Forces
4.1.1, 4.1.3, 4.5.3 Fundamentals of Forces
Learning Outcomes
The student will understand contact and non-contact forces.
The students will:
1. distinguish between contact and non-contact forces, relating the concepts of
fields to non-contact forces.
2. classify common forces as either gravitational or electromagnetic forces
(including classifying friction, pushes, pulls and tension forces as
electromagnetic).
3. use indirect evidence to describe unseen forces.
4. compare and contrast strong and weak nuclear forces.
Misconceptions
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When two stationary objects push on each other, the “stronger” one exerts the
larger force.
When two objects push on each other, the harder one pushes with a greater
force than the softer one.
Gravity is the only natural force.
All forces are unique.
Gravity is the strongest force.
Gravitational and electromagnetic forces are more fundamental than the
strong and weak nuclear forces. f
Electricity and magnetism are two different forces.
Weak and strong are the same force.
All forces are equally effective over all ranges.
All forces have to be contact forces.
Lesson Plans
Contact and Non-Contact Forces
Classifying and Measuring Forces
Fields
1
Forces
Contact and Non-Contact Forces
EXPLORATORY
_____ Matchbox “Magic” (F500A/F500B)
CONCEPT DEVELOPMENT
_____ Contact and Non-Contact Forces (F501)
APPLICATION
_____ Feel the Force (F615)
SUGGESTIONS & STRATEGIES - Contact and Non-Contact Forces
Ask students to define the word “force” in their own words. They will probably include
references to “pushes” and/or “pulls,” and will most likely think only in terms of contact
forces. This lesson helps students recognize the existence of non-contact forces so that
they, too, can be considered when discussing the characteristics and effects of forces.
Encourage students to be creative in the exploratory activity “Matchbox Magic,” but not
to overlook obvious solutions. They may devise ingenious ways of getting the box to
move (by simply blowing on the box, for instance, or maybe by putting one magnet in the
box and “pushing” it with another magnet), but might miss the method of simply
dropping the box! The objective is for them to brainstorm as many ways as possible, and
then think carefully about what they have done.
You might refer to the study of the fundamental forces in the Habits of the Mind unit
during the ensuing discussion, but try to get students to suggest ideas before revealing the
electrical nature of contact forces. This concept is dealt with more completely in a later
lesson.
The students will not have the background to include the normal force in their
discussions yet. When the normal force is introduced in the next lesson, however, the
concept of contact forces can be reinforced.
When students are asked to suggest ways of developing empirical laws to describe the
behaviors of some forces, they may not discover the actual relationships such as Hooke’s
Law. That is not critical at this point, and need not be pursued. The main point is for
them to realize the convenience of studying characteristics and behaviors of some forces
without regard to the true nature of the forces. Even though this is convenient, however,
we still want to answer the questions about the nature of forces for a more complete
understanding of our universe.
The classifications of “contact” and “non-contact” are preliminary to discussions of the
electrical nature of many common forces because these are very intuitive and based upon
concrete observations. The students will be guided to develop more formal reasoning
when considering the abstract ideas of the electrical nature of some forces.
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Forces
Classifying and Measuring Forces
EXPLORATORY
_____ Classifying Forces (F503)
CONCEPT DEVELOPMENT
_____ Classifying Forces Background (F020) and/or
_____ Video Clip: Nuclear Forces (F028A)
APPLICATION
_____ How Large is a Pull? (F024)
SUGGESTIONS & STRATEGIES - Classifying and Measuring Forces
Besides classifying forces, students need to have skills in measuring them. Depending
upon the available equipment, students can use spring scales and/or force probes and
appropriate interfaces (computer or CBL) to measure various forces and get a “feel” for
how strong a newton is.
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Forces
Fields
EXPLORATORY
_____ Fields (F523)
CONCEPT DEVELOPMENT
_____ Fields - Replacing the Idea of “Action-at-a-Distance” (F524)
APPLICATION
_____ Applications of Fields (F525A/F525B)
SUGGESTIONS & STRATEGIES - Fields
Although the concept of fields is a rather abstract one, it is a vital part of physics.
Extending the ideas about gravitational forces to gravitational fields is the third part of
the study of gravity. Students should realize that the non-contact forces can be described
in terms of fields that exert forces on objects within the fields. Fields have both
magnitude and direction, determined by the magnitudes and directions of the forces that
they exert on bodies.
You may choose to use “field lines” to show properties of the field: 1) The direction of
the line indicate the direction of the force at any point on the line, and 2) The “density” of
the lines (how close they are to one another) indicates the magnitude of the field. For
instance, if you draw a circle to represent the earth, radial lines pointing toward the earth
indicate the properties of the gravitational field of the earth. The lines point toward the
earth so any mass in the field would be attracted toward the earth. The lines would be
closest together near the surface of the earth, where the gravitational force would be the
strongest for a particular mass. Have students notice that the field lines extend infinitely
into space, so there are gravitational attractions in outer space. You may want them to
draw comparable gravitational field line patterns for the sun (many more lines since the
sun is so much more massive than the earth) and for the moon (fewer lines, in fact, about
1/6 the number of lines).
