AP Physics C Mechanics – Syllabus

Course Description: AP Physics C is a college level course designed to prepare students for the AP Physics C Mechanics exam given in May. A prior physics course is not required but desired for enrollment, and students must have strong background in math, since a basic understanding of calculus (differentiation and integration) is used to derive formulas in the course. This course uses labs, lecture, guided inquiry, student centered learning, and teacher support to foster the development of critical thinking skills.

Topics are typically introduced with discussions and demonstration. From there, relations are derived from the basic definitions, students work on problems to apply the concepts learned, and solutions are presented so students and the teacher can discuss the solutions. Each class session allows time for students to discuss the previous night’s assignment (typically five problems) to ensure they understand the information. The goal is to have a deep understanding of the concepts and why things happen instead of simply memorizing the formulas. In addition to the availability of the teacher in and outside of class, students are encouraged to participate in study groups for additional support.

Co-prerequisite: Calculus (BC): Calculus (8th edition 2006) by Larson, Hostetler, Edwards: Houston, Miffing Corp

Text Book:

Physics for Scientists and Engineers, by Serway and Beichner, 5th Edition

Homework: 10%. The students will have a set of problems each day and that will be completed for the teacher the following day. Problems from each chapter are assigned. Additional problems are used in the class to develop solution strategies.

Quizzes: 25%. After each five class meetings, the students will receive a one page quiz assessing their understanding of concepts and their ability to solve problems.

Tests: 30%. At the completion of each unit, the students will take a computer test with multiple choice questions and a paper set of free response questions similar to those found on the AP exam.

Labs: 20%. At least one class session each week will have a hands-on lab activity with maximum usage of digital monitoring and measuring devices. A formal lab report will be required for each activity which will be formatted in Excel to maximize its calculation and graphic functionality.

Research Project: 15%. A project will be assigned each quarter that incorporates both literature search and laboratory investigation of a principle under current study.

Organization, reasoning, method and decision making process will be emphasized to be used in decision making and problem solving. Students must be able to solve the multi-concept physics problems by using Newton’s laws of motion and the conservation laws by using differential and integral calculus. They must learn how to translate word problems into calculus problems and solve it by using proper limits.

The class meets 3 days each week for 95 minutes or 1 session. (285 minutes/week)

Mechanics

Kinematics: Vectors And Scalars: 11 sessions:

Introduction to measurement, powers of ten, metric prefixes, density and formula computations. SI units are defined and physical units derived. Basic equation solutions are reviewed, and rules are defined for homework problem formats. Introduce strategies for problem solving.

Homework: p 17-22 Ch. 1: 2, 5, 6, 9, 12, 14, 18, 20, 26, 30, 33, 36, 38, 51, 52, 55

To ask questions in the class about home work is strongly encouraged. Falling behind will make the subject more difficult.

Kinematics: distance, displacement, speed, velocity, acceleration: constant, average and instantaneous: Motion in one dimension, Graphical representation of d, v and a vs. time - Displacement, Velocity, and Speed, Instantaneous Velocity and Speed, Acceleration

Slope and area under the graph and inter-relation between d, v and a. Free fall. Introduction to derivative, integration and application to varying d, v and a.

Motion in two dimensions: Projectile motion- leveled and unleveled ground, horizontal range, maximum height, total time of flight and the important conditions.

Homework: Ch.2: p. 50-57: Problems: 1, 2, 3, 4, 7, 11, 13, 15, 23, 28, 29, 31, 40, 46, 51

Coordinate Systems, Vectors and Scalars, Vector Addition and Subtraction, Vector Components, Unit and i-j-k Vectors Kinematics Graphics—days Difference between scalar and a vector, unit vector and notation of a vector, addition of vectors: Parallelogram, Head –Tail and the decomposition method, Multiplication of vectors: Dot or scalar product and cross or vector product, RHR for the direction of the vector product, mention how and where these will be used in physics, introduction to i, j, k components in rectangular coordinates.

