Download Unit 4: Newton`s Laws - Hickman Science Department

A TIME for Physics First
www.physicsfirstmo.org
PROFESSIONAL DEVELOPMENT CURRICULUM
Draft – September 2008
Summer Academy 2006-08
University of Missouri-Columbia, Columbia, MO
UNIT 4: NEWTON’S LAWS
Primary writers:
DORINA KOSZTIN
and
MEERA CHANDRASEKHAR
Department of Physics and Astronomy, University of Missouri, Columbia, MO
Funded by the Missouri Department of Elementary and Secondary Education
Mathematics and Science Partnership High School Science Reform Grant
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Unit 4 –Newton’s Laws
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Acknowledgements: Curriculum 2005-08
Curriculum Writing:
Meera Chandrasekhar, Department of Physics, University of Missouri, Columbia
Gabriel de la Paz, Clayton High School, St. Louis, MO
Dorina Kosztin, Department of Physics, University of Missouri, Columbia (MU)
Dennis Nickelson, William Woods University, Fulton, MO
Curriculum Analysis:
GLE analysis: Matthew Brouk, Morgan County R-II Schools, Versailles, MO and
Kathy Phillips, Science Education Consultant, Fairfax, VA
Modeling analysis: Kandiah Manivannan, Department of Physics, Astronomy and
Materials Science, Missouri State University, Springfield, and James Roble, John
Burroughs High School, St. Louis
High tech/low tech labs: Jack Richens, Christian Fellowship School, Columbia
Math connections: James Tarr, Learning, Teaching and Curriculum, MU
Overall: Sara Torres and Marsha Tyson, Columbia Public Schools
5E analysis: Mark Volkmann, Learning, Teaching and Curriculum, MU
Notebooking connections: Laura Zinszer, West Junior High School, Columbia \
Timelines: Gabriel de la Paz, Clayton High School, St. Louis
Unit Objectives Analysis: Linda Kralina and Nancy Iannotti, Coach Mentors
Astronomy: Lanika Ruzhitskaya, School of Information Sciences and Learning
Technologies, University of Missouri, Columbia, MO
Teacher Feedback: Ryan McCoy, Francis Howell Central HS; Doug Steinhoff,
Jefferson Jr. High; Amy Campbell, Hazelwood East HS; Jason Bradley, Webb City
HS; Dale Orr, Winnetonka HS.
Sources Include:
Arizona State University Modeling materials: http://modeling.asu.edu/
Thinking Physics, Lewis Caroll Epstein, Insight Press, San Francisco, 1985
Five Easy Lessons, Randall D. Knight, Pearson Education, San Francisco, 2004
Exploring Physics, Meera Chandrasekhar, Rebecca Litherland & Jennifer Geib, 2001
Deborah Rice and Rex Rice, St. Louis, MO, Consultants, 2006
M. Schober’s website, http://www.jburroughs.org/science/mschober/physics.html
CAPER (Conceptual Astronomy and Physics Education Research), Univ. of Arizona
Summer Academy Instructors 2006-08
Faculty Instructors:
Meera Chandrasekhar, University of Missouri, Columbia
Dorina Kosztin, University of Missouri, Columbia
Kandiah Manivannan, Missouri State University, Springfield
Peer Teachers:
Gabriel de la Paz, Clayton High School, St. Louis
Dennis Nickelson, William Woods University, Fulton
James Roble, John Burroughs High School, St. Louis
Science Education Instructors:
Mark Volkmann, University of Missouri, Columbia
Sara Torres, Columbia Public Schools
Mathematics Education Instructor:
James Tarr, University of Missouri, Columbia
Physics Teaching Assistants:
David Arrant (2006-07), Nicholas Criswell (2007), Justin Riffle (2006-08),
Chelsea Brzuchalski (2008), Mason Prashek (2008), Department of Physics and
Astronomy, University of Missouri
Astronomy Observatory Facilitators: Ralph Dumas, Randall Durk, Val Germann,
and Lanika Ruzhitskaya, Central Missouri Astronomical Association
 A TIME for Physics First
Unit 4 –Newton’s Laws
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Table of Contents
Unit 4 Big Ideas ............................................................................................. 4
Unit 4 Objectives ........................................................................................... 5
Student Misconceptions .................................................................................. 7
Sequence of Concepts .................................................................................. 10
Newton's Third Law Lab ................................................................................ 13
Newton’s Third Law with Force Probes Lab ...................................................... 14
Reading Page – Newton’s Third Law ............................................................... 23
4.1. Practice: Identifying Pairs of Forces I ..................................................... 26
4.2. Practice: Identifying Pairs of Forces II .................................................... 28
4.3. Practice: Forces, Acceleration and Collisions ........................................... 33
4.4. Practice: Newton’s Third Law with Blocks................................................ 35
4.5. Practice: Newton’s Third Law Problems .................................................. 37
What Does It Take to Move? – Lab ................................................................. 40
Acceleration, Mass and Force: Pre-Lab Exercise ............................................... 42
Acceleration, Mass and Force Lab ................................................................... 45
Reading Page – Newton’s Second Law ............................................................ 47
4.6. Practice: Force Diagrams, Motion Diagrams and Newton’s Second Law ...... 52
Upward and Downward Ride Lab .................................................................... 61
4.7. Practice: Elevator Problems .................................................................. 64
4.8. Practice: Newton’s Second Law and Motion ............................................. 65
APPENDIX ................................................................................................... 66
Materials List for Unit 4 Labs ......................................................................... 67
Sample Data for Unit 4 Labs .......................................................................... 68
Newton’s Third Law with Force Probes Lab.................................................... 68
Sample Worksheet for What Does It Take to Move? – Lab ................................. 70
Unit 4 - Newton’s Laws: GLE and Process Standards by Activity ......................... 72
Unit 4 Recommended Timeline....................................................................... 74
4.9. Practice: Vertical Acceleration ............................................................... 75
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Unit 4 –Newton’s Laws
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Unit 4 Big Ideas
1. Net force is proportional to mass and acceleration.
2. Forces come in pairs.
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Unit 4 –Newton’s Laws
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Unit 4 Objectives
Core Concept: Newton’s Laws
Newton’s laws describe the connection between forces and motion, and the
interaction between objects.
Learning Goals:
By the end of this unit, the students should know and be able to:
1. Compare the forces on two objects that are interacting (Newton’s Third Law).
(DOK3)
a. Identify the forces acting on an object.
b. Identify the action and reaction forces in an interaction between objects.
c. Identify the objects upon which a given pair of forces acts.
d. Construct a separate force diagram for each object in an interacting pair,
labeling each force with its type, agent and receiver.
e. Label all Newton’s Third Law pairs that occur in given force diagrams.
f. Predict the relationship between action-reaction forces for interacting
objects and then test the predictions, using force probes.
g. Draw the action-reaction pair of forces as equal in magnitude and in
opposite direction (FAB = - FBA)
2. Design and conduct an experiment to explain the relationship between, force,
mass and acceleration. (DOK4)
a. Predict the relationship between force, mass, and acceleration.
b. Investigate the relationship between force, mass, and acceleration, (using
technology, e.g., motion detectors, force probes).
c. Show that force is related to acceleration (but not velocity).
d. Identify the system for a given problem in which Newton’s Second Law is
applied.
e. Show that the directions of net force and acceleration are the same.
f. Plot and interpret a graph of force vs. acceleration, a graph of force vs.
mass and a graph of mass vs. acceleration.
g. Develop the mathematical relationship between force, mass, and
acceleration.
h. Determine the net force in situations where acceleration is known
(Newton’s Second Law).
3. Analyze the forces acting on an object according to Newton’s Laws using
multiple representations (i.e., motion diagrams, force diagrams, verbal
descriptions, graphs, pictures, mathematical models, etc.). (DOK4)
a. Draw force diagrams and motion diagrams of forces acting on objects.
b. Give verbal description of force effects on objects.
c. Draw a physical diagram from a verbal description of forces acting on an
object.
d. Determine algebraically the direction and strength of the net force acting
on each object in an interacting pair.
e. Contrast the paired forces when a large object and a small object interact.
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Unit 4 –Newton’s Laws
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f. Plot and interpret a graph of force vs. acceleration, a graph of force vs.
mass and a graph of mass vs. acceleration.
4. Mathematically and graphically determine the force, mass and/or acceleration of
an object. (DOK3)
a. Determine the acceleration due to gravity from a force vs. mass graph.
b. Resolve forces acting on interacting objects into their x- and ycomponents, then find the net (or resultant) force by taking the vector
sum of the forces (by a graphical method).
c. Solve quantitative problems involving forces, mass and acceleration using
Newton’s Second Law, a = F/m.
d. Determine the velocity or displacement of an object, given the net force
and mass.
5. Analyze the motion of an object based on Newton’s Three Laws. (DOK4)
a. Measure and analyze the forces that occur while riding in an elevator.
b. Recognize that an accelerating object experiences a net force.
c. Compare the forces involved when objects are stationary or moving at a
constant speed.
d. Compare and contrast the motion of two interacting objects, e.g., a small
mass object interacting with a large mass object.
e. Analyze applications of Newton’s Three Laws of Motion in everyday life.
Learning Methods:
The A TIME for Physics First classroom uses inquiry and modeling techniques and
follows the 5E model to teach the curriculum. These methods are described in more
detail in the documents*:
1. Conceptual Framework, Inquiry and Modeling of Physics First, by Mark Volkmann
2. A Modeling Method for High School Physics Instruction by Malcolm Wells, David
Hestenes* & Gregg Swackhamer, Am. J. Phys. 63 (7), July 1995, 606-619.
3. Modeling Instruction in High School Physics by J. Mark Schober
4. Modeling Methodology for Physics Teachers by David Hestenes, Proceedings of
the International Conference on Undergraduate Physics Education (College Park,
August 1996).
* included in the Resources folder of this CD
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Unit 4 –Newton’s Laws
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Student Misconceptions
1. Motion requires a force, or force causes motion or an object will slow down if
there is no net force.