Discussions may include social interactions and “sphere of influence.” Compare and
contrast these situations to physical fields.
The degree to which nuclear force experiments can be done in high school depends
greatly on the availability of equipment. Perhaps the physics lab is equipped with a
Geiger counter or scintillation counter to explore radioactive effects, or your students
may have access to cloud chambers for the study of paths of ionizing radiation. If you
have either of these resources, refer to documentation accompanying the equipment for
instructions on its use.
Nuclear forces are the primary source of the sun’s energy. “Sunshine and Nuclear
Forces” (F029S) provides background information about the nuclear processes that
release such energy.
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Forces
4.3.1, 4.2.2, 4.5.2 Inertia and Weight
Learning Outcomes
The student will understand the gravitational force of the earth on an object and its
mass.
The students will
1. define mass as resistance to change in velocity (Inertia).
2. propose conditions needed for constant velocity (Newton’s First Law)
3. identify examples of translational equilibrium using force diagrams.
4. distinguish between the gravitational force of the earth on an object and the
object’s mass.
5. distinguish between inertial and gravitational mass
6. explain the bending of light by a massive object
7. relate the General Theory of Relativity to present understanding of black holes.
Misconceptions
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A force is required for motion.
No force is required to move objects in space.
All moving objects eventually stop.
Inertia is a force that keeps things moving.
Mass and weight are the same thing.
The force of gravity is the same for all bodies.
A distinction can be made between gravity and acceleration.
Light always travels in straight lines.
A black hole has a greater gravitational force than the star from which it was
formed.
Lesson Plans
Inertia
Mass and Weight
General Relativity
5
Forces
Inertia and Weight
EXPLORATORY
_____ Look Out, No Brakes (F137A/F137B) and/or
_____ Egg and Broom Demo (F141)
CONCEPT DEVELOPMENT
_____ Inertia (F144) and/or
_____ Inertial Mass (M393)
APPLICATION
_____ Barbie, Ken, and Sir Isaac (F138) and/or
_____ Newton’s Laws: Examples of Inertia (F154)
SUGGESTIONS & STRATEGIES - Inertia
The idea of masses having “hold back tendencies” and “keep going tendencies” has
already been introduced, and now it is formalized as inertia. The property of mass known
as inertia can be seen as a special case of Newton’s Second Law: The more inertia an
object has, the larger the force that is required to get the object to attain a given
acceleration, whether that be to speed up the object, to slow it down, or even to get it
moving from a state of rest. If there is no unbalanced force on the object, its motion does
not change. This shows students that the condition for constant velocity is no net force.
The first activity is important as a safety plea: Wear seatbelts! Students can see that a
seatbelt can more safely change the velocity of a rider in a car than, say, the windshield!
The inertia discussion guidelines lead students in reasoning about why objects fall at the
same rate of acceleration regardless of their mass (disregarding air friction). This lesson
requires students to simultaneously apply the inertia and gravitational properties of mass
in the context of free-fall situations. This is not easy for students to do, so care should be
taken to preview the teacher notes, demonstrations, and discussion questions before using
them in class.
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Forces
Mass and Weight
EXPLORATORY
_____ Lift vs. Kick Box (M391)
CONCEPT DEVELOPMENT
_____ Weight and Mass (F072) and
_____ Video Clip: Apple and the Moon (F075)
APPLICATION
_____ Mass and Weight (F078)
SUGGESTIONS & STRATEGIES - Mass and Weight
Mass is a measure of the inertia of an object. Mass is often considered a measure of the
amount of matter in an object. Weight is a force and depends on other factors as well as
mass. The astronauts’ masses on the moon are the same as on Earth, but their smaller
weights make them capable of jumping higher. (By the way, medical studies have shown
that astronauts do lose some bone mass when in space for an extended period. You might
want to discuss this with your students as an “exception” to the statement that the
astronauts’ masses are the same on the moon as on Earth.)
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Forces
General Relativity
EXPLORATORY
_____ Curved Space Lycra Lab (Ma074)
CONCEPT DEVELOPMENT
_____ Principle of Equivalence (M394)
APPLICATION
_____ Video Clip: Curved Space and Black Holes (M392) and
_____ Student guide for “Curved Space and Black Holes” (M392A) and/or
_____ Video Clip: Bending of Starlight (M397) and
_____ Student guide for “ “Bending of Starlight” (M392)
SUGGESTIONS & STRATEGIES - General Relativity I
This is the fourth lesson dealing with gravity. Even though gravitational forces are not
truly understood even today, it would be a disservice to students to lead them to believe
that Newton “had the last word” on the subject. This lesson introduces the first of the
basic principles of Einstein’s Theory of General Relativity.
