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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) 44 QSI AP PHYSICS 1 SEC E04 Copyright © 1988-2015 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: 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 45 QSI AP PHYSICS 1 SEC E04 Copyright © 1988-2015 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. 46 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: 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……………………………. 47 QSI AP PHYSICS 1 SEC E04 Copyright © 1988-2015 SUGGESTED RUBRIC AP PHYSICS 1 E04 Student Name: __________________________ 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) 48 QSI AP PHYSICS 1 SEC E04 Copyright © 1988-2015 Comments