Students hold the Aristotelian idea that an object's natural state is rest. Thus
they believe that objects only move when a net force is exerted upon them. This
stems from common everyday observations, e.g. students seeing that objects
which have been pushed across the floor come to a stop (and not seeing friction
as dissipative force acting on the object).
2. The motion will follow the path of the stronger force on the object.
Rather than associating the direction of the net force with the direction of the
acceleration, some students think that the object will accelerate in the direction
of the force with the largest magnitude.
3. Passive forces don't exist (tables don't exert a normal force).
Some students believe that inert objects cannot exert a force. They can alter an
object's motion, but they don't exert a force.
4. Normal forces won't exceed the weight (active force) on an object.
Many students hold that the normal force acting on an object is equal to the
weight of the object, regardless of the physical situation. Thus the normal force
has an upper (and lower) limit placed on it.
5. An object with a constant net force will have a constant speed.
Some students believe that force is proportional to velocity. Thus if velocity isn't
changing, the net force must be (a non-zero) constant. Furthermore, they
associate an acceleration with an increasing force.
6. Faster moving objects have a larger force acting on them.
Some students believe that force is proportional to velocity. Thus if velocity is
larger, the net force must be larger. Furthermore, they associate acceleration
with an increasing force.
7. A constant force accelerates a body, until the body uses up all the power of the
force.
From common everyday observations, e.g. students pushing on an object which
is sliding across the floor, they find the force which will initially accelerate an
object produces a constant velocity soon after (due to velocity dependent nature
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Unit 4 –Newton’s Laws
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of friction that we all ignore in F = N). Thus students conclude that the force
has been used up by the body.
8. The net force must be in the direction of motion, so objects will travel along a
line in that direction.
Some students believe that force is proportional to velocity. Thus they assume
that net force is in the same direction as velocity. Without seeing acceleration's
role in changing the velocities' direction, they assume that the object will travel
in a straight line.
9. Objects can be trained to follow a certain path by forces, and will continue along
that path, even after the forces are removed.
Some students believe that if an object repeats a motion, it will (inherently)
learn that motion, and continue it regardless of changes in the forces acting on
it. For example, a rock spun on a string is believed to continue on a curved path
after the string is cut or released.
10. Heavier objects fall faster than light objects.
Just like feathers fall more slowly than rocks, students believe that light objects
simply fall slower than heavier objects.
11. Objects will point in the direction of their velocity.
Like the trajectory of a football pass will have the point of the ball pointing in the
direction of its velocity, students believe that objects will point in the direction of
their velocity (regardless of the forces acting on them). The original motion of
the object can define its "point" (which could be one side of a cube).
12. Force must be positive, plotted above the time axis.
Many students have difficulty in associating the opposite direction with a change
in sign. Some students will insist that forces, like their magnitudes, are always
positive.
13. Strings transmit (unchanged) an external force acting on one object to another
object.
Some students believe that if two objects are tied together by a (continuously
taught) string, while one object is pulled by an external force, the second object
experiences a force equal in magnitude to the external force (regardless of its
mass).
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Unit 4 –Newton’s Laws
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14. The tension in a string is the sum of the forces acting on each end.
Students add the magnitudes of the each of the forces acting on strings/ropes
and treat that as the tension in the string/rope.
15. The force of throw travels with the object
Students believe that the force applied to a ball when throwing it travels with
the ball (acts on the ball when the ball is airborne) until all the force is used up
(impetus theory)
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Unit 4 –Newton’s Laws
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Sequence of Concepts
1: Newton’s Third Law
Engage/Explore
Framing Questions
Activities:
Newton’s Third Law Lab
 Develop a force law for two objects interacting with one another.
Explain/Elaborate
Activities:
Newton’s Third Law with Force Probes Lab
 Investigate the similarities/differences between paired forces when a large
and a small object interact
 Investigate the similarities/differences between paired forces when objects
are stationary or moving at a constant speed
 Identifying action-reaction pairs
Practice and Reading Pages (RP):
Reading Page: Newton’s Third Law
Evaluate
Practice and Reading Pages (RP):
4.1 Practice: Identifying Pairs of Forces
4.2 Practice: Forces, Acceleration and Collisions
4.3 Practice: Newton’s Third Law with Blocks
4.4 Practice: Newton’s Third Law Problems
2: Newton’s Second Law
Engage/Explore
Activities:
What does it take to move? – Lab
 Draws upon students’ prior knowledge of connections between force and
motion; connects force diagrams and motion diagrams
 Makes students come to the qualitative conclusion that force is related to
acceleration, not to velocity.
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Unit 4 –Newton’s Laws
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Explain
Activities:
Acceleration, Mass and Force – Pre-Lab Exercise
 Predictive exercise in finding the quantitative relationship between force,
mass and acceleration.
Acceleration, Mass and Force Lab
 Find the quantitative relationship between force, mass and acceleration.
 Identify the system for which Newton’s 2nd law is applied
 Understand the that the directions of force and acceleration are the same
 Understand the source of the constant of proportionality that connects force,
mass and acceleration.
Practice and Reading Pages (RP):
Reading Page: Newton’s Second Law
4.5 Practice: Force Diagrams, Motion Diagrams and Newton’s Second Law
Elaborate
Upward and Downward Ride Lab
 Experience and analyze forces felt in an elevator.
 Recognize that acceleration influences the actual forces felt by an object
Evaluate
Practice and Reading Pages (RP):
4.6 Practice: Elevator Problems
4.7 Practice: Newton’s Second Law and Motion
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Framing Questions
1. Ben and Ronda pull on opposite ends of a
rope in a game of tug-of-war. Ben is stronger
than Ronda. Who exerts the larger force on the
rope?
a) Ben
b) Ronda
c) both exert the same amount
2. Now assume that Ben and Ronda have the same mass. They stand 4 meters
apart and attempt playing tug-of-war on frictionless ice. First they pull on opposite
ends of the rope with equal force, and observe that each one slides 2 meters to a
point midway between them. Next, they start 4 m apart, Ronda has the rope
fastened around her waist and only Ben pulls. How far does each person slide?
3. True or false? If a net force of 20 N oriented toward North acts on an object, the
object moves North. Explain your answer.
4. A mall sports car collides head on with a heavy truck. The greater force of impact
acts on (a) the car, (b) the truck, (c) neither, the force is the same on both.
5. Which vehicle undergoes the greatest magnitude acceleration? (a) the car, (b)
the truck, (c) neither, the accelerations are the same for both.
6. A weight lifter stands on a bathroom scale. He pumps a barbell up and down.
What happens to the reading on the scale? Is it changing, or is it the same? Explain
your answer. Now the weight lifter decides to throw the barbell into the air. How
does the reading on the scale change?
7. When you are rowing a boat, the paddles are pushed backwards. Why is the boat
moving forward?
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Unit 4 –Newton’s Laws
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Newton's Third Law Lab
(low tech version)
Purpose:
Is there a force law for two interacting objects?
This is the low tech version of the lab.
5E: Engage/Explore
Concepts addressed:
Students develop a force law
for two objects interacting with
Materials
one another.
Low-tech: a pair of spring scales (newtons) platform or two bathroom scales
String
Directions:
5. Ask students to predict what would happen if they hooked their spring scales to
each other and pulled on them. Have them predict their scale readings.
6. Have them try it - both students pull on their scales; have them record the force
on each scale.
7. Ask students to predict: What would happen if one student pulled, while the
other holds firm? What if they reversed their roles, each time comparing the
force that one person exerts to the force that the second person exerts? Have
them record their predictions and explain their reasoning.
After student groups have discussed their predictions and reasoning, have them
try it out. Have them discuss their observations and reasoning.
Ask students about the directions of the forces they apply. Have them express
the forces felt/applied by both students in a mathematical expression. Ask the
students to draw a physical diagram for each case, as well as a force diagram
for each object.
8. Next, ask students to predict what would happen (what the scales will read) if
they pushed two bathroom scales against one another. Then have them predict
what would happen if (a) both push, (b) the first one pushes and (c) the second
student pushes.
White boarding and discussion is recommended at this point.
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Unit 4 –Newton’s Laws
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Newton’s Third Law with Force Probes Lab
(high tech version of Newton’s Third Law Lab)
Purpose:
Is there a force law for two interacting
objects?
5E: Explain/Elaborate
Concepts addressed:
- investigate the similarities/differences
Materials:
between paired forces when a large and
a small object interact
Station 1: Two force probes with rubber
- investigate the similarities/differences
stoppers on each end
between paired forces when objects are
Station 2: Two force probes with a
stationary or moving at a constant
rubber band connecting them
speed
Station 3: Two force probes with blocks
- identifying action-reaction pairs
being pushed - one small and one large
Station 4: Two force probes with blocks being towed - one small and one large
Station 5: Two carts with repelling magnetic bumpers on a track, with attached
force probes
Teacher notes:
 When you demonstrate how to use the force probes, show students only one
probe at a time (so you don’t give the experiment away!).
 You will have to set the logger pro settings to “reverse direction” for one of the
force probes. Force vs. time curves for this experiment will show that, regardless
of which person pulls, the
forces measured by the probes
are equal and opposite
(example shown below).
 White boarding and discussion
(with one station per group) is
recommended at this point.
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Unit 4 –Newton’s Laws
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Station 1: Rubber stopper on the end of each force probe
You and your partner will each hold a force probe. First predict how the force student 1 exerts on
student 2 will compare to the force student 2 will exert on student 1. Explain the reasoning behind
each prediction. Then try the activity. After you have performed the experiment, sketch the graph
of force vs. time shown on the computer. Plot the reading from force probe 1 in red, and force probe
2 in blue. Assume that the force experienced by student 1 is indicated in force probe 1. Your
predictions can take the form of F12 > F21, F12 < F21, or F12 = F21 if you wish, or some other form.
Include a force diagram for each of the students in each situation.