The Equivalence Principle states that “No experiment can be done to distinguish between
a gravitational field and an accelerating reference frame.” If a student stands on
bathroom scales and reads his/her “weight,” there is no way (within the reference frame)
of telling whether an object (the earth) is exerting a gravitational force on him/her, or
his/her reference frame is accelerating upward. Suspending a mass from a spring scale
and then accelerating it upward shows that “apparent weight” can be gained by the
motion. This principle accounts for the necessary (not coincidental) equality of a body’s
gravitational mass (determined by the pull of the earth on it) and its inertial mass
(determined by its tendency to retain its present state of motion or rest).
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Forces
4.1.5 Vectors and Free-Body Diagrams
Learning Outcomes
The student will use free-body diagrams.
The students will
1. define and draw vectors.
Misconceptions
• A free-body diagram includes all forces on all bodies.
Lesson Plans
Vectors
Free-Body Diagrams
9
Forces
Vectors
EXPLORATORY
_____ Where Am I? (K046)
CONCEPT DEVELOPMENT
_____ Vectors and Scalars Background (F908) and
_____ Vector Problems (F918A/F918B) and/or
_____ Addition of Force Vectors (F905)
APPLICATION
_____Vector Applications (K110)
SUGGESTIONS & STRATEGIES - Vectors
The introduction of vectors can be customized to the students’ level of mathematical
background and the teacher’s preference. It is assumed that on the conceptual level,
students will be able to combine parallel vectors by addition or subtraction of their
magnitudes, and combine perpendicular vectors graphically. This could also be extended
to include application of the Pythagorean Theorem to perpendicular vectors and/or
analyzing non-perpendicular, non-parallel vectors graphically. The teacher may choose
to employ the “head-to-tail” method or the “parallelogram method” graphically, but the
concurrent nature of forces dictates that free-body diagrams in the next lesson be drawn
so that the vectors originate from the same point.
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Forces
Free-Body Diagrams
EXPLORATORY
_____ 24 Hour Towing (F086A/F068B)
CONCEPT DEVELOPMENT
_____ Recognizing and Interpreting Free-Body Diagrams (F035) and/or
_____ Direction of Forces (F039)
_____ Free-Body Diagrams Background (F038)
APPLICATION
_____ Rafter Physics (F096A/F096B) and/or
_____ Force Components (F729)
SUGGESTIONS & STRATEGIES - Free-Body Diagrams
Free-body diagrams serve as a visual inventory of all the forces acting on a single body.
It is intuitive to recognize that if the forces are not “balanced,” there will be some change
in the object’s motion. This characteristic of free-body diagrams will be used in later
lessons. Emphasize to students that free-body diagrams do not include velocity or
acceleration vectors.
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Forces
4.1.4 Interacting Forces
Learning Outcomes
The student will understand internal and external forces.
The students will
1. distinguish between internal and external forces acting on a system.
2. describe forces as interactions that occur in pairs
3. describe interactions, in words or using a force diagram, between two objects,
where the second force is equal in magnitude and opposite in direction to the first
identify a reaction force, given an action force.
4. explain why the action and reaction for the same pair do not cancel each other.
construct force diagrams for various situation.
Misconceptions
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A system can only be defined to include objects that are in contact.
An internal force can propel an object forward.
Action and reaction forces are on the same body.
Newton’s Third Law contradicts the Second Law.
Action and reaction forces cancel each other.
The reason that a horse can pull a cart is because the horse pulls harder on the
cart than the cart pulls on the horse.
Lesson Plans
Internal and External Forces
Interactions
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Forces
Internal and External Forces
EXPLORATORY
_____ Three-Stage Human Rocket (C036A/C036B)
CONCEPT DEVELOPMENT
_____ Internal and External Forces (F505)
APPLICATION
_____ Pop Goes the Weasel (F506)
SUGGESTIONS & STRATEGIES - Internal and External Forces
As a final means of classifying forces, students are introduced to the concepts of internal
and external forces. This is essential in later applying Newton’s laws of motion to
systems since only external forces are capable of causing a system to accelerate.
It may be tempting to extend discussions to include momentum and its conservation and
Newton’s third law (action-reaction), but the intent of this lesson is merely to have
students recognize the difference between internal and external forces. You might have
them think of examples of their own for each type to further evaluate their understanding.
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Forces
Interactions
Do either Learning Cycle #1 or Learning Cycle #2
EXPLORATORY #1
_____ Passive Forces (F168)
CONCEPT DEVELOPMENT #1
_____ Tug of War (F169)
APPLICATION #1
_____ Newton’s Third Law - Action and Reaction (F174)
EXPLORATORY #2
_____ Exerting Forces (F158)
CONCEPT DEVELOPMENT #2
_____ Action-Reaction Pairs (F176)
APPLICATION #2
_____ Newton’s Third Law - Action and Reaction (F174)
SUGGESTIONS & STRATEGIES
Recognition of Force Pairs
At this point, students begin examining forces on two bodies. Previously, the attention
had been on a single body at a time. Even though Newton’s Third Law is sometimes
referred to as “action-reaction,” this oversimplifies a rather complex concept. In this first
part of the lesson, students are identifying the action-reaction pairs and describing pairs
of forces as well. Have students use the phrase “the force ON _____ BY _____” to
emphasize the interactions.
