Syllabus, AP Physics C: Mechanics

Syllabus, AP Physics C: Mechanics Textbook: Paul A. Tippler and Gene Mosca, Physics for Scientists and Engineers Vol. 1 5th Ed. (W.H. Freeman and Co., NY, 2004). Student Population: Ours is a public high school of approximately 1400 students, grades 9-12. This course is open to 11th and 12th grade students who have taken or are concurrently taking calculus. Approximately 45 students enrolled in 2006/7 (2 sections), the 1st year the course was offered. This is typically their first high school physics class (some physics topics are covered in the 8th grade). For this reason, only the mechanics course is covered. The slower pace this provides is used to emphasize conceptual understanding along side the high level problem solving and critical thinking skills that distinguish the course. In addition, students are required to complete a summer reading assignment prior to beginning the course (see Table). Schedule / Time on Learning: Our school operates on a trimester system, each trimester consisting of about 60 days of instruction. A full year course is completed in 2 of the 3 trimesters. This course is taught over 2 trimesters (Fall and Winter), with classes meeting 4 days a week for 60 minutes and 1 day a week for 90 minutes. There are a total of approximately 130 contact hours. Course Structure: The course is a combination of lectures, demonstrations, small group problem solving, and laboratory activities. With class sizes of 20-25 students, lectures and demonstrations include a good deal of give-and-take between teacher and students. Exemplar problems are presented during lecture and then students break up into small groups of 3-4 to work out related problems on a shared whiteboard. Daily problem-solving homework is assigned for further reinforcement of independent critical thinking skills. To foster student independence, homework problems are rarely gone over in class, but full solutions are available and students are expected to check their own work. Students are tested at the end of each unit. These tests are modeled after the AP exam, with separate multiple choice and free-response sections. Laboratory Structure: (see Table for a full list of laboratories, organized by unit) Of the 130 contact hours, about 35 are devoted to laboratory activities. This represents approximately 27% of contact hours. About 28 of these lab hours are spent on student conducted, inquiry-based hands-on activities (21% of contact hours). The rest is used for virtual labs or paper and pen activities based on data not obtained directly by the students. Laboratory time is not limited to a single day of the week so that it can be fully integrated into the curriculum. Some laboratories continue over several days, while some are short activities designed primarily to enhance conceptual understanding and provide a concrete kinetic experience. Labs that emphasize inquiry tend to take the most time, and these require students to submit full written reports. Students keep a portfolio of their lab reports, including both the longer formal reports and the shorter reports required for other activities. Laboratory Equipment (generally 7 lab stations): Vernier Computer-Based Data Collection including the following probes: sonic motion detectors, photogates, dual range force probes, force plate. 2 meter long aluminum Pasco tracks and magnetic carts, fan carts. Assorted spring scales, calibrated masses, springs, pulleys, balls, digital camera, air table and accessories, rechargeable air pucks, ramps, ring stands, clamps etc. 1 of 10

UNIT TITLE (Time)

TOPICS

SUMMER 1. Conceptual Physics: ASSIGNMENT Mechanics

• READINGS • PROBLEM SETS • ASSESSMENT • Text: Paul Hewitt, “Conceptual Physics” Chapters 2-14

LABORATORY ACTIVITIES DESCRIPTION

TIME, TYPE

• From Hewitt’s Text Chapters 2-8, 13,14: 58 Review Questions, 4 Activities, 29 Think and Explain Questions

UNIT 1: Introduction (1.5 wks)

• Force Concept Inventory administer at the start of the course. • Text Ch.1

1. What is Physics? 2. SI system of units 3. Unit Conversion and • 6 homework sets of ~ Dimensional Analysis 5 textbook problems; 4. Uncertainty in 3 group work Measurement (precision, sessions, ~2 problems accuracy, significant each. figures) 5. Analyzing Experimental • Unit Test Data: perfect graphs and tables, straightening a curve. 6. Order of Magnitude Estimating, Fermi Problems

2 of 10

• Dimensional Analysis of a Pendulum: deduce the expression for T using dim. analysis and experimentally verify it. • Sonic Meter Stick: compare the precision and accuracy of the motion detectors and a meter stick, recognizing appropriate uses for both instruments. • Analyzing Experimental Data: use graphing software to determine the relationship between wire resistance, wire length, and cross sectional area.