1. Student 1 pushes the stopper
while student 2 passively holds
the force probe
Prediction:
Force Diagrams:
Result:
2. Student 2 pushes the stopper
while student 1 passively holds
the force probe
Prediction:
Force Diagrams:
Result:
3. Both students push on each
other
Prediction:
Force Diagrams:
Result:
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Station 2: Rubber band connecting the hook of each force probe
You and your partner will each hold a force probe. First predict how the force student 1 exerts on
student 2 will compare to the force student 2 will exert on student 1. Explain the reasoning behind
each prediction. Then try the activity. After you have performed the experiment, sketch the graph of
force vs. time shown on the computer. Plot the reading from force probe 1 in red, and force probe 2
in blue. Assume that the force experienced by student 1 is indicated in force probe 1. Your
predictions can take the form of F12 > F21, F12 < F21, or F12 = F21 if you wish, or some other form.
Include a force diagram for each of the students in each situation.
1. Student 1 pulls on the rubber
band; student 2 passively
holds his/her force probe
Prediction:
Force Diagrams:
Result:
2. Student 2 pulls on the rubber
band; student 1 passively
holds his/her force probe
Prediction:
Force Diagrams:
Result:
3. Both students pull on each
other
Prediction:
Force Diagrams:
Result:
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Unit 4 –Newton’s Laws
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Station 3: Cars Pushing each other
You and your partner will each hold a force probe. One of the cars should be imagined to be in neutral
with its engine off. The other car has its engine on and pushes on the first one. Your hand will be like
the engine, pushing the car. The cars are simulated by wooden blocks.
First predict how the force student 1 exerts on student 2 will compare to the force student 2 will exert
on student 1. Explain the reasoning behind each prediction. Then try the activity. After you have
performed the experiment, sketch the graph of force vs. time shown on the computer. Plot the
reading from force probe 1 in red, and force probe 2 in blue. Assume that the force experienced by
student 1 is indicated in force probe 1. Your predictions can take the form of F12 > F21, F12 < F21, or
F12 = F21 if you wish, or some other form. Include a force diagram for each of the students.
1. Large car pushes small car at
constant speed on a level
road
Prediction:
Force Diagrams:
Large car
Small Car
Force Diagrams:
Large car
Small Car
Force Diagrams:
Large car
Small Car
Result:
2. Small car pushes large car at
constant speed on a level
road
Prediction:
Result:
3. Small car pushes large car
while speeding up
Prediction:
Result:
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Unit 4 –Newton’s Laws
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4. Small car pushes large car up
a hill at constant speed (make
a ramp)
Prediction:
Force Diagrams:
Large car
Small Car
Force Diagrams:
Large car
Small Car
Force Diagrams:
Large car
Small Car
Result:
5. Large car pushes the small
car up a hill at constant speed
Prediction:
Result:
6. Large car pushes small car
down the hill at constant
speed
Prediction:
Result:
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Station 4: Cars Towing each other
You and your partner will each hold a force probe. One of the cars should be imagined to be in neutral
with its engine off. The other car has its engine on and pulls on the other one. Your hand will be like
the engine, pulling the car. The cars are simulated by wooden blocks.
First predict how the force student 1 exerts on student 2 will compare to the force student 2 will exert
on student 1. Explain the reasoning behind each prediction. Then try the activity. After you have
performed the experiment, sketch the graph of force vs. time shown on the computer. Plot the
reading from force probe 1 in red, and force probe 2 in blue. Assume that the force experienced by
student 1 is indicated in force probe 1. Your predictions can take the form of F 12 > F21, F12 < F21, or
F12 = F21 if you wish, or some other form. Include a force diagram for each of the students.
1. Large car tows small car at
constant speed on a level
road
Prediction:
Force Diagrams:
Large car
Small Car
Force Diagrams:
Large car
Small Car
Force Diagrams:
Large car
Small Car
Result:
2. Large car tows small car while
speeding up
Prediction:
Result:
3. Small car tows large car while
speeding up
Prediction:
Result:
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4. Small car pulls large car up a
hill at constant speed (make a
ramp)
Prediction:
Force Diagrams:
Large car
Small Car
Force Diagrams:
Large car
Small Car
Force Diagrams:
Large car
Small Car
Force Diagrams:
Large car
Small Car
Result:
5. Large car tows small car up a
hill at constant speed
Prediction:
Result:
6. Small car tows large car down
the hill at constant speed
Prediction:
Result:
7. Large car tows small car
down the hill at constant
speed
Prediction:
Result:
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Station 5: Carts colliding
Two carts, of equal or different masses, will collide as described below. The magnetic bumpers will
extend the time of collision. Be sure to keep the cars on the track.
You and your partner will each hold a force probe. First predict how the force student 1 exerts on
student 2 will compare to the force student 2 will exert on student 1. Explain the reasoning behind
each prediction. Then try the activity. After you have performed the experiment, sketch the graph of
force vs. time shown on the computer. Plot the reading from force probe 1 in red, and force probe 2
in blue. Assume that the force experienced by student 1 is indicated in force probe 1. Your
predictions can take the form of F12 > F21, F12 < F21, or F12 = F21 if you wish, or some other form.
Include a force diagram for each of the students in each situation.
1. Cart 1 collides with an
identical cart which is initially
at rest
Prediction:
Force Diagrams:
Result:
2. Two identical carts with equal
speeds have a head-on
collision.
Prediction:
Force Diagrams:
Result:
3. Slow cart collides with fast
cart.
Prediction:
Force Diagrams:
Result:
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4. Large-mass cart collides with
a small-mass cart which is
initially at rest
Prediction:
Force Diagrams:
Result:
5. Large-mass cart collides with
small-mass cart that is
initially at rest.
Prediction:
Force Diagrams:
Result:
6. Large-mass cart collides with
small-mass cart, both of
which are moving toward
each other with equal speeds.
Prediction:
Force Diagrams:
Result:
White boarding and discussions may continue at this point.
Sample data for this lab can be found in the Appendix.
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Unit 4 –Newton’s Laws
Page 22
Reading Page – Newton’s Third Law
What is the connection between forces acting on two objects interacting with each
other? Let’s consider the simple interaction between a hammer and a nail. The
hammer exerts a force on the nail as it drives it into the wall. At the same time, the
nail exerts a force on the hammer. If you are not sure that it does, imagine hitting
the nail with a banana or a glass hammer. It is the force of the nail on the banana
that pokes holes into it or shatters the glass.
Let’s look now at the picture on left: a mom is pulling
on her son, trying to get him away from his computer.
The mom interacts with her son, and her son interacts
with the computer. We have already learned how to
identify all the forces acting on the boy, or on the mom
or on the computer. But how do we deal with objects
that interact with each other, such as the mom and the
boy, or the boy and the computer?
Newton’s Third Law explains how two objects/systems interact with each other.
Every time an object A pushes or pulls on an object B, object B pushes or pulls back
on object A. When the mom pulls on the boy, the boy pulls back (and she feels this
in her arms). The two objects, mom and boy, are interacting. An interaction is the
mutual influence of two systems on each other. The boy and mom are also
interacting with the ground/earth.
Let’s analyze all forces acting on the boy:
And now let’s analyze all forces
acting on the mom:
The pulling force applied by the mom on the boy is the action force, and the pulling
force applied by boy on his mom’s arms is the reaction force. Although we name
one force the action and the other force the reaction for convenience, these two
forces occur simultaneously and one cannot strictly specify which one is the “action”
and which one is the “reaction”. An action/reaction pair of forces exists as a pair, or
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not at all. Also, paired action and reaction forces have (a) the same magnitude, (b)
act in opposite directions and (c) act on different objects.
But how about the rest of the forces acting on the boy and mom? Are they part of
an action/reaction pair? Yes, all forces in the universe are part of action/reaction
pairs – there are no forces that act alone. If you look only at the forces acting on
the boy it may seem that these forces are isolated but that is because we have
chosen our system to be one single object: the boy. All forces acting on the boy
arise from his interaction with the environment (which is outside for the chosen
system). To be able to identify all the action reaction forces we must consider the
expanded system which consists of boy, his mom and the ground.
Let’s now identify all the action reaction pairs that act in the system. In the diagram
below the action reaction forces are connected through a dotted line.
For each force applied on the boy, there is a force the boy applies to another
object. The same holds true for the mom. All interaction forces between boy and
mom, boy and ground, and mom and ground are contact forces. The exception is
the weight applied by earth, which is a long range force.
How do action reaction pairs work for long range forces?
If you let a ball fall, it will move down toward the earth because the earth pulls on it
with a force called weight, the action force. But does the ball pull on the earth? Is
there a “reaction” force acting on the earth? Indeed there is. The ball also attracts
the earth with the same amount of force – the weight of the object. Does the earth
then fall toward the ball? Yes, it does. But since the earth is huge and the ball is
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very small what one observes is a larger effect on the small ball. A similar effect
occurs with two magnets: two magnets attract or repel each other through a long
range force that can act at a distance. If you hold a magnet in each hand, you can
feel the force acting on each magnet because long range forces come in pairs too.
There is only one force in the boy + mom + ground diagram for which a force pair
is not drawn: the friction force applied by the keyboard on the boy’s fingers. Is
there no pair for this force? Yes, there is: the force with which the boy’s fingers act
on the keyboard. We have not drawn the reaction for that force intentionally.
Whenever we deal with Newton’s Third Law we must define the system of
interacting object. In our case the system was boy + mom + ground/earth. The
computer was an external object to our system and thus the force applied by the
computer to the boy’s fingers is considered an external force.
Newton’s Third Law states that:
 Every force occurs as one member of an action/reaction pair of forces.
 The two members of an action/reaction pair act on two different objects.
 The two members of an action/reaction pair point in opposite directions, and
are equal in magnitude.
Rules to follow when identifying action/reaction pairs:
1. Identify the objects that are systems of interest. Other objects whose motion you
don’t care about are part of the environment.
2. Draw each object separately. Place them in the correct position relative to other
objects. Don’t forget to include objects like the earth that may not be mentioned in
the problem.
3. Identify every force. Draw the force vector on the object on which it acts. Label
each with a subscripted label. The usual force symbols can be used.
4. Identify the action/reaction pairs. A force goes with a force. Connect the two
force vectors of each action/reaction pair with a dotted line. When you’re done,
there should be no unpaired forces.
5. Draw a free-body diagram for each object within the system. Include only the
forces acting on the objects in your system, not forces that the objects in your
system exert on other objects.
Newton’s third law is one of the fundamental symmetry principles of the universe.
