinematics and Newton’s First Law.

Found on AP College Board Website. Document Name : ap-physics-1-and-ap-physics-2-inquiry-based-lab-investigations

1.1, 1.4, 1.5, 2.1,

2.2, 3.1, 3.2, 3.3,

4.1, 4.2, 4.3, 5.1,

5.2, 5.3, 6.1, 6.2,

6.4, 7.2

20 Define Me- Center of Mass Place different items on students’ desks (tennis racket, baseball bat, broom, spoon, violin/guitar, large cooking spoon, etc.) and have students first try to identify the center of mass. Typically, students have prior knowledge and relate center of mass to balance point. Once students start balancing objects, they should begin writing a working definition for the center of mass. After this, students are asked to flip the spoons or tennis rackets in the air and try to catch it. Students should then begin to discuss how the end of the object moves as it rotates and how the center of mass moves as the object is rotated.

1.1, 1.2, 1.4, 1.5,

2.1, 2.2, 3.1, 4.1,

4.2, 4.3, 5.1, 5.2,

5.3, 6.1, 6.2, 6.4,

7.1, 7.2

21 Hanging with Atwood Note- students should be familiar with Atwood machines from Unit 4- this could be a review activity or introduction activity. Atwood machines are hung from the ceiling for each lab group. Initially two equal masses are hanging. Students are encouraged to play with machines and record all physic-related observations. Unequal masses are then hung and students observe again. Coins are then placed on one side of the machine. Students must make more observations and then draw conclusions about the center of mass and the system. Misconceptions should be discussed during this activity.

1.1, 1.4, 1.5, 2.1,

2.2, 3.1, 4.1, 4.2,

4.3, 5.3, 6.1, 6.4,

7.2

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22 Modeling Large Atwoods Students work individually to draw a large Atwood machine. Values for m1 and m2 must be greater than 25 kg with differences between 2-5kg. On the (8.5 x 17) paper, the calculation for the systems acceleration is shown and a dot is used to represent the center of mass. Once acceleration is known, students determine how much distance exists between the larger mass and the bottom edge of the paper and calculate the time needed to reach the bottom edge. This time is divided into fifths and the students calculate the location of the mass for these intervals and mark the relative position for the center of mass and m1 and m2.

1.1, 1.4, 1.5, 2.1,

2.2, 3.1, 4.1, 4.2,

4.3, 5.3, 6.1, 6.4,

7.2

23 Hidden Masses Students working in small groups are challenged to first discover a way to change the center of mass motion of a simple system from the outside of the system and then from the inside of the system. A demonstration involving wheels with hidden masses may be utilized as a discrepant event to get students asking questions (as the two seemingly identical objects roll down an incline at different rates). Students can use and manipulate the demonstration apparatus if they wish. Students are promised a special prize if they can develop a way to change the center of mass motion from within the system. A logical explanation (including mathematical and/or graphical proof) of any change in motion is required, as are any explanations that it is not possible.

Teacher Produced materials needed: Two wheels, one of which has four small masses hidden near the axis of rotation and one of which has the same amount of mass hidden near the outer edge)

1.1, 1.4, 1.5, 2.1,

2.2, 3.1, 4.1, 4.2,

4.3, 5.3, 6.1, 6.4,

7.2

24 Unit Assessment A modified Atwood’s machine lab is used in place of a regular multiple choice and/or free-response test. Students are given basic instructions for setting up a modified Atwood’s machine. Students are also givenfour objectives to solve for:1. Acceleration of the system2. Final velocity of the system3. Tension in the string4. Coefficient of friction between the bench top and the dragged object(The order of the four calculations is designed to enable students to figure out how to solve for μ.) Students work together in their lab groups and turn in a formal lab report that details their analysis (both qualitatively and quantitatively) and includes a full discussion of potential error and uncertainty.

Modified from Madison County High SchoolDanielsville, Georgia AP Physics Assessments.