• 30 min, student conducted • 30 min, student conducted • 90 min, student conducted

UNIT TITLE (Time) UNIT 2: One Dimensional Kinematics (3 wks)

TOPICS

1. Graphical Representations of Motion. 2. Position, Distance, Displacement, Average Speed, Velocity, and Acceleration. 3. Instantaneous Velocity and Acceleration: Derivatives and the Equations of Motion. 4. Constant Acceleration and Free Fall. 5. Integration and the Equations of Motion.

• READINGS • PROBLEM SETS • ASSESSMENT • Text Ch. 2 • 10 homework sets of ~5 textbook problems each; 5 group work sessions, ~2 problems each. • Unit Test

3 of 10

LABORATORY ACTIVITIES DESCRIPTION • Motion Lab, Position and Velocity Graphs: predict and observe graphical representations of your own motion through the use of ultrasonic motion detectors. • Car on a Ramp: calculate final velocity and average acceleration of a toy car based on stop watch measurements and understanding of average velocity. • Acceleration on a Ramp Lab: acceleration of a low friction cart using ultrasonic motion detector. Determine dependence ramp angle and perform quantitative comparison with the accepted relationship. • Reaction Time Lab: ruler drop measurement of reaction time (relating to stopping distance)

TIME, TYPE • 90 min, student conducted • 30 min, student conducted • 90 min., student conducted

• 30 min., student conducted

UNIT TITLE (Time) UNIT 3: Two Dimensional Motion (3 wks)

TOPICS

1. Vectors: Notion, unit vectors, arithmetic. 2. Rectangular Vector Components. 3. Position, velocity and acceleration vectors. 4. Relative Motion 5. Projectile Motion 6. Circular Motion

• READINGS • PROBLEM SETS • ASSESSMENT • Text Chapter 3 • 10 homework sets of ~5 textbook problems each; 5 group work sessions, ~2 problems each. • Unit Test

4 of 10

LABORATORY ACTIVITIES DESCRIPTION • Orienteering Lab: compass and individual pace to walk a 5 vector course. Then construct a scale drawing of the course and calculate average speed and velocity. • Town of King’s Court Map Lab: map, protractor and ruler used to determine displacement, average and instantaneous speed, average and instantaneous velocity. • Vector River Lab: Students place themselves in a boat on a river and calculate their velocity and displacement from relative to the shore, and other objects on the river. • Projectile Motion Lab: Using Vernier photogates to measure velocity of marble launched from lab bench, calculate landing position. Based on calculation, place a target on the floor and compare prediction to result. • Projectile Motion Simulation: Web-based investigation of the effects of angle, velocity, mass and air resistance.

TIME, TYPE • 1 h, student conducted • 1 h, student conducted • 1 h, “virtual”, student conducted • 1 h, student conducted

• 1 h, “virtual”, student conducted

UNIT TITLE (Time) UNIT 4: Newton’s Laws (2.5 wks)

TOPICS

1. Forces: contact forces and the 4 fundamental forces, units of force. 2. Static Equilibrium: 1st Law and inertia 3. Dynamics of a single particle: 2nd Law and cause and effect. 4. Systems of two objects: 3rd Law and interaction forces. 5. Net force and Free-body diagrams. 6. Mass, weight, and apparent weight. 7. Tension and pulleys 8. Springs and Hooke’s Law

• READINGS • PROBLEM SETS • ASSESSMENT • Text Chapter 4 • 9 homework sets of ~5 textbook problems each plus additional tension problems; 5 group work sessions, ~2 problems each.

LABORATORY ACTIVITIES DESCRIPTION • Inertia Activities: inertia and everyday situations. •

• Unit Test • •

•

5 of 10

TIME, TYPE • 1 h, student conducted Investigating Forces Lab: • 90 min., Observations connecting forces and student motion in ordinary situations conducted (medicine ball toss, pulling people on low friction carts, elevators etc. Written reflections of their connection to Newton’s Laws. Empirical Forces Lab: paper • 1 h, activity comparing relative sizes of student forces under different conditions. conducted Recognizing and Interpreting • 1 h, Free-Body Diagrams: paper student activity. conducted Hooke’s Law Lab: Traditional lab with springs and rulers.