By the way, a student may say that the reaction force of the earth pulling down on
him/her is the force of the floor pushing up on him/her. This is incorrect. The reaction
force would be the force of the student pulling upward on the earth because of
gravitational attraction as well. You could re-focus the question by asking students to
name the two bodies involved.
Magnitudes of Interactions
From the Exploratory, students should learn that interactions come in equal and opposite
pairs. If they are not convinced, ask two students to hook together two spring scales and
pull so that one scale reads 10 N while the other reads 15 N simultaneously. Impossible!
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Forces
The traditional example of the horse pulling on the cart can lead to the discussion of noncancellation of action-reaction forces. They key concept here is that the force of the
horse pulling on the cart is not canceled by the force of the cart pulling on the horse
because these forces are acting on two different objects. (Contrast with two people
pulling in opposite directions on the same cart.)
Be sure that students realize that the force diagrams that they drew in the “Newton’s
Third Law - Action and Reaction” exercise are not free-body diagrams because they
simultaneously show forces acting on more than one body.
15
Forces
Newton’s Second Law
Learning Outcomes
The student will understand force, momentum, and time.
The students will
1. identify forces on an object by analyzing and drawing free-body diagrams.
2. define and calculate the net force.
3. formulate the relationship between force, mass, and acceleration (Newton’s
Second Law).
Misconceptions
• The acceleration in Newton’s Second Law and the acceleration studied in
kinematics are different.
• Net force can always be determined by adding the magnitudes of all the
forces.
Lesson Plans
Net Force
Force and Acceleration
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Forces
Net Force
EXPLORATORY
_____ Sailing Through Physics (F088)
CONCEPT DEVELOPMENT
_____ Combining Forces (F094) and/or
_____ Force Components (F729A/F729B)
APPLICATION
_____ Can a String Support Lateral Forces? (F100)
SUGGESTIONS & STRATEGIES - Net Force
It is important to help students gain familiarity with the phrase “net force.” The analogy
of “net pay” may help students recognize that we are concentrating on the unbalanced or
“leftover” force. All of the net forces activities can be accomplished with graphical
analysis of the free-body vector diagrams. For instance, in the activity “Can a String
Support Lateral Forces?” draw an inaccurate diagram that shows only horizontal tension
forces and the vertical weight force. Ask students if this represents the situation. No!
There must be some “sag” in the string so that the tension forces are pulling both
sideways and upward. This can be discussed intuitively even without using the concept
of components of forces.
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Forces
Force and Acceleration
EXPLORATORY
_____ Can You Change Your Motion? (F052A/F052B)
CONCEPT DEVELOPMENT
_____ Space Catch (F062S) and/or
_____ Video Clip - Inertia (F058)
APPLICATION
_____ Who Has the Pull Around Here? (F064A/F064B) and/or
_____ Force and Motion (F065)
SUGGESTIONS & STRATEGIES - Force and Acceleration
Although the traditional treatment of Newton’s Laws involves the “1, 2, 3” order of
presentation, this curriculum introduces Newton’s Second Law, the Law of Acceleration
first, and then considers the First Law (Inertia) as a special case of the Second Law, and
the Third Law (Interactions) as an extension to two-body systems.
Rather than just revealing the relationships between force, mass, and acceleration, it is
best for the teacher to have students experimentally discover these relationships for
themselves. Using graphs of Force vs. Time in comparison to motion graphs is
especially helpful for discovering and reinforcing these relationships. The statement “a
= F/m” is more intuitive to students than “F = ma.” Once again, concentrate on the
cause-and-effect nature of the experiments, and have students incorporate previouslylearned concepts of external forces and net force into their analyses of the activities.
The Space Catch discussion notes help students see that forces can produce either
positive or negative accelerations, depending upon the direction of the forces, and for a
given acceleration, the magnitude of the mass dictates the magnitude of force. This
discussion can lead to the concept of inertia by relating the “hold back tendency” and
“keep going tendency” to the mass of the object. In the absence of an unbalanced force,
there is no acceleration, so the object just conforms to those “tendencies.”
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Forces
4.2.3 Forces and Friction
Learning Outcomes
The student will understand friction.
The students will
1. list the factors affecting the magnitude of the surface frictional force.
2. solve problems involving frictional forces (including coefficient of friction;
frictional forces and motion; and, static and kinetic friction.).
3. recognize factors affecting air resistance in simple situations.
4. describe the magnitude and direction of forces on a body that has reached
terminal velocity.