1.1, 1.4, 1.5, 2.1,

2.2, 3.1, 4.1, 4.2,

4.3, 5.3, 6.1, 6.4,

7.2

Suggested Materials:1. Giancoli, D.C. Physics: Principles with Applications. Englewood Cliffs, NJ: Pearson

Education.2. Appel, K, Ballen, C, Gastineau, J, Vernier, D. Physics with Vernier. Beaverton, OR;

Vernier Software and Technology, 2010. 3. Puri, O; Zober, P. Physics. A laboratory manual; Boston, Mass. N.Y: Pearson Custom

Pub., 2002. 8th edition

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Suggested Technology Resources:Labs, in class activities, videos and demos:

Brian Cox Explains the Forces of Nature Video- Good introduction for TSW 1 (use 1st two minutes of video) http://www.theguardian.com/science/video/2011/mar/04/brian-cox-forces-nature-video

Forces and Newton’s Law Video (22 minute- possible homework assignment) It can be used as a pre-lesson for introducing Newton’s Laws of Motionhttp://www.tiros.ca/videos/laws.html

Newton’s 2nd Law Inquiry Lab (Lab #16) http://media.collegeboard.com/digitalServices/pdf/ap/ap-physics-1-and-ap-physics-2-inquiry-based-lab-investigations.pdf

Inertial vs Gravitational Mass- Web Lesson (lab #17) http://dev.physicslab.org/Document.aspx?doctype=3&filename=Dynamics_InertialGravitationalMass.xml

2.11 Modified Atwood Machine http://media.pearsoncmg.com/bc/aw_young_physics_11/pt1a/Media/ForcesMotion/ModifiedAtwood/Main.html

Distinguishing between Newton’s Laws- Online Worksheets http://dev.physicslab.org/Document.aspx?doctype=5&filename=Dynamics_Distinguishing2nd3rdLawForces.xml

Ropes and Pulleys Static Equilibrium- Interactive Worksheet http://dev.physicslab.org/Document.aspx?doctype=5&filename=Dynamics_StaticEquilibrium.xml

The Physics Classroom review notes and questions for Newton’s Laws http://www.physicsclassroom.com/reviews/newtlaws/newtlawsprint.cfm

System of two or more bodies- many activities and worksheetshttp://ocw.mit.edu/high-school/physics/exam-prep/newtons-laws-of-motion//systems-two-or-more-bodies-3rd-law/

Table Cloth Trick- YouTube- http://www.youtube.com/watch?v=0F4QJU-qvYY Horse and Carriage Problem- http://www.hitxp.com/phy/cph/021202.h or

https://www.lhup.edu/~dsimanek/physics/horsecart.htm Pulley and Atwood machines online notes and questions-

http://www.physics247.com/physics-homework-help/pulley.php Newton’s Third Law Quiz (6 questions) http://www.dctech.com/physics/help/tests.php?

maketest=yes&selection%5B%5D=motion-newton-third

Online quizzes or homework assignments:Skydiver phenomenon briefly explored. (two questions.)

http://media.pearsoncmg.com/bc/aw_young_physics_11/pt1a/Media/ForcesMotion/ SkyDiver/Main.html

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Net Force Quiz- http://www.physics247.com/physics-homework-help/netforce.php Newton’s Second Law Quiz http://www.dctech.com/physics/help/tests.php?maketest=yes&selection%5B%5D=motion-newton-second

Students work to solve changing representations problems (similar to AP FR questions) that require use of Newton’s 2nd Law. These include incline, friction and pulley questions. Hieggelke, Maloney, Karim- questions 31, 34, 52-53, 63-,64,76, 78, 87

Note- All links to online resources were verified before publication. In cases where links are no longer working, we suggest that you try to find the resource by a keyword internet search.

RUBRIC FOUND ON FOLLOWING PAGE……………………………….

