Brief Description of Course Physics C: Mechanics 2007-2008 The AP Physics C Mechanics course is offered to students who have successfully completed Regents Physics. In this course students will develop the ability to: * Analyze physical phenomenon verbally, mathematically, and graphically. * Use mathematical techniques to solve real world problems. * Use experiments to gather, analyze, and intrepret data that is collected. Students will also gather information to develop and visualize relationship between variables in an experiment. * Will become familiar with Classical Mechanics and use calculus to help anlayze and solve problems. will be performed at least once per week with the expectation that the students will be able to collect, analyze, interpret, and organize this information in an appropraite manner. Students will be assessed by their problem solving (done outside of class), quizzes, and an oral presentation done at the end of the year. Unit Information Unit 1 - Vectors - Serway Chapter 3 (18 days) Content and/or Taught: : 1. Definition of vectors 2. Adding vectors 3. Breaking vectors into components 4. Define unit vectos 5. Write vectors in unit vector form 6. Adding vectors in unit vector form 1. Using trigonometry to add vectors at any angle or break vector into their components. 2. Drawing vectors to scale. 3. Using trig to convert vectors into unit vector form. Lab 1. Map Lab - Students will use a map of the United States to read and draw displacement vectors. Students will use unit vector form and polar coordinates to label displacement vectors. 2. Force Board Lab - Student will add force together to try to balance a system of 3 or more forces. Student will use mathematical techinques to predict a balancing force and then test their prediction on the force board. 1
Unit 2 - One Dimensional Motion - Serway Chapter 2 (18 days) Content and/or Taught: 1. Define kinematics and terms distance, displacement, speed, velocity, average velocity, average speed, instanteous velocity, and acceleration. 2. Use graphing techiques to analzye one dimensional motion constant velocity and acceleration. 3. Use problem solving skills to answer real world situations. 4. Use calculus (derivative and intregral) to analyze complex one dimesional motion. 5. Make the connection between the graphing of motion and derivative and integrals. 6. Analzye, graph, and problem solve free fall motion. 1. Drawing, reading, and intrepreting distancee-time, speed-time, and acceleration time graphs. Also do all of the above using the appropriate software on the computer. 2. Use algrebra to solve real world problems. 1. Constant Speed - Measure the speed of a cart on a long track moving at a constant speed. Draw distance-time and speed-time graphs for this motion. Test the students to see if they can walkat a constant speed. What must time intervals look like if a person walks at a constant speed? 2. Constant Acceleration - same as the lab above, but now set the cart to move at a constant acceleration. Also, have the students predict and test how to walk at a constant acceleration. 3. Ramp lab - The student will roll a ball down a ramp at different inclines and calculate the acceleration and speed of the balls. Student will chart and graph the information using appropriate technology. 4. Free Fall Lab - Students will drop objects off the tower at the football field. They will take measurement to calculate the acceleration of the object and compare them to "g". Students will draw graphs of the motion to see how they compare with the theory taught in lecture. Students will discuss error in measurements as part of this experiment. 2
Unit 3 - Two Dimensional Motion - Serway Chapter 5 & 6 (16 days) Content and/or Taught: 1. Motion in the xy plane. 2. Split motion into horizotnal and vertical directions. 3. Breaking vectors into components. 4. Uniform cicular motion 5. Non uniform circular motion. 1. Use the techiques of problem solving, graphing, and calculus and apply that in two directions by breaking motion into horizotnal and vertical problems. 2. Students will express terms in unit vector form. 3. Students will describe the acceleration of an object moving ina circle. 1. An Object Projected Horizontally - Students will take measurement of a launcher shooting objects horizontally. Using this data they will measure the initial speed of the projectile. In the second part of the lab, students will use the speed they calculated to try and hit a target. 2. Projectile Motion - Students will calculate the distance horizontally and vertically that an object projected at an angle will go. Using the internet they will check their results with the answers calculated. 3. Centripetal Force Lab - Using the centripetal force set up students will take measurements to see how centripetal force is related to many variables. Students will graph the information to make the connected between relationships and graphs. Unit 4 - Newton s Laws - Serway Chapter 5 & 6 (12 days) 3
