Download essential unit 4 (e04)

AP PHYSICS 1
(SECONDARY)
ESSENTIAL UNIT 4 (E04)
(Circular Motion: Gravitation)
(Giancoli chapter 5)
(July 2015)
Unit Statement: In physics, circular motion is a movement of an object along the
circumference of a circle or rotation along a circular path. It can be uniform, with constant
angular rate of rotation (and constant speed), or non-uniform with a changing rate of rotation.
The rotation around a fixed axis of a three-dimensional body involves circular motion of its
parts. The equations of motion describe the movement of the center of mass of a body.
Gravity is a natural phenomenon by which all physical bodies attract each other. It is most
commonly experienced as the agent that gives weight to objects with mass and causes them
to fall to the ground when dropped. Gravitation is one of the four fundamental interactions of
nature. This unit will focus on how Newton’s Laws of motion apply to circular motion and
gravitation. (Estimated class time three weeks)
Essential Outcomes: (must be assessed for mastery)
1. The Student Will design a plan for collecting data to measure gravitational mass and
to measure inertial mass, and to distinguish between the two experiments. (LO
1.C.3.1)
2. TSW apply F= mg to calculate the gravitational force on an object with mass m in a
gravitational field of strength g in the context of the effects of a net force on
objects and systems. (LO 2.B.1.1)
3. TSW describe gravitational force as the interaction of one object that has mass with
another object that has mass. Including each of the 3 points:
a. The gravitational force is always attractive.
b. The magnitude of force between two spherically symmetric objects 𝐹 =
𝑚 𝑀
𝐺 ( 𝑟12 2 ), where r is the center-to-center distance between the objects.
(EK 3.C.1)
c. In a narrow range of heights above the Earth’s surface, the local
gravitational field, g, is approximately constant.
4. TSW applies Newton’s Law and rules of center of mass to gravitation and orbital
motion. (EK 4.A.3)
5. TSW uses appropriate formulas to calculate and prove the gravitational field is caused
by a spherically symmetric object with a radial mass and, outside the object, the
field varies as the inverse square of the radial distance from the center of that
object changes. (EK 2.B.2)
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Implied and Practiced Outcomes: (not formally assessed)
1. The Student Will will demonstrate gravitation, inclined planes, Atwood’s machines
and their applications and modifications
2. TSW demonstrate static and kinetic friction, horizontal and vertical circles and
planetary motion.
3. TSW write down the relationship between the normal and frictional forces on a surface.
4. TSW analyze under what circumstances an object will start to slip, or to calculate the
magnitude of the force of static friction.
Guided or Essential Questions:
 What does it mean for a force to be fundamental?
 What force or combination of forces keeps an object in circular motion?
 How is the motion of the moon around the Earth like the motion of a falling apple?
 How does the effect of Earth’s gravitational field on an object change as the object’s
distance from Earth changes?
 Why do you stay in your seat on a roller coaster when it goes upside down in a
vertical loop?
 What conditions are necessary for a planet to obtain a circular orbit around its host star?
 How can Newton’s second law of motion be related to the universal law of
gravitation?
 How can the motion of the center of mass of a system be altered?
Key Concepts:
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Uniform circular motion
Radial acceleration
Frequency
Gravitational Field
Contact Force
Kepler’s Laws
Newton’s Synthesis
Centripetal acceleration
Fundamental forces
Period
Centrifugation
Law of Universal Gravitation
Weightlessness
Perturbations
Some Common Equations for this Unit:
𝑣𝑟 2
𝑟
1
𝑇=
𝑓
2𝜋𝑟
𝑣=
𝑇
centripetal acceleration
𝑎𝑐 =
∑ 𝐹𝑟 = 𝑚𝑎𝑟 = 𝑚
Period and Frequency relation
Constant speed in circular motion
(𝑣 2 )
𝑟
Net force in the radial Direction
𝑚1 𝑚2
𝑟2
2
𝑇1
𝑟1 3
( ) = ( )
𝑇2
𝑟2
Law of Universal Gravitation
𝐹=𝐺
Kepler’s 3rd Law
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Schedule of suggested laboratory experiments (guided inquiry format is suggested for labs
shaded in gray)
TSW #
Lab #
Name of Laboratory
Description of Lab
1
25
Centripetal Force Lab
Students working in small groups are challenged to determine the
relationships among centripetal acceleration, centripetal force,
mass, velocity, and radius. Students accomplish this using a device
that they build based on provided instructions. They use the device
to swing a rubber stopper at various speeds while keeping a
hanging mass (another rubber stopper) stationary. The device has
a fishing line threaded through a PVC pipe with rubber stoppers
tied to both ends.