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SUGGESTED RUBRIC AP PHYSICS 1 E03

Student Name: __________________________ Date: _______________________ To receive a ‘B’, the student must show ‘B’ level mastery on all essential outcomes (TSW’s). The teacher’s discretion on the student’s holistic performance on the unit, including such items as: the above ‘A’ level rubric, the unit project, group work and class

discussions will determine ‘A’ level mastery.The Student Will ‘A’* LEVEL ‘B’ LEVEL Comments

1. TSW explain that forces exerted on an object is always due to the interaction of that object with another object. Including the ideas that:

a. An object cannot exert a force on itself.

b. Even though an object is at rest, there may be forces exerted on that object by other objects.

c. The acceleration of an object, but not necessarily its velocity, is always in the direction of the net force exerted on the object by other objects. (EK 3.A.3)

Uses appropriate concepts (gravity, weight, friction, tension, basic push/pull of objects) to analyze a scenario (develop arguments, justify assertions) about the forces exerted on an object by other objects for different types of forces or components of forces.

For example: The student will be able to accurately describe the effect of gravity, friction and inertia of the following scenario: A school bus comes to a sudden stop, all backpacks fall to the ground and start to slide forward.

Describes a force as an interaction between two objects and identify both objects for any force. (LO 3.A.3.3)

For example: The student can identify the downward force (gravity) and the upward force (tension) of a lamp suspended from a chain with negligible mass.

2. TSW challenge a claim that an object can exert a force on itself. [LO 3.A.3.2, SP 6.1]

Justification on claim is clearly stated and understood.

For example: Students should be able to explain why Newton’s Third Law is not broken in the horse and carriage problem.

Approach chosen is clearly shown, clearly written or articulated with valid elements. (Claims may have minor errors as long as basic understanding is not disrupted.)

For example: Students can clearly justify which MC choices are correct and incorrect.

Joanne exerts a force on a basketball as she throws the basketball to the east. Which of the following is always true? (A) Joanne accelerates to the west. (B) Joanne feels no net force because she and the basketball are initially the same object. (C) The basketball pushes Joanne to the west. (D) The magnitude of the force on the basketball is greater than the magnitude of the force on Joanne.

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3. TSW justify if one object exerts a force on a second object, the second object always exerts a force of equal magnitude on the first object in the opposite direction. [EK 3.B.4]

Analyze situations involving interactions among several objects by using free-body diagrams that include the application of Newton’s third law to identify forces. ( LO 3.A.4.3)

Uses Newton’s third law to construct explanations, make claims and predictions about the action-reaction pairs of forces when two objects interact. (LO 3.A.4.1)

For example: Students build a wind-powered vehicle. A fan attached to the vehicle is powered by a battery located inside the vehicle. Describe the motion of the vehicle when the fan is powered on. Justify your answer in a clear, coherent, paragraph-length explanation.

4. TSW represent forces in free body diagrams using appropriately labeled vectors with magnitude, direction, and units during the analysis of a situation. [EK 3.B.2]

Reexpresses a free-body diagram representation into a mathematical representation and solve the mathematical representation for the desired force of the object. (LO 3.B.1.3):

For example: Curves can be banked at just the right angle that vehicles traveling a specific speed can stay on the road with no friction required. Given a radius for the curve and a specific velocity, at what angle should the bank of the curve be built?

Accurately draws and labels free body diagrams. (LO 3.B.2.1)

For example: Curves can be banked at just the right angle that vehicles traveling a specific speed can stay on the road with no friction required. Draw the free body diagram and pseudo-FBD to describe this scenario.

5. TSW calculate net force and predict motion of objects interacting with each other. [EK 3.B.1]

Designs a plan to collect and analyze data for motion (static, constant, or accelerating) from force measurements and carries out an analysis to determine the relationship between the net force and the vector sum of the individual forces. (LO 3.B.1.2)

Predicts the motion of an object subject to forces exerted by several objects using an application of Newton’s second law in a variety of physical situations with acceleration in one dimension. (Clearly demonstrating that the net force is the vector sum of the individual forces.) (LO 3.B.1.1)

6. TSW identify contact forces result from the interaction of one object touching another, and they arise from the interatomic electric forces. These forces include tension, friction, normal and spring. [EK 3.C.4]