Content and/or Taught: 1. Define terms force, equilibrium, mass, weight, friction. 2. Define Newton s 3 laws. 3. Calculate net forces. 4. Find the relationship between net force and acceleration. 5. Draw free body diagrams. 1. Students will draw free bosy diagrams, and learn to draw them using an appropriate scale. 2. Students, using graphical techinques, will analyze the relationship between force and acceleration according to Newton s 2nd Law. 3. Students will use vector addition techniques to find net forces. Answers may be expressed in unit vector form. 4. Students will be able to calculate the force of friction on an object at rest or sliding. Students will analyze the variables that the force of friction depends on. 1. Weight Lab - Students will analyze the relationship between weight and mass. Students will use graphical analysis to determine g from their information. 2. Atwood s Machine - Students wioll build an Atwood s Machine. They will make theorectical calcuations about the device. Tehy will test their results with the actual machine. Studetns will then use the internet to use an ideal machine. This will allow for a discussion on sources of error in an experiment. 3. Friction Lab - Students will calculate the coefficient of friction for many different surfaces and see how their data compares with accepted values. Students will discover how the fore of friction relates to certain variables. 4. Unit 5 - Applications of the 2nd Law - Serway Chapter 6 (12 days) Content and/or Taught: 1. Define centripetal forces, resistive forces, terminal velocity. 4
1. This unit is a very short unit which covers some very specific cases involving forces. It allows to the discussion of real work examples of forces. Lab 1. Show video on the banking of race tracks. Use this video as a catalyst on the calcculations of the force of friction on race tracks. 2. Show video on sky diving. This video will lead to problem solving techiques involved in object bieng under the influnece of resistive forces. Unit 6 - Work and Energy - Serway Chapter 7 (12 days) Content and/or Taught: 1. Define work, kinetic energy, conservation of energy, mechanical power. 2. Demonstrate and practice a dot product 3. Demonstrate and practice integrals 4. Use integrals to find work done by a varying force. 5. Find the work done on a spring. 6. Find the work done on a spring by a varying force. 7. Work-Energy Theorem. 8. Find the work done on a non-isolated system. 9. Show energy conservation. 10. Calculate mechanical power. 1. Students will be able to draw vector diagrams and then take a scalar dot product. Students will compare a dot product to finding a resultant. 2. Students will apply the dot product to the real world situation of calculating work done. 3. Students will be able to find the integral of simple fuctions. 4. Students will calculate the work done by a varying force using the integral. 5. Students will be able to find work done from force vs distance graphs. 6. Students will use conservation of energy to solve real world situations. 1. Power Lab - Students will use a flight of stairs to calculate the work done and power output of thier classmates. The will use their data to find relationship between different variables in the lab. 5
2. Elevator Lab - Students will use a simple motor and a pulley to lift various weight. Students will be able to compare the power output of the motor to the power needed to lift the weights. 3. Lost PE Lab - Students will use ball from different sports to calculate how much enery is lost when a ball bounces off the floor. Students are able to make predictions and then compare their hypothesis to their results. Students will use this lab to discuss different materials and their properties and how that affects its rebound property of the balls. 4. Hooke s Law - Student will measure the elongaton of different sized springs find the reltionship between force and distance stretched. Students will also calculate the spring constant for all. Unit 7 -Potential Energy - Serway Chapter 8 (14 days) Content and/or Taught: 1. Define gravitational PE, conservation of energy, elastic PE, conservative force, non-coservative force. 2. Describe forces and their relationship to energy. Gravity, friction, path dependence on energy. 1. Students will be able to use appropriate formulae to calculate the potential stored in an object lifted above the surface of the earth. 2. Students will be able to use appropriate formulae to calculate the potential stored in a stretched spring. 3. Students will use conservation of energy relationship to solve problems. This will be done using conservative and non-conservation forces. 6