Students carefully swing the upper stopper in a circle of constant
radius while watching the lower (stationary) stopper to ensure it
does not bob up and down. Formal reports presenting evidence
and analysis (both qualitative and quantitative) of the results are
exchanged with peer groups for critique before final submission
for grading.
1-5
3
5
26
27
28
Gravity Force Lab
My Solar System
Change Center of Mass
From Outside
Hoffman (see link bleow)
Students working in small groups utilize the PhET simulation to do
the
following:
1. Discover the relationship between masses of objects, the
distance between them, and the gravitational force of attraction.
2. Derive an equation that relates mass, distance, and the
gravitational force of attraction.
3. Determine the magnitude of the universal gravitational
constant.
Then, they must test their equation by determining the
gravitational force exerted on their body by the Earth and
comparing this force to their known weight in newtons. Finally,
students are asked to use their equation and Newton’s second law
to derive an equation and solve for the gravitational field (g) at the
Earth’s surface.
PhET (See link below)
Students working in small groups use the simulation to investigate
how a planet’s mass, velocity, and distance from a star are related
to the planet’s orbit. Then they must predict a correct combination
of parameters (mass, velocity, and distance) necessary to maintain
a circular orbit around a star of whatever mass they choose.
Students back up their prediction by deriving an equation relating
the universal law of gravitation to centripetal force (showing their
calculations) and by using the simulation to test their prediction.
PhET (See links below)
Students working in small groups are challenged to first discover a
way to change the center of mass motion of a simple system from
the outside of the system and then from the inside of the system.
A demonstration involving wheels with hidden masses may be
utilized as a discrepant event to get students asking questions (as
the two seemingly identical objects roll down an incline at
different rates). Students can use and manipulate the
demonstration apparatus if they wish. Students are promised a
special prize if they can develop a way to change the center of
mass motion from within the system. A logical explanation
(including mathematical and/or graphical proof) of any change in
motion is required, as are any explanations that it is not possible.
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QSI AP PHYSICS 1 SEC E04
Copyright © 1988-2015
Associated Science
Practices
1.1, 1.2, 1.4, 1.5, 2.1,
2.2, 3.1, 4.1, 4.2, 4.3,
5.3, 6.1, 6.4, 7.2
1.1, 1.2, 1.4, 1.5, 2.1,
2.2, 3.1, 4.1, 4.2, 4.3,
5.3, 6.1, 6.4, 7.2
1.1, 1.2, 1.4, 1.5, 2.1,
2.2, 3.1, 4.1, 4.2, 4.3,
5.3, 6.1, 6.4, 7.2
1.1, 1.2, 1.4, 1.5, 2.1,
2.2, 3.1, 4.1, 4.2, 4.3,
5.3, 6.1, 6.4, 7.2
Suggested Materials:
1. Giancoli, D.C. Physics: Principles with Applications. Englewood Cliffs, NJ: Pearson
Education.
2. Appel, K, Ballen, C, Gastineau, J, Vernier, D. Physics with Vernier. Beaverton, OR;
Vernier Software and Technology, 2010.
3. Puri, O; Zober, P. Physics. A laboratory manual; Boston, Mass. N.Y: Pearson Custom
Pub., 2002. 8th edition
Suggested Technology Resources:
Labs, in class activities, quizzes, videos and demos:
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PowerPoint by Paul E. Tippens, Professor of Physics- Uniform Circular Motion –
https://www.stcharlesprep.org/01_parents/vandermeer_s/Useful%20Links/Honors%2
0Physics/pdf%20lectures/Circular%20Motion.pdf
Conical Pendulum Worked out problemhttps://www.youtube.com/watch?v=8kNNrl-eHKU
Gravity and Orbitals PhET- http://phet.colorado.edu/en/simulation/gravity-and-orbits
My Solar System PhET- http://phet.colorado.edu/en/simulation/my-solar-system.