Homework: Ch.3: p. 71-75: Problems: 1, 3, 5, 6, 8, 9, 11, 14, 15, 17, 19, 20, 21, 25, 27, 31, 33, 35


Two Dimensional Motion with Constant Acceleration, Motion in a Plane and Projectiles, Uniform Circular Motion, Relative Motion

Homework: Ch.4: p. 101—108: Problems: 3, 4, 5, 6, 9, 10, 13, 14, 15, 19, 20, 21, 22, 23, 24, 27, 29, 30,31, 32, 33, 34, 35, 39, 41, 47, 48, 53, 57, 59, 69, 82, 84

Dynamics-Newton’s Laws of Motion: 9 sessions:

Law of inertia, linear equilibrium Net F = 0, rest or constant velocity

Law of acceleration, Net F = ma =m dv / dt.

Law of action and reaction.

Forces: Pull or push, gravity, normal and frictional, Tension, electric and magnetic

Labeled free body diagrams, Technique of isolating the bodies and applying Newton’s laws.

Homework: Ch.5: p. 140-149: Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 19, 21, 23, 24, 25, 26, 27,29, 30, 31, 33, 34, 35, 37, 39, 41, 45, 49, 51,55, 57, 63, 67, 69, 77, 78, 82, 85, 87, 88

Circular motion, curved and banked roads, motion in horizontal and vertical circles and park rides, centripetal force and acceleration. Newton’s 2nd law for circular motion. Direction of F, a and v in linear and circular motion. Nonuniform Circular Motion, Motion in a Resistive Medium

Homework: Ch.6: p. 173-181: Problems: 1, 2, 3, 4, 5, 7, 8, 11, 12, 14, 15, 16, 17, 21, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 39, 41, 43, 45, 48, 49, 50, 52

Work, Energy, Power, KE and PE: 8 sessions:

Units defined, Work as a line integral and force as a space derivative of work,

Power as time rate of change of work, graphical representation,

Work-Energy principle derived from Newton’s 2nd law as space dependent by using chain rule and definition of KE. Work Done by a Constant Force, Scalar Product, Work Done by a Variable Force, Work Done by a Spring, Kinetic Energy and the Work-Energy Theorem, Power and Efficiency, Conservative and non-conservative forces, Gravitational and elastic potential energy.

Homework: Ch.7: p. 207-213: Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 20,21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35 36, 37, 38, 39, 40 41, 42, 43, 44, 45,46, 47, 48, 49, 50, 52, 53, 55, 56, 57, 59, 70, 71, 73, 75 77, 79, 81, 86

Potential Energy, Conservative and Nonconservative Forces, Conservative Forces and Potential Energy, Conservation of Mechanical Energy, Potential Energy Function

Potential energy curves, KE + PE = mechanical energy, Law of conservation of energy when external force is zero. Use of calculus in solving problems.

Gravitational PE, U equal to negative of the line integral of the force of gravity,

Force expressed as the negative of the space derivative of the potential energy function, F = - dU(r) / dr.

Homework: Ch.8: p. 239-249: Problems: 1, 2, 3, 4, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41 43, 46, 47, 49,52, 53, 55, 57, 58, 60, 61, 63, 67, 68, 69

Momentum: 6 sessions:

Linear Momentum and its Conservation, Impulse and Momentum, Collisions in One Dimension, Two Dimensional Collisions, Center of Mass, Rocket Propulsion Property of motion and a vector quantity defined by using Newton’s 2nd law as time dependent. Net F = dp/dt, where p = mv, Impulse theorem and definition of impulse. Graph of t vs. F and its relation to change in momentum, graph of p vs. t and its relation to force. Law of conservation of momentum from impulse theorem when an external force is zero.

To emphasize special conditions for conservation laws. Interactions and elastic and inelastic collisions in 1D and 2D and conservation laws.

Perfectly elastic collisions: KE and Momentum both are conserved when external force is zero and the relative velocity before collision is equal to the negative of the relative velocity after collision.

In inelastic collision KE is lost and only Momentum is conserved.

Center of mass, center of gravity and center of mass motion.

Homework: Ch.9: p. 282-291: Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20 22,23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 41, 43, 45 51, 52, 53, 54, 57,58, 59, 60, 63, 65, 69, 71, 72, 73, 75, 80, 81, 82, 84, 85

Rotation Dynamics: 7 sessions:

Rotational Dynamics: Define torque = r x F and derive N’s 2nd law for rotation

Net Torque = M of I times angular acceleration. Units of torque and work and the difference, Rotational KE, Linear KE for rolling objects.