Misconceptions
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Friction cannot act in the direction of motion.
The force of friction depends only on the smoothness of the surfaces.
Surfaces can be made smooth enough to eliminate friction altogether.
An object eventually falls at a constant speed because that is the natural
motion of falling objects.
Lesson Plans
Normal Forces
Surface Friction
Air Friction
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Forces
Normal Forces
EXPLORATORY
_____ Perpendicular Forces (F116)
CONCEPT DEVELOPMENT
_____ Normal Forces (F117) and
_____ Homework for Normal Forces (F007S)
APPLICATION
_____ Is This Force Normal? (F502)
SUGGESTIONS & STRATEGIES - Normal Forces
The Physicist’s View
A number of interesting questions and examples are raised by students in the discussions
during this lesson. The teacher may wish to anticipate some of the difficulties below
such as:
• “How does the table know how to push on an object?”, “Is it intelligent?” This is
another important discussion question. It may be fruitful to direct the discussion back
to the spring at this point. The physicist’s view is that the larger weight deforms that
table more so that the table provides a greater normal force.
• A harder question is: “If a feather is sitting next to a football player on the table,
how does the table know how hard to push on each?” Here one needs to refer to both
compression and bending of the imaginary “network of springs” in the table, the
compression under the football player being larger.
While the term “normal forces” is used as a title for this lesson, these words have not
been used within the lesson. When introducing the term, it is important to clarify the
meaning of the word “normal” in this context. Many high school math curricula do not
use the word “normal” to mean perpendicular so some students may interpret “normal” as
meaning something like “ordinary.”
Here are some additional notes regarding normal forces:
1.
Should students complain that they don’t know what you really mean by “force,”
assure them that they are asking an important question and the struggles in this lesson
will help them become clearer about what physicists mean by “force.”
2.
The “push or pull” definition of force suggests muscular force, and more
generally, contact forces. Some physicists may object that this is too limited a
definition. But the most rigorous definition is not always the most useful for a
beginner. We want to start by building on the learner’s intuitive ideas. There will be
time for the concept of force to be refined and generalized. It would be useful to
point out to students that this definition is an initial one, to be elaborated as their
physics understanding grows.
3. If the equality of the forces arises during discussion of the first day, avoid it by saying
you want to concentrate on whether the force exists and how to explain it.
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Forces
4. Introducing the molecular model as a mental image also makes it available later for
the study of collisions, friction and tension. It is important to point out that this is
only a model and that all models have limitations.
5.
TEACHER DEMO:
Have a mirror set up on a table so that a laser light can reflect off the mirror onto a
nearby wall. Stand on the table and repeat. The deflection of the spot on the wall
helps show the forces involved. This demonstration is fun and very helpful to some
students. The teacher should practice this a bit, but the general setup in worked well
for our classes. The downward deflection of the light will be greater if the mirror is
placed between the side and the center of the table closer to the light source. Even a
small deflection of the spot on the wall seems to impress students. If you don’t have
a laser, you should be able to use a good “pencil” light beam made from a bright
point source bulb or carbon arc and a screen with a small hole.
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Forces
Surface Friction
EXPLORATORY
_____ Why Do You Slip On a Water Slide? (F106)
CONCEPT DEVELOPMENT
_____ Chair Friction Lab (F123A/123B) and/or
APPLICATION
_____ Slippery As An Eel (F104A/F104B)
SUGGESTIONS & STRATEGIES - Surface Friction
Students are expected to discover the factors affecting sliding friction. It is important
that they maintain a constant velocity for the objects they are examining. Earlier activities
in the unit have pointed out the electrical nature of the friction force, and Faustus’
arguments can be challenged by students with their own ideas dealing with the structure
of matter and factors affecting friction. Have students speculate about why lubrication
and polishing really reduce friction, and why even though starting friction is greater than
sliding friction, the friction force still exists once the object begins to move.
Although the terms “static friction” and “kinetic friction” are not used in the student
activities, you may choose to introduce those terms. Furthermore, the passive nature of
friction might bring up some student questions. For instance, if it takes a force of 20 N to
get a box to begin sliding across the floor, and only a force of 10 N is applied to the box,
then the force of friction is exactly 10 N as well. Discuss with students why the frictional
force changes as the applied force changes until the object begin to move.
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Forces
Air Friction
EXPLORATORY
_____ Terminal Velocity (F114)
CONCEPT DEVELOPMENT
_____ Coffee Filter Lab (F130)
APPLICATION
_____ Falling and Air Resistance (F129A/F129B)
SUGGESTIONS & STRATEGIES Aristotle failed to adequately describe motion because he did not separate the effects of
air resistance from the fundamental nature of the object’s motion. Students do not
observe motions without the presence of air friction either, so their observations and
descriptions should be guided to the correct concepts. They are probably aware of air
friction and other types of fluid friction, but may not recognize the need to include these
forces in analysis of objects’ motion.