Since we have no examples of it being violated in nature, it is a useful tool for
analyzing situations which are somewhat counter-intuitive. For example, when a
small truck collides head-on with a large truck, your intuition might tell you that the
force on the small truck is larger. Not so! Both cars experience the same force. But
why does the small car sustain much more damage than the truck? That has to do
with Newton’s Second Law!
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4.1. Practice:
Identifying Pairs of Forces I
Identify one pair of actionreaction forces acting on the
objects in the pictures below:
A.
Draw a force diagram of all forces acting on each
one of the objects interacting and write explicitly
which forces make up a pair.
Force from plate pushing up on cake = Force from
cake pushing down on plate
B. 
C. 
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D.
E.
F.
G.
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Unit 4 –Newton’s Laws
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4.2. Practice:
Identifying Pairs of Forces II
Recommended:  = class, whiteboard;  = homework;  = challenge problems
For each of the following problems, draw a physical diagram; construct a separate
force diagram for each object, labeling each force with its type, agent and receiver.
Label any Newton’s 3rd law pairs that occur in your force diagrams.
1.  One book lies on top of another book, which rests on a table. System: the
two books.
Physical Diagram
Force Diagrams:
Force Diagrams:
2.  A person exerts an upward force of 40N to hold a sack of groceries. System:
person’s hand and sack of groceries.
Physical Diagram
Force Diagrams:
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Force Diagrams:
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3.  A magnet is suspended from the ceiling by a string. A second magnet is held
up by the first magnet. System: the two magnets (they don’t touch each other).
Physical Diagram
Force Diagrams:
Force Diagrams:
4. (a) Eric holds a ball in his hand, and is in the process of throwing the ball
upward. System: hand and ball.
Physical Diagram
Force Diagrams:
Force Diagrams:
(b)  The ball just left Eric’s hand. System: ball and hand.
Physical Diagram
Force Diagrams:
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(c)  The ball is on its way down. System: ball and hand.
Physical Diagram
Force Diagrams:
Force Diagrams:
(d)  The ball has just hit the ground, and is slowing down. System: ball and
ground.
Physical Diagram
Force Diagrams:
Force Diagrams:
5.  You are pushing a box across a very rough floor with a constant speed.
System: you and the box.
Physical Diagram
Force Diagrams:
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6.  You are sitting on a chair on the ground. Draw well-separated diagrams for
your body, the chair and the whole earth. Show the relative sizes of the forces
via the lengths of the force arrows.
Physical
Diagram
Force Diagrams:
Force Diagrams:
Force Diagrams:
7. You are standing on the ground in a shed. You are pulling vertically downward
on a string that is attached to the bottom of a block. The block is attached to
the ceiling by a rope. Draw well-separated diagrams for your body, the string,
the block, the rope, the shed and the earth.
Physical Diagram
Force Diagrams:
Force Diagrams:
Force Diagrams:
Force Diagrams:
Force Diagrams:
Force Diagrams:
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8.  A mass of 250 g is hung from springs in the following configurations. What do
you think the spring scales will read in each case? Each spring scale reads
forces, not masses. Draw force diagrams and explain your reasoning.
A.
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B.
C.
Unit 4 –Newton’s Laws
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4.3. Practice:
Forces, Acceleration and Collisions
Recommended:  = class, whiteboard;  = homework;  = challenge problems
1.  A large truck and a small
car collide. For each situation
below (1 and 2) choose one
answer (A though G) that best
describes the forces between the
car and the truck.
A. The truck exerts a greater amount of force on the car than the car exerts on
the truck.
B. The car exerts a greater amount of force on the truck than the truck exerts on
the car.
C. Neither exerts a force on the other; the car gets smashed simply because it is
in the way of the truck.
D. The truck exerts a force on the car but the car doesn't exert a force on the
truck.
E. The truck exerts the same amount of force on the car as the car exerts on the
truck.
F. Not enough information is given to pick one of the answers above.
G. None of the answers above describes the situation correctly.
Case 1: the truck is much heavier than the car.
1. They are both moving at the same speed when they collide. Which choice
describes the forces?_______________
2. The car is moving much faster than the heavier truck when they collide. Which
choice describes the forces? _______________
3. The truck is moving much faster than the car when they collide. Which choice
describes the forces? _______________
4. The car is standing still when the truck hits it. Which choice describes the
forces? _______________
5. The heavier truck is standing still when the car hits it. Which choice describes
the forces? _______________
Case 2: the truck is a small pickup truck and has the same mass as the car.
1. They are both moving at the same speed when they collide. Which choice
describes the forces? _______________
2. The car is moving much faster than the truck when they collide. Which choice
describes the forces? _______________
3. The truck is moving much faster than the car when they collide. Which choice
describes the forces? _______________
4. The car is standing still when the truck hits it. Which choice describes the
forces? _______________
5. The truck is standing still when the car hits it. Which choice describes the
forces? _______________
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2.  A large truck breaks down and receives a push back to town from a small
compact car. For each situation below (1
through 4) choose one of the choices A
through F that correctly describes the
forces between the car and the truck.
A. The force of the car pushing against the truck is equal to that of the truck pushing
back against the car.
B. The force of the car pushing against the truck is less than that of the truck
pushing back against the car.
C. The force of the car pushing against the truck is greater than that of the truck
pushing back against the car.
D. The car's engine is running so it applies a force as it pushes against the truck, but
the truck's engine isn't running so it can't push back with a force against the car.
E. Neither the car nor the truck exerts any force on each other. The truck is pushed
forward simply because it is in the way of the car.
F. None of these descriptions is correct.
1.
The car is pushing on the truck, but not hard enough to make the truck move.
_______________
2.
The car, still pushing the truck, is speeding up to get to cruising speed.
_______________
3.
The car, still pushing the truck, is at cruising speed and continues to travel at
the same speed. _______________
4.
The car, still pushing the truck, is at cruising speed when the truck puts on its
brakes and causes the car to slow down. _______________
3.  Farmer Brown hitches Old Dobbin to his wagon one day, then says, "OK, Old
Dobbin, let's go!" Old Dobbin turns to Farmer Brown and says "Do you remember
how Newton's Third Law says that every action force has an equal and opposite
reaction force?,” says Old Dobbin. Ignoring Farmer Brown's impatience, he
continues, "If the wagon's pull is always equal and
opposite of my pull, then the net force will always
be zero, so the wagon can never move! Since it is
at rest, it must always remain at rest! Get over
here and unhitch me, since I have just proven that
Newton's Laws say that it is impossible for a horse
to pull a wagon!"
At this point, Farmer Brown throws up his hands in dismay and turns to you.
"Please help me!" he says, "I really should have paid more attention in physics
class! I know that Newton's Laws are correct, and I know that horses really can pull
wagons.”
Help Farmer Brown by drawing separate force diagrams for the wagon, the horse,
and the horse and the cart together. Then explain in words the flaw in the horse’s
reasoning.
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4.4. Practice:
Newton’s Third Law with Blocks
Recommended:  = class, whiteboard;  = homework;  = challenge problems
For each of the situations below compare the forces exerted by the blocks on each
other as they move on a table with some friction. Note: the 100 g block
experiences twice as much frictional force as the 50 g block.
For each of the problems A through F, select from the following choices:
a) block A exerts a greater force
b) block B exerts a greater force
c) the forces are equal
Also draw separate force diagrams for block A, for block B, and for a system that
includes both blocks.
A.
B.
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C.
D.
E.
F. 
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4.5. Practice:
Newton’s Third Law Problems
Recommended:  = class, whiteboard;  = homework;  = challenge problems
1.  While driving down the road, an unfortunate butterfly strikes the windshield of
your car. You are thinking: this is a case of Newton's third law of motion! The
butterfly hit the car windshield and the car windshield hit the butterfly. Which of the
two forces is greater: the force on the butterfly or the force on the car’s windshield?
Explain.
2.  Andy goes hunting for the first time. He has just learned Newton’s Third Law
and is now ready to explain to his dad why the gun recoils when it is fired. He tells
his dad that the recoil is the result of action-reaction force pairs. As the gases from
the gunpowder explosion expand, the gun pushes the bullet forwards and the bullet
pushes the gun backwards. His dad has two questions for Andy (and you must
answer them):
a) How are the forces that act on the gun and on the bullet related and why?
b) Are the accelerations of the gun and the bullet the same? Explain your answer.
3.  Wherever there is an action force, there must be a reaction force which
A) always acts in the same direction.
B) is slightly smaller in magnitude than the action force.
C) is slightly larger in magnitude than the action force.
D) is exactly equal in magnitude.
4.  An archer shoots an arrow. Consider the action force to be exerted by the
bowstring against the arrow. The reaction to this force is the
A) combined weight of the arrow and bowstring.
B) air resistance against the bow.
C) friction of the ground against the archer's feet.
D) grip of the archer's hand on the bow.
E) arrow's push against the bowstring.
5.  A player catches a ball. Consider the action force to be the impact force of the
ball against the player's glove. The reaction to this force is the
A) player's grip on the glove.
B) force the glove exerts on the ball.
C) friction of the ground against the player's shoes.
D) muscular effort in the player's arms.
E) none of these
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6.  A player hits a ball with a bat. The action force is the impact force of the bat
against the ball. The reaction to this force is the
A) air resistance on the ball.
B) weight of the ball.
C) force that the ball exerts on the bat.
D) grip of the player's hand against the ball.
E) weight of the bat.
7.  A karate chop delivers a blow of 3000 N to a board that breaks. The force that
acts on the hand during this event is
A) zero.
B) 1500 N.
C) 3000 N.
D) 6000 N.
8.  Arnold Strongman and Suzie Small each pull very hard on opposite ends of a
massless rope in a tug-of-war. The greater force on the rope is exerted by
A) Arnold, of course.
B) Suzie, surprisingly.
C) both the same, interestingly enough.
9.  An automobile and a small empty wagon traveling at the same speed collide
head-on. The impact force is
A) greater on the automobile.
B) greater on the small empty wagon.
C) the same for both.
10.  A Mack truck and a Volkswagen traveling at the same speed have a head-on
collision. The vehicle that undergoes the greatest change in velocity will be the
A) Volkswagen car.