Angular Displacement, Velocity, and Acceleration, Rotational Kinematics, Angular and Linear Quantities, Rotational Energy. Calculations of Moments of Inertia, Use calculus to find the M of I of a uniform rod, a ring, a disc, etc. Torque and Angular Acceleration, Work, Power, and Energy in Rotational Motion, Parallel axis and perpendicular axis theorem.

Homework: Ch.10; p. 317-327: Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 20,21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 37, 40, 42, 43, 44, 47, 48 50, 51, 52, 54

Law of conservation of energy. Angular momentum L = r x p and L = M of I x angular velocity and Net Torque = dL/dt as Net F = dp/dt in linear dynamic.

Law of conservation of angular momentum when Net torque is zero.

Comparison with Liner momentum will help. Motion of spinning top and gyroscope, precession motion, center of percussion. Rolling Motion of a Rigid Body, The Kinetic Energy of a Rolling Body, The Angular Momentum of a Particle, The Angular Momentum of a Rolling Rigid Body, The Conservation of Angular Momentum

Homework: Ch.11; p. 350-359: Problems: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 14, 15, 16, 17, 21, 24, 25, 27, 28,29, 31, 32, 33, 34, 35, 36, 37, 39, 41, 42, 43, 44, 45, 49, 50, 54, 55, 56

Equilibrium: 5 sessions:

The Conditions for Equilibrium, The First Condition of Equilibrium. The Second Condition of Equilibrium, Cranes, Ladders, and Other Systems, Thermal Expansion, Elasticity, Free body diagrams, Linear and rotational equilibrium, Net F = 0 and net Torque about axis = zero are to necessary and sufficient conditions for equilibrium.

Direction of rotation, torque and angular momentum by RHR. All the forms of Newton’s laws will be presented. Labeling the axis of rotation is a must.

Homework: Ch.12; p. 377- 387: Problems: 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 19, 20, 21, 23, 24,25, 26, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 41, 42, 46, 47, 49, 50, 53, 54 55, 57

Simple Harmonic Motion: 6 sessions:

Hooke’s law, F = -kx, Elastic PE. For spring mass system KE + PE constant, velocity and acceleration of the mass as a function of displacement. Energy curve, simple pendulum and compound pendulum. Motion in small oscillations. Linear and rotational SHM. Displacement, velocity and acceleration as function of time. Acceleration a = -kx /m and a = -ω2x . Solution of the second order differential equation of the form d2x/dt2= -ω2x. x = C sinωt + D cosωt .

Homework: Ch.13: p.414-421 Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20 21,23, 25, 26, 27, 28, 29, 31, 35, 36, 37, 39, 41, 43, 44, 45, 46, 47, 48, 54, 56, 57, 59, 60, 61,62, 65

Gravitation: 7 sessions:

Newton’s law of universal gravitation-an inverse square law. Gravity PE U = mgh, for constant force on the earth and U =0 on the surface. For variable force Gravity U = -GmM/ r, and U at infinity is zero as a reference. Satellite motion in circular orbits. Planetary motion in elliptical orbits. Kepler’s 3 laws of planetary motion. Laws of conservation of total energy and that angular momentum. Orbital or tangential velocity, escape velocity and terminal velocity. Two body system and reduced mass.

Geocentric satellite. 3 in 1 equation: mgr = GmM/r2 = mv2 /r.

Homework: Ch 14: p. 450-457: Problems: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 19, 20, 21 22,23, 25, 26, 28, 29, 30, 31, 32, 35, 36, 37, 40, 41, 42, 43, 44, 45, 4849, 52, 54, 56, 57, 58, 61, 62, 64, 65, 66

References: Physics by Holliday and Resnick

Physics for scientists and engineers by Serway

Physics for scientists and engineers by Tippler

Hands-On Lab Activities:

1. Constant velocity of battery powered cars or wind-up toys. Constant acceleration, ticker tape timer, Plot t vs. d graph and derive t vs. v and t vs. a graph. Conversely drive t vs. v graph from the t vs. a graph and t vs. d graph from t vs. v.

2. Design the experiment to predict the landing of a projectile and verify given a ball, a ramp, a horizontal table, meter stick, a timer.

3. Circular motion in horizontal circle, conical pendulum- a toy battery powered airplane. Find the tension in the string and verify by taking required different measurement. Draw the free body diagram and analyze the forces and determine which measurements you would take. Can you calculate acceleration due to earth’s gravity by this method? Explain