The activities provided do not involve complicated mathematics or complex concepts
associated with fluid mechanics on an advanced level. Rather, they aim to have students
always remember when air friction is present, and to describe factors that influence the
magnitude of the retarding force.
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Forces
4.2.1 Force, Impulse, and Momentum
Learning Outcomes
The student will understand force, momentum, and time.
The students will
1. formulate the relationship between force, change in momentum, and time.
2. define impulse as a force acting over time.
4. solve impulse and change in momentum problems .
Misconceptions
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•
•
Momentum applies only to collisions.
Direction of momentum is insignificant.
Moving masses in space do not have momentum.
Momentum and kinetic energy are the same thing.
“ma” is a force.
Lesson Plans
Force, Impulse, and Momentum
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Forces
Force, Impulse, and Momentum
Do either Learning Cycle #1 or Learning Cycle #2
EXPLORATORY #1
_____ Air Bags and Bumpers (C015S)
CONCEPT DEVELOPMENT #1
_____ Go With the Force, Luke (C016) and/or
_____ MBL Lab: Impulse Measurements for Forces Under 2gs (C010)
APPLICATION #1
_____ Seat Belts and Air Bags (C013)
EXPLORATORY #2
_____ Recoil or Remain (C009)
CONCEPT DEVELOPMENT #2
_____ Go With the Force, Luke (C016) and/or
_____ MBL Lab: Impulse Measurements for Forces Under 2gs (C010)
APPLICATION #2
_____ All-American Egg Drop (C011A/C011B)
SUGGESTIONS & STRATEGIES - Force and Change in Momentum
Once students have acquired some tools for analyzing forces, attention is given to the
cause-and-effect relationship between an unbalanced force and the change in an object’s
motion. Students are now introduced to the concept of momentum, an extension of the
kinematics principle of velocity that includes the object’s mass as well. This could be
developed intuitively with students: Ask “Which would you say has more motion, a
locomotive traveling at 80 mph or a sports car traveling at 80 mph?” Isaac Newton
actually used the expression “mv” (or momentum) for “motion.” The activities included
in this lesson are intended to help students recognize that an unbalanced force will
produce a change in the object’s momentum, and an object’s momentum can only be
changed by the presence of an unbalanced force. When guiding students through the
activities, focus upon these concepts.
The definition of impulse is developed and related to the change in momentum. Writing
the impulse-change in momentum equation on the board several times with the size of
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Forces
letters for change in momentum staying the same and the size of letters for force and
change in time changing inversely is a nice illustration:
F ∆t = m ∆v
F ∆t = m ∆v
This is an excellent opportunity to discuss safety features of automobiles. Two of the
activities address this important issue. The Application activity “Seat Belts and Air
Bags” (C013) requires quite a bit of prior set-up. You may choose instead to have
students design an experiment in which they change the momentum of a dynamics cart in
several ways. They should outline their procedures and record measurements such as
force, mass, velocity and time. (If you do use “Seat Belts and Air Bags,” do not blow up
the small balloon very much.)
Newton’s relationship between the force impressed and the rate of change of
momentum can be used to develop the familiar form of Newton’s Law of Acceleration
(2nd Law):
∆p
∆t
∆v
F =m
∆t
F = ma
F=
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Forces
4.6.1 Projectile Motion and Forces
Learning Outcomes
The student will understand projectile motion.
The students will
1. recognize that the curved path of a projectile is due to a combination of an
accelerated motion and a non-accelerated motion.
2. draw free-body diagrams for a projectile at different points in its path.
3. describe the components of motion of a projectile at different points in its
path.
4 identify factors affecting how high a projectile goes, how far it travels, and
how long it stays in the air.
5. solve problems involving projectiles (E1).
Misconceptions
• A force acts in the direction of motion all along the path of a projectile.
• The vertical component and horizontal component of the motion affect each
other.
Lesson Plans
Projectile Motions
Forces On Projectiles
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Forces
Projectile Motions
Do either Learning Cycle #1, Learning Cycle #2, Learning Cycle #3
or Learning Cycle #4
EXPLORATORY #1
_____ Ups and Downs (F213) and/or
CONCEPT DEVELOPMENT #1
_____ Roll ‘Em, Roll ‘Em, Roll ‘Em (F519A/F519B) and/or
_____ Bull’s Eye (F226)
APPLICATION #1
_____ Motion of a Projectile (F224A/F224B) and/or
EXPLORATORY #2
_____ One Ending From Two Happenings (F201/202)
CONCEPT DEVELOPMENT #2
_____ Motion Diagram for a Projectile (F215A/F215B)
APPLICATION #2
_____ Determining Trajectory (F213B2)
EXPLORATORY #3
_____ Let’s Do Launch (F196A/F196B)
CONCEPT DEVELOPMENT #3
_____ Motion Diagram for a Projectile (F215A/F215B)
APPLICATION #3
_____ Launching on the Links (C704)
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Forces
EXPLORATORY #4
_____ Forces on Projectiles (F526)
CONCEPT DEVELOPMENT #4
_____ Free-Body Diagrams for Projectiles (F527)
APPLICATION #4
_____ Take it to the Field (F217S)
SUGGESTIONS & STRATEGIES - Projectile Motions
There are four different learning cycles that are separated by “or” in the above lesson
plans.