B) Mack truck.
C) same for both.
11.  A 10.0 N force is pulling vertically up on the ring of spring scale that weighs
2.0 N. If an 8.0 N mass is attached to the bottom hook of the scale, the scale
reading would be
A) 0 N.
B) 2.0 N.
C) 8.0 N.
D) 10.0 N
E) 12.0 N
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12.  A horse exerts 500 N of force on a heavy wagon. The wagon pulls back on
the horse with an equal force.
A) The wagon still accelerates because these forces are not an action-reaction pair.
B) The wagon still accelerates because there is an unbalanced force on the wagon.
C) The wagon still accelerates because the horse pulls on the wagon a brief time
before the wagon reacts.
D) The wagon does not accelerate because these forces are equal and opposite.
E) The wagon does not accelerate the wagon is not alive.
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What Does It Take to Move? – Lab
Purpose:
What is the connection between force
and motion–related factors such as time,
displacement, velocity and acceleration?
Materials:
Cart and spring scale on low-friction
floor
Or large spring scale and a skateboard
Or car, spring scale and track
5E: Engage/Explore
Concepts addressed:
- Draws upon students’ prior knowledge
of connections between force and
motion; connects force diagrams and
motion diagrams
- Makes students come to the
qualitative conclusion that force is
related to acceleration, not to velocity.
Pre-lab discussion:
In this activity, students will pull a cart (or car) with a spring scale, and note the
connection between force and the motion as they tune specific factors. Students
make several predictions and then try the experiments. Make sure that the
prediction-trial steps are not short-circuited, and have students explain their
reasoning at each step. Students are known to have strong preconceptions of the
relationship between force and motion. Their ideas must be discussed in detail.
Note: this lab can be used as a low tech version of the Newton’s second law lab.
Directions:
1. Have students discuss and then predict the forces on a car(t) when it is
stationary.
Questioning strategies: What forces act on a cart that is sitting motionless on a
frictionless surface? Draw a force diagram and a motion diagram.
2. Next, students predict what must happen to make the cart start moving.
Questioning strategies: If you want to make the car(t) move, what must you
do? Suppose you were to attach a spring scale to the cart and pull on it to
make it move. What do you think the spring scale will read? Will the reading
change once the cart is moving? Now try it. As the car(t) just begins to move,
note what the spring scale does, and describe it. Draw a force diagram and a
motion diagram.
3. Next, we want students to start the cart in motion, and keep it moving, with
zero net force. Predict: Is this possible? Explain your reasoning.
Now try it. Describe what happens. Draw a force diagram and a motion
diagram.
What conclusion can you draw about the connection between force and velocity?
4. In this step we want students to start the cart in motion, and keep it moving,
but with a constant force of 2 N. First predict: What do you think the motion
will look like? Explain your reasoning.
Now try it. Describe what happens. Draw a force diagram, and a motion
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diagram.
What conclusion can you draw between force and acceleration?
White boarding and discussion is recommended at this point.
Post-lab discussion- Conclusions
Questioning strategies:
 If an object is moving at a steady speed, what force must be exerted on it?
What if it were moving at twice the speed? (Make sure that students’ answers
are consistent with step 3.)
 If an object is accelerating, what can one conclude about the force on the object?
(Make sure that students’ answers are consistent with step 4.)
 From students’ observations above, have them write four things they learned
about how force is related to the motion factors of speed and acceleration.
These statements should be clearly stated, with evidence from their lab. Have
them return to these conclusions and add to them after the next lab.
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Acceleration, Mass and Force: Pre-Lab Exercise
Purpose:
What is the quantitative relationship
between force, mass and acceleration?
5E: Explain
Concepts addressed:
Predictive exercise in finding the
quantitative relationship between
force, mass and acceleration
The picture on the right is a sketch of a
car or cart attached to a mass hanger with
a light string. The car(t) sits on a
frictionless track, and the pulley is frictionless too. The car(t) is held in place by the
experimenter’s hand.
1. If the car(t) is released, what type of
motion do you expect it to have?
Explain your reasoning.
2. When the car(t) is released, what kind of
motion will the mass hanger have?
Explain your reasoning.
3. Draw force diagrams below for:
A system that consists
A system that consists
only of the mass hanger
only of the car(t)
The net force for this
system is:
The net force for this
system is:
A system which consists of
the car(t), the string, and
the mass hanger
The net force for this
system is:
4. Discuss whether the force diagrams you just drew are consistent with the
predictions you made in steps 1 and 2.
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5. Design an experiment where you can use the motion detector to test your
predictions in step 1.
What factors can you measure? What factors need to be kept constant?
Be sure to address this question: “What kind of motion occurs when a system of
constant mass experiences a constant net force?” What specific motion factor do
you think will be affected by the force?
In order to measure this motion factor, explain what graphs you have to
produce, and how you would use these graphs to test your predictions.
For the next few questions, assume that you have the system pictured previously,
plus anything you choose to add to the car and/or the mass hanger.
6. Question: What effect does changing the net force on a system have on the
acceleration of the system when the mass of the system is held constant? Write
a hypothesis that describes your prediction:
7. Design an experiment that would allow you to test the effect of changing the net
force on the system on the acceleration of the system. Include a description of
the variables you would keep constant in the experiment, and how you would
keep those variables constant.
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Question: What effect does changing the mass of a system have on the
acceleration of the system when the mass of the system is held a constant? Write
a hypothesis that describes your prediction:
8. Design an experiment that would allow you to test the effect of changing the
mass of the system on the acceleration of the system. Include a description of
what variables you would keep constant in the experiment, and how you would
keep those variables constant.
White boarding and discussion is recommended at this point.
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Acceleration, Mass and Force Lab
Purpose:
What is the quantitative relationship
between force, mass and acceleration?
5E: Explain
Concepts addressed:
- find the quantitative relationship
between force, mass and acceleration.
- identify the system for which Newton’s
2nd law is applied
- understand net force and acceleration
have the same direction
- understand the source of the constant
of proportionality that connects force,
mass and acceleration.
Materials:
Car(t) and track
Mass hanger and masses
Pulley and string
Motion detector or smart pulley
Pre-lab discussion:
As a result of the pre-lab exercise, you should know that:
 The system is the car(t), the mass hanger, string plus anything you add to the
cart or hanger
 The total mass of the system is the sum of the masses of all components
described above.
 For a given run, the total mass of the system (hanger + cart) needs to be kept a
constant. When you remove a mass from the hanger, put it on the cart.
 The net force acting on the system is the gravitational force due to the hanger +
any added masses.
 Allow a suspended mass to tow a cart (glider) across the track; ask students to
observe its motion. We’ve already established that a force is required to produce
acceleration. We just haven’t quantified the relationship. Rather than
brainstorming general observations, ask them to identify other factors that might
affect the acceleration of the cart. To proceed, the list must include mass,
amount of friction, and amount of force used to tow the cart.
 Ask them for ideas on how to minimize the effect of friction. After some
discussion, they will hopefully come to the idea of inclining the ramp slightly to
compensate for friction.
 Ask them how to measure the acceleration of the cart. While they cannot
measure it directly, there are at least two ways to determine the acceleration.
One can calculate it from rearrangement of the kinematical model
   12 a t 
1
x  vi t  a t
2
2
2
since vi  0
(Note: The use of this model requires the assumption that acceleration is
constant. The rationale for such an assumption could be based on an "extra
credit" lab.) Another method is to use a motion detector. The slope of the
velocity vs time graph yields the acceleration.
 The dependent variable is the acceleration of the cart.
 The independent variables are the mass of the cart/hanger system and the force
used to pull the cart.
 Make sure to stress that the mass that is being accelerated is the total mass of
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the system (the cart and hanging mass are connected, so both must accelerate
at the same rate).
Directions:
NOTE: The experimental parameters may vary with your equipment
1. Experimental Notes:
Use small mass hangers (e.g. 5g) and change by 10 to 20 g increments.
Increase cart mass by 10-20 g at a time (from the car to the hanger).
Adjust the angle of incline so that the cart can move at a constant speed with a
very small initial push.
Convince students that they must transfer mass from the cart to the hanger in
order to keep the total mass constant when they vary the force.
Convert the hanging mass to newtons.
2. As before, students’ documentation should contain:
The Experimental Question, Constants of the experiment, Hypothesis, IV, DV,
Materials List, Procedure, Data table, and a Graph with a smooth line through
data points.
3. Conclusions:
Questioning strategies: What slope did you get for the graph? What are its
units? What is the intercept, and what does the intercept mean?
White boarding and discussion is recommended at this point.
Post-lab discussion
 Since the units of slope are not intuitive, focus on proportionalities.
 Discuss the combination of two proportionalities into one:
a  Fnet
a
1
m
a
Fnet
m
 Turn the proportionality into an equation; rearrange to solve for k.
ak
Fnet
ma
k
m
Fnet
 Substitute values from regression line to solve for k. With luck, students’ values
should cluster around 1.0. Now is the time to point out that the slope of force of
gravity vs mass (9.8 N/kg) and the slope of velocity vs time (9.8 m/s2) have the
same numerical value due to the way the newton was defined.
 Describe whether and if yes, how the directions of net force and acceleration are
related to one another (since both force and acceleration are vectors and
therefore have associated directions). What does this relationship mean?
 Describe whether and if yes, how the directions of the net force and velocity are
related to one another.
 Have students write four things they learned from this lab.
 Have students return to the conclusions you wrote after the “What does it take to
move?” lab and add the conclusions from this lab.
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Unit 4 –Newton’s Laws
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Reading Page – Newton’s Second Law
Newton’s first law told us what happens when no net external force acts:
 Things that are sitting still will not move on their own, they need an outside
force to make them move.
 Things that are moving in a straight line will not stop, slow down or speed up
on their own, they need an external force to change their motion.
 Things that are moving in a straight line will not change direction unless a
force makes them do so.
So it



is pretty clear that if a net external force does act,
Things that are sitting still can begin to move.
Things that are moving can be made to slow down, speed up or even stop.
Things that are moving in one direction can be made to change direction.