Explains contact forces (tension, friction, normal, buoyant, spring) as arising from interatomic electric forces and therefore having certain directions. [LO 3.C.4.2, SP 6.2]

Makes claims about various contact forces between objects based on the microscopic cause of those forces. [LO 3.C.4.1, SP 6.1]

7. TSW articulate situations when the gravitational force is the dominant force and when the electromagnetic, weak, and strong forces can be ignored. [LO 3.G.1.1, SP 7.1]

Identifies when gravitational forces are the dominate force and all other forces can be neglected. For example: A student should be able to explain why when a person steps on an escalator moving downward at a constant speed the normal force

41QSI AP PHYSICS 1 SEC E03Copyright 1988-2015

exerted on him by the step is equal to his weight when he is off the escalator.

8. TSW examine the relationship between gravitational field, g, an object with mass, m. [EK2.B.1]

Applies F = mg to calculate the gravitational force on an object with mass m in a gravitational field of strength, g, in the context of the effects of a net force on objects and systems. [LO 2.B.1.1, SP 2.2, SP 7.2]

9. TSW describe linear motion of a system by the displacement, velocity, and acceleration of its center of mass.

Calculates linear motion of a system by the displacement, velocity, and acceleration of its center of mass.

For example- Using the B-level example, the student accurately determines the speed of the remaining piece of the firecracker immediately following the explosion. Neglecting air resistance. Answer 70m/s

Note- This problem could also be approached as conservation of linear momentum problem.

Represents the center of mass of an isolated two-object system to analyze the motion of the system qualitatively and semiquantitatively. [LO 4.A.1.1, SP 1.2, SP 1.4, SP 2.3, SP 6.4]

For example- Students should recognize that the following question is a center-of-mass problem with no external forces. A firecracker is launched with an initial velocity of 70m/s at an angle of 73 degrees with the horizontal. The firecracker explodes at its highest point, splitting into three equal pieces. One piece continues at the same horizontal speed, but moved vertically upward at 10 m/s immediately after the explosion. A second piece moves vertically downward at 10m/s, but with horizontal velocity of 30 m/s backward immediately after the explosion.

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If grading for AP test preparation, please refer to Course Outcome Rubric.

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2. TSW justify that acceleration is equal to the rate of change of velocity with time, and velocity is equal to the rate of change of position with time. Including the ideas that:

a. The acceleration of the center of mass of a system is directly proportional to the net force exerted on it by all objects interacting with the system and inversely proportional to the mass of the system.

b. Force and acceleration are both vectors, with acceleration in the same direction as the net force. [EK 4.A.2]

Creates mathematical models and analyzes graphical relationships for acceleration, velocity, and position of the center of mass of a system and use them to calculate properties of the motion of the center of mass of a system. (LO 4.A.2.3):

For example: In a lab setting, the students should be able to justify what is needed to calculate the mass of block B in the following scenario. Answer C

Accurately makes predictions about the motion of a system based on the fact that acceleration is equal to the change in velocity per unit time, and velocity is equal to the change in position per unit time. (LO 4.A.2.1) For example: Answer D

3. TSW validate in a lab setting (virtual or practical) that forces that systems exert on each other are due to interactions between objects in the systems. If the interacting objects are parts of the same system, there will be no change in the center-of-mass velocity of that system. [EK 4.A.3]

The student is able to apply Newton’s second law to systems to calculate the change in the center-of-mass velocity when an external force is exerted on the system. (LO 4.A.3.1)

The student is able to use visual or mathematical representations of the forces between objects in a system to predict whether or not there will be a change in the center-of-mass velocity of that system. (LO 4.A.3.2)

4. TSW be able to solve problems in which application of Newton’s laws leads to two or three simultaneous linear equations involving unknown forces or accelerations.

Correct starting equations; All mathematical stepsare clearly shown and they flow easily toward the correct answer.

Correct starting equations. All mathematical steps are clearly shown but minor errors yield wrong answer.

ORCorrect starting equations with correct final result but the mathematical steps are hard to follow.

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