UNIT TITLE (Time) UNIT 5: Applications of Newton’s Laws (2.5 wks)

TOPICS

1. Normal forces and friction, (coefficient of friction). 2. Slipping and static friction. 3. Motion w/ friction (horizontal and inclined planes). 4. Motion of stacked objects. 5. Circular motion and centripetal force. 6. Drag forces and terminal velocity. 7. 2nd Law as a differential equation for velocity.

• READINGS • PROBLEM SETS • ASSESSMENT • Text Chapter 5 • 9 homework sets of ~5 textbook problems each plus additional friction problems; 5 group work sessions, ~2 problems each. • Unit Test

6 of 10

LABORATORY ACTIVITIES DESCRIPTION TIME, TYPE • Friction Lab: Vernier force probes • 90 min., to measure the force of static and student kinetic friction w/ various surfaces conducted while varying normal force. Graphical analysis used to calculate coefficients of kinetic friction. • Centripetal Force Lab: hanging • 90 min., weights used to quantify centripetal student force while swinging small objects conducted in a horizontal circle. • Terminal Velocity Lab: Paper • 30 min., activity examining the effects of student drag and weight on terminal conducted velocity.

UNIT TITLE (Time) UNIT 6: Work, Power and Energy (3 wks)

TOPICS

1. Work- average force x distance and by integration. 2. Kinetic Energy 3. Scalar Products 4. Vector definition of Work: 2 and 3-D. 5. The Work-Kinetic Energy Theorem and Newton’s 2nd. 6. Power 7. Potential Energy Function and Conservative Forces. 8. Gravitational & Spring PE. 9. Stable and unstable equilibrium. 10. Conservation of Energy. 11. Problem solving using energy conservation as an alternative to Newton’s Laws.

• READINGS • PROBLEM SETS • ASSESSMENT • Text Chapter 6 & 7.17.3 • 9 homework sets of ~5 textbook problems each; 5 group work sessions, ~2 problems each. • Unit Test

7 of 10

LABORATORY ACTIVITIES DESCRIPTION • Your Power Lab: measuring human power output walking stairs (watts and HP) and comparing w/ power usage of common appliances. • Work-Kinetic Energy Lab: Vernier force probes and ultrasonic motion detectors to measure the work done on a low friction cart and comparing it to kinetic energy gained. Students develop sophisticated methods of manipulating sensor data to measure the desired quantities. • Cut Short and Flying Lab: Predict where a pendulum cut at its low point will land and then test by doing. • Pulley Lab: Using 1, 2, 3 pulley’s, build various machines to lift weight and analyze mechanical advantage. • Roller Coaster Simulation: (http://funderstanding.com/k12/coas ter/) Manipulate a virtual roller coaster to see the effects of friction, hill heights, starting velocity, gravity etc.

TIME, TYPE • 1 h, student conducted • 2 h, student conducted

• 1 h, student conducted • 1 h, student conducted • 30 min., virtual, student conducted

UNIT TITLE (Time) UNIT 7: Systems of Particles and Center of Mass (3 wks)

TOPICS

• READINGS • PROBLEM SETS • ASSESSMENT • Text Chapter 8

1. Center of mass- systems of particles and symmetrical continuous objects. • 10 homework sets of 2. CM of non-uniform objects ~5 textbook problems by integration. each; 5 group work 3. Balance and equilibriumsessions, ~2 problems Center of Gravity & each. Potential Energy. 4. CM velocity and linear • Unit Test momentum. 5. CM acceleration and Newton’s 2nd Law. 6. Conservation of Linear Momentum and external forces. 7. Kinetic Energy of a system. 8. Impulse-Momentum theorem (impulse by average force and integration). 9. Collisions: • 1-D elastic and inelastic. • 2-D perfectly inelastic. • 2-D elastic collisions & special case equal masses. 10. Explosions: momentum and energy considerations.