In the previous activity we saw that a net external force changes the motion of an
object by making it accelerate. How does that go along with the statements above?
 Things that are sitting still can begin to move: the object had a velocity of
zero to begin with, and after a force is applied, it accelerates to a higher
velocity.
 Things that are moving can be made to slow down (force is applied to change
a high velocity to low velocity) speed up or even stop.
 Things that are moving in one direction can be made to change direction –
this is also a change in velocity, namely, the amount of velocity may not
have changed, but the direction has, so there is a net acceleration.
We also saw in the previous activity that the amount of mass affects the force
applied. In other words, for two masses to have the same acceleration, the larger
mass needs a larger force. In equation form,
uuur
r
Force = mass x acceleration, or Fnet  ma or
ur uuur
r
F

F

ma

net
A lot of the applications of Newton’s second law deal with the fact that several
forces can act on an object, but if the forces don’t all balance out and there is a net
external force. This net force causes acceleration – and the acceleration will be
along the direction of that net force.
Teacher Notes:
Force anduracceleration
are both vectors, as indicated by the arrow above the
r
symbolur( F and
r a ).
uuur
r
F

ma
Since F and a are related through the equation net
the directions of the force
ur
and
r acceleration are the same (if a force F is along the south-west, the acceleration
a that it causes is also along the south-west direction).
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Unit 4 –Newton’s Laws
Page 47
 A TIME for Physics First
Unit 4 –Newton’s Laws
Page 48
4.1. Practice:
Newton’s Second Law
Recommended:  = class, whiteboard;  = homework;  = challenge problems
For each of the problems below, explain the reasoning behind your answer!!
1.  A 10-kg brick and a 1-kg book are dropped in a vacuum. The force of gravity
on the 10-kg brick is
A) the same as the force on the 1-kg book.
B) 10 times as much
C) one-tenth as much.
D) zero.
2.  If an object's mass is decreasing while a constant force is applied to the
object, would its acceleration decrease, increase, or remain the same? Explain.
3.  An object is propelled along a straight-line path in space by a force. If the
object sweeps up extra particles and its mass becomes twice as much, its
acceleration
A) quadruples.
B) doubles.
C) stays the same.
D) halves.
E) none of these
4.  The force of friction on a sliding object is 10 newtons. Would the applied force
needed to maintain a constant velocity be more than 10 N, less than 10 N or 10
N? Explain.
5.  A 10-N falling object encounters 4 N of air resistance. The net force on the
object is
A) 6 N upwards.
B) 4 N upwards.
C) 6 N downwards.
D) 10 N downwards.
E) none of these.
6.  A 10-N falling object encounters 10 N of air resistance. The net force on the
object is
A) 0 N.
B) 4 N.
C) 6 N.
D) 10 N.
E) none of these
7.  An apple weighs 1 N. When held at rest above your head, what is the net
force on the apple?
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Unit 4 –Newton’s Laws
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8.  An apple weighs 1 N. If Tammy throws it up in the air, what is the force on it
while it is on its way up? What is its acceleration on the way up? What is the
direction of the acceleration?
9.  An apple at rest weighs 1 N. What is the net force on the apple when it is in
free fall? What is its acceleration? What is the direction of the acceleration?
10. A 1-kg rock that weighs 9.8 N is thrown straight upward at 20 m/s.
Neglecting air resistance, would the net force that acts on it when it is half way
to the top of its path be less than 9.8 N, 9.8 N, or more than 9.8 N?
11. Which has zero acceleration? An object
A) at rest.
B) moving at constant velocity.
C) in mechanical equilibrium.
D) all of these
E) none of these
12. Whenever the net force on an object is zero, would its acceleration be less
than zero, zero, or more than zero? Explain.
13. Your car is coasting on level ground at 60 km/h and you apply the brakes
until the car slows to 40 km/h. If you suddenly release the brakes now, would
the car tend to momentarily regain its higher initial speed, continue moving at
40 km/h, or decrease in speed if no other forces act? Explain.
14. When you hang from a pair of gym rings, the upward support forces of the
rings will always
A) each be half your weight.
B) each be equal to your weight.
C) add up to equal your weight.
15. A car has a mass of 2000 kg and accelerates at 2 meters per second per
second. What is the magnitude of the net force exerted on the car?
16. A tow truck exerts a force of 3000 N on a car, accelerating it at 2 meters per
second per second. What is the mass of the car?
17. A girl pulls on a 10-kg wagon with a constant horizontal force of 30 N. If there
are no other horizontal forces, what is the wagon's acceleration in meters per
second per second?
A) 0.3
B) 3.0
C) 10
D) 30
E) 300
18. A force of 1 N accelerates a mass of 1 kg at the rate of 1 m/s2. The
acceleration of a mass of 2 kg acted upon by a net force of 2 N is
A) half as much.
B) twice as much.
C) the same.
D) none of these.
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Unit 4 –Newton’s Laws
Page 50
19. An object following a straight-line path at constant speed
A) has a net force acting upon it in the direction of motion.
B) has zero acceleration.
C) has no forces acting on it
D) none of these
20. A man weighing 800 N stands at rest on two bathroom scales so that his
weight is distributed evenly over both scales. The reading on each scale is
A) 200 N.
B) 400 N.
C) 800 N.
D) 1600 N.
E) none of these
21. When a woman stands at rest with both feet on a scale, it reads 500 N. When
she gently lifts one foot, the scale reads
A) less than 500 N.
B) more than 500 N.
C) 500 N.
22. A 10-N block and a 1-N block lie on a horizontal frictionless table. To provide
them with equal horizontal acceleration, we would have to push with
A) equal forces on each block.
B) 10 times as much force on the heavier block.
C) 10 squared or 100 times as much force on the heavier block.
D) 1/10 as much force on the heavier block.
E) none of these
23. A block is dragged without acceleration in a straight-line path across a level
surface by a force of 6 N. What is the force of friction between the block and the
surface?
A) less than 6 N
B) more than 6 N
C) 6 N
D) need more information to say
24. Suppose a particle is being accelerated through space by a 10-N force.
Suddenly the particle encounters a second force of 10 N in the opposite direction
from the first force. The particle with both forces acting on it
A) is brought to a rapid halt.
B) decelerates gradually to a halt.
C) continues at the speed it had when it encountered the second force.
D) theoretically tends to accelerate toward the speed of light.
E) none of these
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Unit 4 –Newton’s Laws
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4.6. Practice:
Force Diagrams, Motion Diagrams
and Newton’s Second Law
Recommended:  = class, whiteboard;  = homework;  = challenge problems
1. For each of the situations below, draw a picture and then the force diagram.
A. A rightward force is applied to a book in order to
move it across a desk with a rightward acceleration.
Consider frictional forces. Neglect air resistance.
Diagram the forces acting on the book.
B.  A force is applied to the right to drag a sled across
loosely-packed snow with a rightward acceleration.
Diagram the forces acting upon the sled.
C.  A football is moving upwards towards its peak
after having been booted by the punter. Diagram the
forces acting upon the football as it rises upward
towards its peak.
D.  A car is coasting to the right and slowing down.
Diagram the forces acting upon the car.
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Unit 4 –Newton’s Laws
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E.  An egg falls from a nest in a tree. Neglect air
resistance. Diagram the forces acting on the egg as it
falls.
2. In the following problems you are given a representation of the motion that
occurs. Fill in the rest of the table.
A. Picture of motion (the points are drawn at equal 1 second time intervals)
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram:
Verbal description of motion:
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Unit 4 –Newton’s Laws
Page 53
B. Picture of motion (the points are drawn at equal 1 second time intervals)
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram:
Verbal description of motion:
C.  Picture of motion (the points are drawn at equal 1 second time intervals)
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram:
Verbal description of motion:
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Unit 4 –Newton’s Laws
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D.  Picture of motion (the points are drawn at equal 1 second time intervals)
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram
Verbal description of motion
E.  Picture of motion
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram:
Verbal description of motion
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Unit 4 –Newton’s Laws
Page 55
F.  Picture of motion
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram
Verbal description of motion
G.  Picture of motion
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram:
Verbal description of motion and force diagram
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Unit 4 –Newton’s Laws
Page 56
H.  Picture of motion
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram
Verbal description of motion
I.  Picture of motion
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram
Verbal description of motion
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Unit 4 –Newton’s Laws
Page 57
3. In the following table you are given either the motion diagram, force diagram,
verbal description, or a graph. Fill in the rest of the table.
A.  Motion Diagram
Force Diagram (you must
label all forces)
Verbal Description
Position, velocity and acceleration vs time graphs
B.  Motion Diagram
Force Diagram (you must
label all forces)
Verbal Description:
You throw a ball up into the air. Describe what
happens from the instant it leaves your hand up
until it reaches its highest point.
Position, velocity and acceleration vs time graphs
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C.  Motion Diagram of an airplane on a runway
Force Diagram (you must
label all forces)
Verbal Description
Position, velocity and acceleration vs time graphs
D.  Motion Diagram
Force Diagram (you must
label and draw all forces)
Verbal Description:
A ball is pulled up a ramp that has no friction.
Continue the description of its motion:
Position, velocity and acceleration vs time graphs
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Unit 4 –Newton’s Laws
Page 59
E.  Motion Diagram
Force Diagram (you must
label and draw all forces)
Verbal Description:
Position, velocity and acceleration vs time graphs
4.  The motion of a cart in three different situations is described below. Match the
diagram to the motion described and explain your reasoning.
A. A cart is released from the top of a frictionless ramp. Which of the following best
describes the situation after the cart was released? Explain your reasoning.
B. After the cart reaches the bottom of the ramp, a boy gives it a shove and sends
it moving up the ramp. Which of the following best describes the situation just after
the cart was shoved?
C. After it was shoved upward in the previous problem, the cart reaches the highest
point it can reach on the ramp. Which of the following best describes the situation
at the instant when the cart is at its highest point?
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Unit 4 –Newton’s Laws
Page 60
Upward and Downward Ride Lab
Purpose:
What kinds (types) of forces are felt
while riding an elevator?
5E: Elaborate
Concepts addressed:
- experience and analyze forces felt in an
elevator.
