Download AP PHYSICS 1

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-ofmass 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:
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Force
Vector nature
Weight
Normal Force
Dynamic Equilibrium
Free Body Diagrams
Net Force
Factors of Acceleration
Friction
String Tension
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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
T = W + ma
Weight formula where g= 9.8ms-2
Tension if the body is moving upward
Friction Formula
T = W – ma
FGP= -FPG
Tension if the body is moving downward
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 #
11
12
13
14
15
Name of Laboratory
Y Spring and Free Body
Diagrams
Drawing Free Body Diagrams
Inertia Mini Labs
Bowling Grand Prix
Coffee Filter Drop
Description of Lab
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
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
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
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 onlinehttp://slapt.org/resources/labs/bowlingprix.html
Using motion detectors students drop different numbers
of basket-like coffee filters. The graphs are printed and
analyzed detailing each segment of the graph.
Associated Science
Practices
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
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
1.4, 2.1, 2.2, 3.1,
4.1, 4.2, 4.3, 5.3,
6.1, 6.4, 7.2
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
1.4, 2.1, 2.2, 3.1,
4.1, 4.2, 4.3, 5.3,
6.1, 6.4, 7.2
Vernier
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17
AP Physics 1 Sample Lab # 1:
Newton’s Second Law
What Factors Affect the
Acceleration of a System?
Inertial vs Gravitational Mass
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 @Amrita
If equipment is not availablehttp://amrita.vlab.co.in/index.php?sub=1&brch=74&sim
=207&cnt=4 virtual lab (must register- free)
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.
1.4, 2.1, 2.2, 3.1,
4.1, 4.2, 4.3, 5.3,
6.1, 6.4, 7.2
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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19
20
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Bungee Jump Accelerations
AP Physics Sample Lab #1 –
Newton’s Second Law
Define Me- Center of Mass
Hanging with Atwood
Link is listed in technology link
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
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-labinvestigations
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.
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.
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1.4, 2.1, 2.2, 3.1,
4.1, 4.2, 4.3, 5.3,
6.1, 6.4, 7.2
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
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
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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Modeling Large Atwoods
Hidden Masses
Unit Assessment
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.
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)
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 given
four objectives to solve for:
1. Acceleration of the system
2. Final velocity of the system
3. Tension in the string
4. 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.
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
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
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
Modified from Madison County High School
Danielsville, Georgia AP Physics Assessments.
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-2inquiry-based-lab-investigations.pdf
 Inertial vs Gravitational Mass- Web Lesson (lab #17)
http://dev.physicslab.org/Document.aspx?doctype=3&filename=Dynamics_InertialGra
vitationalMass.xml
 2.11 Modified Atwood Machine
http://media.pearsoncmg.com/bc/aw_young_physics_11/pt1a/Media/ForcesMotion/Mo
difiedAtwood/Main.html
 Distinguishing between Newton’s Laws- Online Worksheets
http://dev.physicslab.org/Document.aspx?doctype=5&filename=Dynamics_Distinguish
ing2nd3rdLawForces.xml
 Ropes and Pulleys Static Equilibrium- Interactive Worksheet
http://dev.physicslab.org/Document.aspx?doctype=5&filename=Dynamics_StaticEquili
brium.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 worksheets
http://ocw.mit.edu/high-school/physics/exam-prep/newtons-laws-of-motion//systemstwo-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 questionshttp://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=moti
on-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/Sky
Diver/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=moti
on-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
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)
2. TSW challenge a claim that an object can exert
a force on itself. [LO 3.A.3.2, SP 6.1]
‘A’* LEVEL
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.
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.
‘B’ LEVEL
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.
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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Comments
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]
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]
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)
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?
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)
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]
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Uses Newton’s third law to construct explanations,
make claims and predictions about the actionreaction 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, paragraphlength explanation.
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.
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)
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]
8. TSW examine the relationship between
gravitational field, g, an object with mass, m.
[EK2.B.1]
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.
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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
exerted on him by the step is equal to his weight
when he is off the escalator.
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]
Represents the center of mass of an isolated twoobject 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.
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]
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):
11. 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]
12. 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.
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 centerof-mass velocity of that system. (LO 4.A.3.2)
Correct starting equations; All mathematical steps
are 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.
OR
Correct starting equations with correct final result but the
mathematical steps are hard to follow.

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
If grading for AP test preparation, please refer to Course Outcome Rubric.
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QSI AP PHYSICS 1 SEC E03
Copyright 1988-2015
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