Kepler Law online Notes- http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html
Practice and Data Analysis- Satellites Orbit-Analyze the orbital motion of satellites
moving about a central massive object – much like the planets in the solar system
moving around the
sun.http://media.pearsoncmg.com/bc/aw_young_physics_11/pt1a/Media/CircularMot
ion/SatellitesOrbit/Main.html
Sports Demo Podcast- http://www.nasa.gov/audience/foreducators/diypodcast/sdvideo-index-diy.html#.VOVvn_mUcR0
Gravity Force PhET- http://phet.colorado.edu/en/simulation/gravity-force-lab
How to Weigh the Earth- YouTube Videohttps://www.youtube.com/watch?v=9yMQM5AN8mc
Law of Gravitation Online Labhttp://dev.physicslab.org/Document.aspx?doctype=3&filename=UniversalGravitation
_UniversalGravitation.xml
Universal Gravitation and Satellites Online Worksheethttp://dev.physicslab.org/Document.aspx?doctype=5&filename=UniversalGravitation
_Satellites.xml
Circular Motion Interactive Tutorialhttp://www.mhhe.com/physsci/physical/giambattista/circular/circular.html
Lab 1- Hoffman http://wwwlhs.beth.k12.pa.us/faculty/Hoffman_M/Expt%2006%20Centripetal%20Force%20Lab
.pdf
My Solar System Lab – http://phet.colorado.edu/en/simulation/my-solar-system
MS Document to follow simulation –
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&
uact=8&ved=0CDEQFjAD&url=http%3A%2F%2Fphet.colorado.edu%2Ffiles%2Fac
tivities%2F3015%2Fmy%2520Solar%2520System%2520Lab.doc&ei=lVbsVPv5Jm
muogSCoID4Dg&usg=AFQjCNEh_kQv3wy7JbNHtROTCAhaPKi4A&bvm=bv.86475890,d.cGU
Note- All links to online resources were verified before publication. In cases where links are no
longer working, we suggest that you try to find the resource by a keyword internet search.
RUBRIC FOUND ON FOLLOWING PAGE…………………………….
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QSI AP PHYSICS 1 SEC E04
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SUGGESTED RUBRIC AP PHYSICS 1 E04
Student Name: __________________________
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1.
2.
3.
a.
b.
c.
4.
5.
Date: _______________________
To receive a ‘B’, the student must show ‘B’ level mastery on all essential outcomes (TSW’s).
The teacher’s discretion on the student’s holistic performance on the unit, including such items as: the above ‘A’ level rubric, the unit project, group work and
class discussions will determine ‘A’ level mastery.
If grading for AP test preparation, please refer to Course Outcome Rubric.
The Student Will
TSW design a plan for collecting data to
measure gravitational mass and to measure
inertial mass, and to distinguish between the two
experiments. (LO 1.C.3.1)
TSW apply F= mg to calculate the gravitational
force on an object with mass m in a gravitational
field of strength g in the context of the effects of
a net force on objects and systems. (LO 2.B.1.1)
TSW describe gravitational force as the
interaction of one object that has mass with
another object that has mass. Including each of
the 3 points:
The gravitational force is always attractive.
The magnitude of force between two spherically
symmetric objects
𝑚 𝑚
𝐹 = 𝐺 1 2 2 where r is the center-to-center
𝑟
distance between the objects.
In a narrow range of heights above the Earth’s
surface, the local gravitational field, g, is
approximately constant. (EK 3.C.1)
TSW applies Newton’s Law and rules of center
of mass to gravitation and orbital motion.
TSW uses appropriate formulas to calculate and
prove the gravitational field is caused by a
spherically symmetric object with a radial mass
and, outside the object, the field varies as the
inverse square of the radial distance from the
center of that object changes. (EK 2.B.2)
‘A’* LEVEL
‘B’ LEVEL
Approach chosen is clearly shown, clearly written &
all elements are valid.
Correct starting equations; All mathematical steps
are clearly shown and they flow easily toward the
correct answer.
Uses Newton’s law of gravitation to calculate the
gravitational force the two objects exert on each other
and use that force in contexts other than orbital
motion. (LO 3.C.1.1)
Uses Newton’s law of gravitation to calculate the
gravitational force between two objects and uses that
force in contexts involving orbital motion. (LO
3.C.1.2)
Applies Newton’s second law to systems to calculate
the change in the center-of-mass velocity when an
external force is exerted on the system. (specially
gravitational forces) (LO 4.A.3.2)
Uses visual or mathematical representations of the
forces between objects in a system to predict whether
or not there will be a change in the center-of-mass
velocity of that system. (specially gravitational
forces) (LO 4.A.3.1)
𝑀
Applies 𝑔 = 𝐺 2 to calculate the gravitational field
𝑟
due to an object with mass M, where the field is a
vector directed toward the center of the object of
mass M. (LO 2.B.2.1)
Approximates (predicts) a numerical value of the
gravitational field (g) near the surface of an object
from its radius and mass relative to those of the Earth
or other reference objects. (LO 2.B.2.2)
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QSI AP PHYSICS 1 SEC E04
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