- recognize that acceleration influences the
actual forces felt by an object
Materials:
An elevator
A bathroom scale or
A spring scale (preferably 0-10 or 0-20 N) and an object of weight 5-8 N
Pre-lab discussion:
 Students, in groups of two or three ride in an elevator. One of them stands on
the bathroom scale (or holds a spring scale with object hanging on it) and the
others record observations.
 Have students make their predictions before they get on the elevator.
 Test your elevator ahead of time: some elevators will show a larger effect
traveling upward, others while traveling downward.
Directions:
Downward: Beginning -- starting from rest
Prediction (circle one):
Data (circle one):
I think the scale will read
The scale reads
MORE
MORE
LESS
SAME
as the elevator just starts
moving
LESS
Force diagram Beginning:
SAME
as the elevator just starts
moving
Explain:
Fnet =
a=
Downward: Middle -- steady
Prediction (circle one):
Data (circle one):
I think the scale will read
The scale reads
MORE
MORE
LESS
SAME
in the middle of the ride
LESS
Force diagram Middle:
SAME
in the middle of the ride
Explain:
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Fnet =
a=
Unit 4 –Newton’s Laws
Page 61
Downward: End -- coming to a stop
Prediction (circle one):
Data (circle one):
I think the scale will read
The scale reads
MORE
MORE
LESS
SAME
as the elevator comes to a
stop
LESS
Force diagram End:
SAME
as the elevator comes to a
stop
Explain:
Fnet =
a=
Now you will repeat this activity when the elevator is going upward
Upward: Beginning -- starting from rest
Prediction (circle one):
Data (circle one):
I think the scale will read
The scale reads
MORE
MORE
LESS
SAME
as the elevator just starts
moving
LESS
Force diagram Beginning:
SAME
as the elevator just starts
moving
Explain:
Fnet =
a=
Upward: Middle -- steady
Prediction (circle one):
Data (circle one):
I think the scale will read
The scale reads
MORE
MORE
LESS
SAME
in the middle of the ride
LESS
Force diagram Middle:
SAME
in the middle of the ride
Explain:
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Fnet =
a=
Unit 4 –Newton’s Laws
Page 62
Upward: End -- coming to a stop
Prediction (circle one):
Data (circle one):
I think the scale will read
The scale reads
MORE
MORE
LESS
SAME
as the elevator comes to a
stop
LESS
Force diagram End:
SAME
as the elevator comes to a
stop
Explain:
Fnet =
a=
White boarding and discussion is recommended at this point.
Post-Lab discussion:
 Remember that your "true weight" is equal to the force of gravity acting on you.
 What does the reading on the scale tell you? Did the true weight ever change?
What was changing and why?
 What would happen if the elevator went faster during the “middle” phase of its
motion?
 What would happen if the elevator accelerated faster when it was starting on its
way down? On its way up?
 Is there any way by which you could get a zero net force acting on an object in
an elevator?
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Unit 4 –Newton’s Laws
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4.7. Practice:
Elevator Problems
Recommended:  = class, whiteboard;  = homework;  = challenge problems
1.  An elevator is moving up at a constant velocity of 2.5 m/s, as illustrated in
the diagram below: the man has a mass of 85 kg.
o Construct a force diagram for the man.
o How much force does the floor exert on the
man?
2.  The elevator now accelerates upward at 2.0 m/s2.
o Construct a force diagram for the man.
o What force does the floor now exert on the man?
3.  Upon reaching the top of the building, the
elevator accelerates downward at 3.0 m/s2.
o Construct a force diagram for the man.
o What force does the floor now exert on the man?
4.  While descending in the elevator, the cable suddenly breaks. What is the force
of the floor on the man?
5.  Consider the situation where a person that has a mass of 68 kg is descending
in an elevator at a constant velocity of 4.0 m/s. At some time "t", the elevator
starts to slow to a stop at the rate of 2.0 m/s2.
o Construct a qualitative motion diagram indicating the positions, velocities and
accelerations of the elevator as it descends.
o Construct quantitative force diagrams (include magnitudes) for the person
in the elevator as it descends at (i) constant speed and (ii) during its period
of acceleration.
o If the person in the elevator were standing on a bathroom scale calibrated in
newtons, what would the scale read while the elevator was (i) descending at
constant speed and (ii) while slowing to a stop? Explain your answers.
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Unit 4 –Newton’s Laws
Page 64
4.8. Practice:
Newton’s Second Law and Motion
Recommended:  = class, whiteboard;  = homework;  = challenge problems
For each of the problems below, you must begin your solution with a force diagram.
Some require more than one diagram.
1.  The maximum force that a grocery bag can withstand without ripping is 250
N. Suppose that the bag is filled with 20.0 kg of groceries and lifted with an
acceleration of 5.0 m/s2. Do the groceries stay in the bag? Explain your
reasoning.
2.  A student, standing on a scale in an elevator at rest, sees that his weight is
840 N. As the elevator rises, his weight increases to 1050 N, then returns to
normal. When the elevator slows to a stop at the 10th floor, the reading on the
scale drops to 588 N, then returns to normal. Draw a motion diagram for the
student during his elevator ride. Determine the acceleration at the beginning
and end of the trip.
3.  A sign in an elevator states that the maximum occupancy is 20 persons.
Suppose that the safety engineers assume the mass of the average rider is 75
kg. The elevator itself has a mass of 500 kg. The cable supporting the elevator
can tolerate a maximum force of 30,000 N. What is the greatest acceleration
that the elevator’s motor can produce without snapping the cable? What is the
direction of this acceleration?
4.  A race car has a mass of 710 kg. It starts from rest and travels 40.0 m in 3.0
s. The car is uniformly accelerated during the entire time. What net force is
acting on the car?
5.  Suppose that a 1000 kg car is traveling at 25 m/s (~55 mph). Its brakes can
apply a force of 5000 N. What is the minimum distance required for the car to
stop?
6.  During a head-on collision, a passenger in the front seat of a car accelerates
from 13.3 m/s (~ 30 miles/hour) to rest in 0.10 s.
o What is the acceleration of the passenger?
o The driver of the car holds out his arm to keep his 25 kg child (who is not
wearing a seat belt) from smashing into the dashboard. What force must he
exert on the child?
o What is the weight of the child?
o Convert these forces from N to pounds (1 lb = 4.45 N ). What are the
chances the driver will be able to stop the child?
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Unit 4 –Newton’s Laws
Page 65
APPENDIX
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Unit 4 –Newton’s Laws
Page 66
Materials List for Unit 4 Labs
General Supplies
Materials for Labs
 a pair of spring scales (Newtons);
 platform or two bathroom scales
 Two Force plates
 String
 Two force probes
 Two rubber stoppers to attach to end of force probe
 A rubber band
 A small and a large wood block, with Velcro to attach force probe to block
 (Optional) Two carts with repelling magnetic bumpers
 Track for carts above
 Cart and spring scale on low-friction surface
 Or large spring scale and a skateboard
 Or car, spring scale and track
 Car(t) and track
 Mass hanger and masses
 Pulley
 Motion detector or smart pulley and picket fence to measure acceleration
 An elevator
 A bathroom scale or
 An object of weight 5-8 N
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Unit 4 –Newton’s Laws
Page 67
Sample Data for Unit 4 Labs
NEWTON’S THIRD LAW WITH FORCE PROBES LAB
Students are expected to get graphs that look like the ones below:
Station 1 (1,2)
Station 1 (3)
Station 2 (1)
Station 2 (2)
Station 2 (3)
Station 2 (2)
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Unit 4 –Newton’s Laws
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Station 3 (1)
Station 3 (2)
Station 3 (3)
Station 3 (4)
Station 3 (5)
Station 3 (6)
Station 4 (3)
Not all possibilities are shown here.
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Unit 4 –Newton’s Laws
Page 69
Sample Worksheet for What Does It Take to Move? – Lab
Purpose:
What is the connection between force and motion–related factors such as time,
displacement, velocity and acceleration?
Materials:
A cart
A spring scale on low-friction floor
Or, a large spring scale and a skateboard
Or, a spring scale and track
Directions:
1. Identify all the forces acting on the cart when it is sitting motionless on the
frictionless surface. Using appropriate names, list them below.
2. Draw a force diagram for the motionless cart. Draw the corresponding motion
diagram next to it. What conclusion can you draw about the connection
between the net force exerted on the moving cart and its velocity?
3. Describe in words what you need to do to make the cart move?
4. Suppose you were to attach a spring scale to the motionless cart and pull on it
to make it move. What do you think the spring scale will read during the time
the cart is being pulled but has not moved yet? Write down your predictions
below and try it.
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5. As the cart just begins to move, carefully watch what the spring scale read and
write down the details below. Draw a force diagram and a motion diagram.
6. Suppose you wish to pull the cart and keep it moving with zero net force. Predict
whether this is possible or not. Explain your reasoning. Now try it. Describe in
detail what happens.
7. Draw a force diagram and a motion diagram for the above situation. What
conclusion can you draw about the connection between the net force exerted
on the moving cart and its velocity?
8. In this step, pull and keep the cart moving while maintaining a constant force of
2 N. First make a prediction: What do you think the motion will look like?
Explain your reasoning. Draw a force diagram and a motion diagram.
9. Now try it. Describe what happens. Draw a force diagram, and a motion
diagram. What conclusion can you draw between the net force exerted on the
moving cart and its acceleration?
10.Based on your experimental evidence, answer the question: “What does it take
to move?” Write down four things you learned about the qualitative connection
between force and motion-related factors such as time, displacement, velocity,
and acceleration.