Since it was determined that the parabolic path of projectiles resulted from constant
horizontal velocity and accelerated vertical motion, these motions can be traced to the
absence or presence of forces in keeping with Newton’s laws. Be sure that students
recognize that the vertical force on a projectile, the gravitational force, is constant
throughout the path for that object (neglecting very small differences in the distance
between the object and the center of mass of the earth). Neglecting air friction, there are
no horizontal forces acting on a projectile during its flight, so its horizontal velocity must
remain constant - an example of the principle of inertia.
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Forces
4.5.1 Law of Universal Gravitation
Learning Outcomes
The student will understand the Law of Universal Gravitation.
The students will understand the foundation of General Relativity
1 explain the inverse square relationship.
2. solve problems using the Law of Universal Gravitation
3. explain the bending of light by a massive object
4. relate the General Theory of Relativity to present understanding of Black
Holes
Misconceptions
•
•
The moon is not falling.
The force the earth exerts on a falling apple and the force the earth exerts on
the moon are not the same kind.
• The force of gravity is the same on all falling bodies.
• Gravitational force is not mutual.
• There is no gravity in space or on the moon.
• Black holes are big
• Black holes cannot exist
• Light always travels in straight lines
• A black hole has a greater gravitational force than the star from which it was
formed
• A distinction can be made between gravity and acceleration
Lesson Plans
Inverse-Square Law
Universal Gravitation & Weight
General Relativity
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Forces
Inverse-Square Law
EXPLORATORY
_____ Spray-paint a Spot (F180)
CONCEPT DEVELOPMENT
_____ Mechanical Universe Video Clip--Inverse Square Law for Light (F184) and/or
_____ Inverse-Square Law (F186)
APPLICATION
_____ Shine Your Light (F982A/982B)
SUGGESTIONS & STRATEGIES - Inverse Square Law
This lesson is the first of four dealing with gravitation. The inverse-square relationship is
an important one in physics, and should be understood by students before exploring the
concept of gravitational forces and fields.
The two main points about an inverse-square relationship are that 1) one quantity
decreases as another increases, and 2) this decrease of the one quantity is very rapid. For
instance, doubling the distance reduces the intensity of light by a factor of four, and
tripling the distance reduces the intensity by a factor of nine. (Light is used to
demonstrate the effect of the law since gravitational forces cannot be “seen.”)
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Forces
Universal Gravitation & Weight
EXPLORATORY
_____ Apparent Weightlessness (K550A/K550B)
CONCEPT DEVELOPMENT
_____ Gravitational Interactions (F188A/F188B) and
_____ Mechanical Universe Video Clip--Astronauts In Orbit (F607)
APPLICATION
_____ Universal Gravitation Problems (F187) and/or
_____ Gravitational Interactions (F188A/F188B)
SUGGESTIONS & STRATEGIES - Universal Gravitation & Weight
It is difficult to get students to accept the fact that every bit of matter attracts every other
bit of matter because the gravitational effects are so small in comparison to forces that
they normally experience. Furthermore, many students associate the gravitational
attraction of the earth as some “aura” that the earth possesses and that gravity disappears
as soon as you pass the atmosphere. Once students understand the relationships between
the variables and their effects on the force of gravitational attraction, reinforce the ideas
of interactions by confirming that if your weight is 700 N that means two things: 1) The
earth is pulling down on you with a force of 700 N, and 2) You are pulling upward on the
earth with a force of 700 N.
Although Newton formulated the principle of Universal Gravitation, he did not measure
the gravitational constant, G. Henry Cavendish did so with an exquisite experiment
involving spheres on a torsion bar. By determining G, he, in a sense, “weighed the earth”
because an object’s weight could be used to solve for the mass of the earth.
This is a good opportunity to review the difference between mass and weight. Often, the
term “weightlessness” is used to describe situations in which an object is accelerating
(“falling”) at the same rate as its surroundings. Students may have experience the
somewhat disconcerting feeling of “floating” if they have ridden amusement park rides in
which the passenger cart falls almost freely for a portion of the ride. Use this opportunity
to have students develop their reasoning skills to apply concepts they have learned to
explain space phenomena. Be certain that they learn that the astronauts in the video clips
are not in a region of space where gravity is absent!
