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Content Area: Newtonian Mechanics Unit: 5 Topic (s): Circular Motion, Universal Gravitation, and Simple harmonic Motion Pre Assess* I can… 1. Compare and contrast circular acceleration with linear acceleration 2. Adapt the concept of a net (or unbalanced) linear force (as defined by Newton’s Second Law of Motion) for use with net circular (centripetal) force 3. Identify the contributing factors for Universal Gravitation 4. Combine concepts of weight and universal gravitation to determine the local gravitational acceleration (aka: gravitational field) 5. Distinguish between periodic motion and simple harmonic motion 6. Analyze the acceleration and velocity of an object undergoing simple harmonic motion 7. Solve problems involving simple harmonic motion 8. Solve problems involving circular motion (including orbits) for specific forces and/or physical constants * Assign a value of 1 (no clue), 2 (some idea), or 3 (confident) Vocabulary: Centripetal Acceleration Centripetal Force Circular Velocity Frequency Orbital Velocity Period Radius of Curvature Restoring Force Sinusoidal Simple Harmonic Motion Tangential Velocity Post Assess* Equations new to this unit: T=1/f (modified from AP Sheet) Quantity, Symbol, [units] Centripetal Acceleration Tangential velocity Radius of circle (curve) Period of SHO Spring/mass Mass on spring Spring constant Period of SHO Pendulum Length of pendulum Universal Gravitation Distance between masses Position Amplitude Frequency Period Time ac v r TS m k TP l Fg r x A f T t [m/s2] [m/s] [m] [s] [kg] [N/m] [s] [m] [N] [m] [m] [m] [Hz] [s] [s] Physics Classroom Resources http://www.physicsclassroom.com/class/circles I can… 1. Compare and contrast circular acceleration with linear acceleration 2. Adapt the concept of a net (or unbalanced) linear force (as defined by Newton’s Second Law of Motion) for use with net circular (centripetal) force 3. Identify the contributing factors for Universal Gravitation 4. Combine concepts of weight and universal gravitation to determine the local gravitational acceleration (aka: gravitational field) 5. Distinguish between periodic motion and simple harmonic motion 6. Analyze the acceleration and velocity of an object undergoing simple harmonic motion 7. Solve problems involving simple harmonic motion 8. Solve problems involving circular motion (including orbits) for specific forces and/or physical constants http://www.physicsclassroom.com/calcpad/circgrav/problems Physics Classroom Lesson Lesson 1 Lesson 1 and Lesson 2 Lesson 3 Lesson 3 N/A N/A N/A Lesson 2, Lesson 4b and 4c Additional Internet Resources Centripetal Force: http://www.gpb.org/chemistry-physics/physics/504 Gravity: http://www.gpb.org/chemistry-physics/physics/505 Calendar Unit Date Activity/Assessment for Date Unit: NM Unit 5 HW Problems Day 1 HW: Read (5.1 and 5.2) 1) A 0.045kg coin is placed 0.27m from the center of a record. The record spins at 33 revolutions per minute. What coefficient of friction is needed to keep the going from slipping off of the record? 2) The Rotor (or Gravitron) spins riders and then drops the floor out from underneath them. Fortunately nobody slides down the wall to their deaths. If the Rotor has a radius of 15m and the coefficient of friction between a 100kg rider and the wall is 0.45, how fast must the ride spin to make sure the rider remains safe? Day 2 HW: Read (5.5-5.7) 1) A satellite orbits the earth 2.25x105 m above the surface of the earth. What are the orbital velocity and the orbital period of the satellite? More Day 2 on next page 2) The moon has an acceleration due to gravity of 1.67 m/s 2 and a mass of 7.35x1022kg. What is the radius of the moon? 3) Bill (m=55kg) and Ted (m=60kg) are standing 25m apart, what is the force of gravitational attraction between them? Day 3 HW: 1) A 60kg person riding a roller coaster is at the bottom of a dip in the coaster. At this dip the person feels as though they weight 850N. If the radius of the dip is 6m, how fast is the person moving? 2) The acceleration due to gravity on a planet is 12.5 m/s 2. If the planet has a radius equal to the Earth’s radius, what must the mass of the unknown planet be? Day 5 HW: Read (11.1, 11.3, and 11.4) 1) The Amazing Rando (m=85kg) is swinging through the air with the greatest of ease on a flying trapeze that has a string length of 3.1m. (a) What is the period of Rando's oscillation? (b) If the Amazing Rando was to sit on a seat that was attached to a spring, what would the spring constant need to be so that he experienced the same period of oscillation you calculated in part a? Day 6 HW: 1) The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the velocity of this system as a function of time? a) b) c) d) graph a graph b graph c graph d