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Unit 4 –Newton’s Laws
Page 71
Unit 4 - Newton’s Laws: GLE and Process Standards by
Activity
Activity
Newton’s Third Law Lab
Newton’s Third Law with
Force Probes Lab
Reading Page—Newton’s
Third Law
4.1. Practice: Identifying
Pairs of Forces I
4.2. Practice: Identifying
Pairs of Forces II
4.3. Practice: Forces,
Acceleration and Collisions
4.4. Practice: Newton’s
Third Law with Blocks
4.5. Practice: Newton’s
Third Law Problems
What Does It Take To
Move?—Lab
Acceleration, Mass and
Force: Pre-Lab Exercise
Acceleration, Mass and
Force Lab
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GLEs
2.2.A.a; 2.2.D.e; 2.2.D.f;
2.2.D.g; 2.2.D.h; 7.1.A.a;
7.1.A.c; 7.1.B.a; 7.1.B.b;
7.1.B.c; 7.1.C.a; 7.1.C.b;
7.1.E.a
2.2.A.a; 2.2.D.e; 2.2.D.f;
2.2.D.g; 2.2.D.h; 7.1.A.a;
7.1.A.c; 7.1.B.a; 7.1.B.b;
7.1.B.c; 7.1.C.a; 7.1.C.b;
7.1.E.a
2.2.A.a; 2.2.B.a; 2.2.B.c;
2.2.D.g; 2.2.D.h
2.2.A.a; 2.2.D.g; 7.1.C.a;
7.1.E.a
2.2.A.a; 2.2.D.d; 2.2.D.e;
2.2.D.g; 2.2.E.b; 7.1.C.a;
7.1.E.a
2.2.A.a; 2.2.D.e; 2.2.D.g;
2.2.D.h; 7.1.C.a; 7.1.D.a;
7.1.D.b; 7.1.E.a; 7.1.E.b
2.2.A.a; 2.2.D.c; 2.2.D.e;
2.2.D.f; 2.2.D.g; 7.1.C.a;
7.1.E.a
2.2.A.a; 2.2.D.f; 2.2.D.g;
2.2.D.h; 7.1.C.a; 7.1.E.a
2.1.A.a; 2.2.A.a; 2.2.D.e;
2.2.D.f; 2.2.D.g; 2.2.D.h;
7.1.B.a; 7.1.B.b; 7.1.B.c;
7.1.C.a; 7.1.C.b; 7.1.D.a;
7.1.E.a; 7.1.E.b
2.2.A.a; 2.2.D.c; 2.2.D.d;
2.2.D.e; 2.2.D.f; 2.2.D.g;
2.2.D.h; 7.1.A.a; 7.1.A.b;
7.1.A.c; 7.1.E.a
2.2.D.c; 2.2.D.d; 2.2.D.e;
2.2.D.f; 2.2.D.g; 2.2.D.h;
7.1.A.c; 7.1.B.a; 7.1.B.b;
7.1.B.c; 7.1.C.a; 7.1.C.b;
7.1.D.a; 7.1.E.a
Unit 4 –Newton’s Laws
DESE Show Me
Standards Knowledge
Goals Goals
1.3; 1.6; 1.8; 2.3; 2.4;
3.5; 4.1; 4.6
1.3; 1.6; 1.8; 2.3; 2.4;
3.5; 4.1; 4.6
N/A
1.6; 1.8; 2.4; 3.2
1.6; 1.8; 2.4; 3.3
1.6; 1.8; 2.4; 3.3; 4.1
1.6; 1.8; 3.3
1.6; 2.4; 3.3; 4.1
1.2; 1.3; 1.6; 2.3; 2.4;
3.5; 4.1; 4.6
1.1; 1.2; 1.3, 2.4
1.2; 1.3; 1.6; 1.8; 2.3;
2.4; 3.5; 4.1; 4.6
Page 72
Reading Page—Newton’s
Second Law
4.6. Practice: Newton’s
Second Law
4.7. Practice: Force
Diagrams, Motion
Diagrams and Newton’s
Second Law
Upward and Downward
Ride Lab
4.8. Practice: Elevator
Problems
4.9. Practice: Newton’s
Second Law and Motion
2.2.D.a; 2.2.D.c; 2.2.D.f
N/A
2.2.A.a; 2.2.B.d; 2.2.D.c;
2.2.D.d; 2.2.D.e; 2.2.D.f;
2.2.D.g; 2.2.D.h; 7.1.C.a;
7.1.D.a; 7.1.E.a; 7.1.E.b
2.1.A.a; 2.1.B.a; 2.2.A.a;
2.2.B.d; 2.2.D.c; 2.2.D.d;
2.2.D.e; 2.2.D.f; 2.2.D.g;
2.2.D.h; 7.1.C.a; 7.1.C.b;
7.1.D.a; 7.1.E.a; 7.1.E.b
2.2.A.a; 2.2.D.d; 2.2.D.e;
2.2.D.f; 2.2.D.g; 7.1.A.c;
7.1.B.a; 7.1.B.b; 7.1.B.c;
7.1.C.a; 7.1.C.b; 7.1.D.a;
7.1.E.a; 7.1.E.b
2.1.A.a; 2.1.B.a; 2.2.A.a;
2.2.B.c; 2.2.D.d; 2.2.D.e;
2.2.D.f; 2.2.D.g; 7.1.C.a;
7.1.D.a; 7.1.E.a;
2.1.A.a; 2.1.A.c; 2.1.B.a;
2.1. B.b; 2.2.A.a; 2.2.B.c;
2.2.D.c; 2.2.D.d; 2.2.D.e;
2.2.D.f; 2.2.D.g; 2.2.D.h;
7.1.C.a; 7.1.E.a
1.6; 2.4; 3.2; 4.1
1.6; 1.8; 2.4; 3.3; 4.1
1.3; 1.6; 1.8; 2.3; 2.4;
4.1; 4.6
1.6; 1.8; 2.4; 3.2; 4.1
1.6; 1.8; 2.4; 3.3; 4.1
Note: Many of the Mathematics Knowledge Standards may apply. Each teacher
should check with the math department to determine which standards are
appropriate.
 A TIME for Physics First
Unit 4 –Newton’s Laws
Page 73
Unit 4 Recommended Timeline
This timeline is based on each “day” being approximately 50 minutes long.
Day
Classwork
1
Framing Questions. Prelab Newton’s 3rd Law Lab
2
Do N3 Lab
3
Whiteboard postlab of N3 Lab. Have each lab group
take a station.
4
Practice identifying N3 pairs.
5
6
4.1 Practice: ID Pairs of Forces II (first 3 pages)
Whiteboarding of Practice as needed and In class
demo: forces on carts. Two students on carts pull
each other. Which moves farther? Why? This will
bridge students into thinking about Newton’s 2nd law
Prelab Acceleration, Mass and Force Lab
Do Acceleration, Mass and Force Lab lab
Continue to do N2 lab
7
8
9
10
11
12
13
14
15
16
17
18
19
Begin post lab of N2 lab
Finish post lab of N2 lab. Depending on your students,
you might want to break it into two independent
labs—changing net force, and changing mass of the
system. Post lab each part individually and even give
some practice data to analyze.
Show how to apply Newton’s 2nd law to situations
involving unbalanced forces. 4.5 Practice: Force
Diagrams, Motion Diagrams and N2. Regular kids can
do 1-2 Honors can do 3-4 also
Whiteboard homework
Upward and Downward Ride Lab
Postlab discussion. What is “weightlessness?” Do
example elevator word problem
Whiteboard Elevator Problems 4.6 Practice
Whiteboard 4.7 Practice
Review
Test
 A TIME for Physics First
Unit 4 –Newton’s Laws
Homework
Finish predictions for
N3 Lab
Start working on
force diagrams for
N3 lab
Continue working on
force diagrams for
N3 lab. Only honors
students should do
2D force diagrams
Reading Page: N3
4.1 Practice: Pairs of
Forces I
Make graphs
Continue making
graphs
Reading Page:
Newton’s 2nd Law
Finish 4.5 Practice
4.6 Practice
4.7 Practice
Page 74
4.9. Practice:
Vertical Acceleration
(for honors students)
For questions 1-5 consider the 50 kg woman shown at right.
Sketch the force diagram, motion map, including acceleration,
and a graph for the woman appropriate to each situation. Find
the value of each force acting on the woman. This elevator
moves only in the vertical dimension with the kinematic
quantities indicated for each problem. Upward is positive.
Assume the elevator remains at rest once it comes to a stop.
The elevator moves with a constant velocity of +2 m/s.
1. The elevator moves with a constant velocity of -3 m/s.
2. The elevator moves downward with a velocity of -4 m/s and
has acceleration of +1 m/s2.
3. The elevator moves upward with a velocity of +3 m/s and
has an acceleration of +1 m/s2.
4. The elevator moves downward with a velocity of -4 m/s and has an acceleration
of -2 m/s2.
5. A helicopter holding a 90. kg box suspended from a rope 5.0 m long accelerates
upward at a rate of 2.1 m/s2. Air resistance is negligible.
o Draw and label a force diagram for the box.
o Determine the tension in the rope.
o At the moment that the upward velocity of the helicopter is 12 m/s, the rope
is cut. The helicopter from then on accelerates upward at 2.5 m/s2.
Determine the distance between the helicopter and the package 3.0 seconds
after the rope is cut.
6. Having fallen down a well, a boy finds himself with
the water bucket tied to a rope which goes over a
pulley at the top. Fortunately the other end of the
rope has fallen down to the bottom of the well, too.
So, he decides to get into the bucket and start pulling
on the other end of the rope in order to get himself
out. His mass is 32 kg and the bucket has a mass of
3.0 kg. How much force will the boy have to exert on
the rope in order to pull himself up with a relatively
constant velocity?
 A TIME for Physics First
Unit 4 –Newton’s Laws
Page 75
7. A crane is used to hoist a load of mass m1
= 500 kg. The load is suspended by a cable
from a hook of mass m2 = 50 kg, as shown
above. The load is lifted upward at a
constant acceleration of 2 m/s2.
o
o
Draw a force diagram for the hook, and
label each force clearly, identifying the
agent exerting it.
Determine the tension T1 in the lower
cable and the tension T2 in the upper
cable.
8. An elevator is rising at a speed
of 5.00 m/s. It comes to a halt
in 4.0 s. The guide rails on the
side of the elevator each exert a
110 N frictional force on the
elevator. The pulley has
negligible friction and mass for
the purposes of this analysis.
o Find the tension in the cable
during the slowing of the
elevator.
o Find the mass M that the
counterweight must have in
order for the elevator to stop
as stated above.
 A TIME for Physics First
Unit 4 –Newton’s Laws
Page 76