8 of 10

LABORATORY ACTIVITIES DESCRIPTION TIME, TYPE • Observing Collisions Lab: 2-body • 90 min., elastic and inelastic collisions and student explosions using Pasco magnetic conducted carts. Create various collisions and record qualitative observations. Reflect on momentum and energy conservation. In class follow up at the end of the unit to compare observations with theory. • Hanging the USA Lab: Finding the • 30 min., CM of an irregular object (map of student the USA) by suspending. conducted • Baseball and Basket Ball Bounce • 30 min., Activity: Baseball held over teacher basketball is dropped from a few demo feet off the ground. Students predict (calculate) what will happen, then predictions are tested by teacher demonstration. • Impulse and Momentum Lab: • 90 min., Vernier force probes and ultrasonic student motion detectors used to measure conducted and calculate impulse applied to a cart as it reaches the end of an elastic cord. This is then compared to the carts change in momentum. • 2-D Collisions Video Analysis: • 15 min., Video analysis of glancing angle air teacher puck collisions showing right angle demo final velocities.

UNIT TITLE (Time) UNIT 8: Rotation and Angular Momentum (3 wks)

TOPICS

1. Rotational Kinematics: • Angular displacement, velocity and acceleration. • Kinematic equations for constant acceleration. 2. Rotational Kinetic Energy and Moment of Inertia of discrete objects. 3. Calculating Moment of continuous objects. 4. Parallel Axis Theorem. 5. Torque and Newton’s 2nd Law for rotation. 6. Rotational Equilibrium. 7. Rolling without Slipping. 8. Rolling and energy conservation. 9. Cross Product (right hand rule and unit vector notation). 10. Vector nature of angular velocity, acceleration and torque. 11. Angular Momentum and Newton’s 2nd Law. 12. Gyroscopes and Precession 13. Conservation of Angular Momentum

• READINGS • PROBLEM SETS • ASSESSMENT • Text Chapter 9-10 • 10 homework sets of ~5 textbook problems each; 5 group work sessions, ~2 problems each. • Unit Test

9 of 10

LABORATORY ACTIVITIES DESCRIPTION • Rotations Stations Lab: A series of activities with ordinary objects and toys that students complete before starting Unit 8. Students record their observations. At the end of the unit, students then write explanations of the various phenomena they observed. • Rolling Lab: Measure the relative speeds of solid and hollow spheres and cylinders rolling down a ramp, then use energy conservation to calculate their velocities at the bottom of the ramp and compare with the observed behavior. Finally, predict where the solid sphere and hollow cylinder will land on the floor when allowed to roll down a ramp and off the end of the lab bench. Test the prediction by doing. • Mobile Activity: Design a mobile on paper such that it is in equilibrium, then test the design by building it.

TIME, TYPE • 90 min., student conducted



UNIT TITLE (Time) UNIT 9: Gravitation and Oscillations (2.5 wks)

TOPICS

• READINGS • PROBLEM SETS • ASSESSMENT • Text Chapter 11 & 14

1. Interaction of masses, “masslet” concept. 2. Inverse square laws. • Universal gravitation 3. Newton’s Law of Universal worksheet; 10 Gravitation. homework sets of ~5 4. “g” and “G”. textbook problems 5. Gravitational and inertial each; 5 group work mass. sessions, ~2 problems 6. Coulomb’s Law. each. 7. Kepler’s Laws • 2nd Law and Conservation • Unit Test of Angular Momentum. • 3rd Law derived (circular). 8. Gravitational Potential Energy, escape velocity and classification of orbits. 9. Gravitational fields inside and outside uniform sphere. 10. Simple Harmonic Motion: differential equation for spring-like restoring forces. 11. SHM: displacement, velocity and acceleration. 12. SHM: Energy 13. Mass on a spring: vertical 14. Pendulum: small amplitude. 15. Physical Pendulums. 16. Resonance: over, under and critically damped. 17. Forced oscillations and Q.

10 of 10

LABORATORY ACTIVITIES DESCRIPTION TIME, TYPE • Masslet Model of Gravitation: • 30 min. teacher demonstration and followteacher up paper activity. demo • Newton’s Cannon Activity: Web • 30 min. simulation “virtual”, (http://galileo.phys.virginia.edu). student Find the velocity that results in near conducted circular orbit, then calculate how high the mountain must be. • Kepler’s Laws Activity: Interact • 30 min. with the web simulation to answer a “virtual”, series of questions about Kepler’s student Laws. conducted • Simple Harmonic Motion Lab: • 90 min. Vernier ultrasonic motion detectors student to measure position and velocity as conducted a function of time for a vertical mass on a spring system. Determine the relationship between mass, amplitude, period, frequency and spring constant. Use software analysis to fit the observed motion to the mathematical model and adjust the model to explore the effects of phase and frequency.