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Forces
General Relativity II
(Bending of Light and Black Holes)
EXPLORATORY
_____ Laser Light and Projectile (M402)
CONCEPT DEVELOPMENT
_____ Mechanical Universe Video — Bending of Starlight (M397) and/or
_____ Bending of Starlight — Student Guide (M397A)
APPLICATION
_____ Closed Elevator (M400) and/or
_____ Mechanical Universe Video - Black Holes (M408) and
_____ Black Holes ---Student Guide (M408A)
SUGGESTIONS & STRATEGIES - General Relativity II
The presence of mass “warps” space (actually, space-time) so that an inertial path is not
really a straight line, but rather a geodesic or curved line toward the object. The greater
the mass, the greater the warp of space. Freely-falling bodies can be thought of as
following an inertial path in the region of the “gravitating” body rather than “falling”
under the influence of a gravitational force.
Although Einstein formulated this idea without experimental evidence, his idea of
curved space and the bending of light by the presence of mass was verified by Arthur
Eddington’s observations of starlight during an eclipse while on an expedition to the
South Pole. The apparent positions of stars in the darkened sky as the light passed the
sun was different from their positions in the night sky by just the amount that Einstein
had predicted.
Why do we not see light travel in such curved paths? The masses encountered in
everyday life are not large enough to warp space sufficiently for us to notice bending
light in such short paths. Light does, nevertheless, bend as it passes any mass; our
measurement techniques are just not sophisticated enough to detect the actual curve.
The amount that an object “warps” space depends upon its mass. Black holes are
extremely massive objects with very small radii, so they disrupt the “smoothness” of
space considerably. In fact, they are so massive that not even light can escape their
apparent “pull.”
The study of black holes is a high-interest activity for students, especially those
interested in astronomy and/or science fiction
4.6.2 Circular Motion
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Forces
Learning Outcomes
The student will understand circular motion.
The student will
1. describe the directions of a particle’s velocity and acceleration during uniform
circular motion.
2. describe the characteristics of the force causing an object to move in uniform
circular motion (centripetal force).
3. give examples of centripetal forces and solve related problems.
4. relate orbital motion to free-fall (encompasses analysis of forces on satellites).
5. identify the conditions necessary for experiencing apparent weightlessness.
Misconceptions
•
•
•
•
•
No force is needed for circular motion.
Centrifugal forces are real.
An object moving in a circle with constant speed is not accelerating.
Objects will continue in circular motion when released.
The moon stays in orbit because the forces acting on it are balanced.
Lesson Plans
Circular Motion
Orbital Motion
Centripetal Force
34
Forces
Circular Motion
EXPLORATORY
_____ Stop the World, I Want to Get Off! (F235)
CONCEPT DEVELOPMENT
_____ Video Clip: Moving in Circles (F238) and
_____ Stopper on a String (F236)
APPLICATION
_____ Firing Pellet Into Spiral Tube (F250A/250B)
SUGGESTIONS & STRATEGIES - Circular Motion
Circular motion is examined as a special case in which there is an acceleration
perpendicular to the path (i.e., perpendicular to the tangential velocity at any point).
Previously, accelerations were along the path and constituted a speeding up or slowing
down of the object. Now, a new kind of acceleration does not change the speed of the
object, but does re-direct the velocity.
35
Forces
Orbital Motion
EXPLORATORY
_____ Satellite Motion (F258A/258B)
CONCEPT DEVELOPMENT
_____ Video Clip - Cannonball in Orbit (F261)
APPLICATION
_____ Everyday Connections (F531A/F531B)
SUGGESTIONS & STRATEGIES - Orbital Motion
This lesson ties together many principles studied in the Forces unit - types of force, mass
and weight, net forces, force and acceleration, gravitation, projectile motion, and circular
motion. Many students are fascinated with space exploration and space travel, making
this a high-motivation topic.
36
Forces
Centripetal Force
EXPLORATORY
_____ Circular Motion as a Special Case of Motion Along the Path (F529)
CONCEPT DEVELOPMENT
_____ Circular Motion Representation Changes (F248A)
APPLICATION
_____ Practice with Circular Motion (F248B)
SUGGESTIONS & STRATEGIES - Centripetal Force
Since circular motion is accelerated motion, it must be caused by a net (“unbalanced”)
force in the same direction as the acceleration. Students “feel” the force when rounding
corners or going over hills in an automobile. The biggest challenge is to overcome the
perception that “centrifugal” force pulls an object outward. Ask students what force is
causing the circular motion, and what is the direction of that force? A simple
demonstration is to have them try to walk quickly in a tight circle in sock feet. They will
recognize that they are relying upon the force of friction to accomplish the circular
motion, and will “feel” themselves pushing outward on the floor. Therefore, the floor
must be pushing them inward. (This is a nice review of interactions, too.)
Students may think that centripetal is a new “brand” of force, but it is simply a
designation given to the acting force to describe the type of motion it causes. Any type
of force can be centripetal; A good exercise is to have students list situations of circular
motion and then identify what type of force the centripetal force is for each situation.
The Application activity includes many exercises; either select a few from them, or
assign different exercises to small groups and then have them share with the rest of the
class.
37