Unit 8 - Linear Momentum - Serway Chapter 9 (12 days) Content and/or Taught: 1. Define and calculate momentum. 2. Relate momentum to Newton s 2nd Law. This will account using the derivative of momentum as a function of time. 3. Define conservation of momentum. Connect to other conservations laws in physics. Since momentum is a vector quantity, this will allow of the use of vector addidtion learned earlier in the course. 4. Solve problems using conservation of momentum. 5. Define impulse using integrals. 6. Define elastic, inelastic, and perfectly inelastic collisions. 7. Problem solve collision questions. 8. Analyze momentum in two dimensions. 9. Define and calculate the center of mass of a group of particles. 1. Students will be able to use a derivative of momentum to calculate a net force. 2. Students will be able to calculate the momentum of an object. 3. Students will be able to demonstrate that linear momentum is conserved in one direction. 4. Students will be able to calculate impulse applied by ingrating a force with a respect to time. 5. Students will be able to show momentum is conserved in two directions. They will use the unit vector notation taught earlier in this course. 6. Students will calculate the center of mass of and object using unit vector notation. 1. Newton Device - Using the device students will analyze conservation of momentum and energy. Why if two balls pulled back that two must bounce off after the collision? 2. Ballistic Pendulum - Using a virtual ballistic pendulum off the web, students will calculate the velocity of a projectile and them compare that to the data calculated. 3. Air Track - Students will take measurements using the air track to demonstrate linear momentum in one dimension. 4. Virtual Collisions - Students will use a web based program to demonstrate and measure collisions in two directions. 7
Unit 9 - Rotational Motion - Serway 10 (18 days) Content and/or Taught: 1. Define polar coordinates. 2. Compare and contrast polar and rectangular coordinates. 3. Define rigid object. 4. Define radian. 5. Define angular displacement, angular speed, angular acceleration. 6. Define and analyze angular kinematics. 7. Compare and contrast linear and angular motion. Demonstrate how to convert angular measurements to linear measurements. 8. Define rotational kinetic energy. 9. Compare and contrast rotational and translational kinetic energy. 10. Define moment of inertia. 11. Calculate the moment of inertia of various arrangements of particles. 12. Define torque. 13. Compare and contrast a torque and a force. 14. Analyze how a torque affects the motion of an object. 15. Analyze the motion of an object rolling. What variables affect the motion of rolling objects? 16. Define static equilibrium. 1. Students will be able to plot point using polar coordinates. 2. Students will be able to transfer from rectangulr to polar coordinates. 3. Students will be able calculate the angular distance an object rotates. 4. Students will be able to measure an angular distances using radians. 5. Students will be able to calculate angular speed. 6. Students will be able to calculate angular acceleration. 7. Students will be able to rotational kinetic energy. 8. Students will be able to calculate the moment of inertia of regular and irregular objects and be able to determine what factors affect the moment of inertia of objects. 9. Students will analyze how the moment of inertia affects the motion of rotating objects. 10. Students will be able to calculate the torque applied to objects. 11. Students will determine the relationship between torques, forces, and moment arm. 12. Students will analyze rolling motion. What variables affect how an object rolls down an incline? 13. Students will sum forces and torques to analyze objects in static equilibrium. 14. Students will solve static equilibrium problems. 1. Torque Lab - To show that the torque acting on system can be calculated by taking the product of the perpendicular distance between the point of application of an applied force and the magnitude of that force. To demonstrate that for a system to be completely at equilibrium opposite torques, as well 8
as opposite forces, must be equal. 2. Rotational Equilibrium - Balance forces and torques along a stationary beam. Calculate where certain masses should be and verify your prediction in the lab sitting. Unit 10 - Angular Momentum - Serway Chapter 11 (12 days) Content and/or Taught: 1. Define the vector cross product. 2. Define the direction of a cross product. 3. Show the cross product of unit vectors. 4. Connect a torque to a vector cross product. 5. Define angular momentum. 6. Connect angular momentum to a vector cross product. 7. Define angular momentum as it relates to angular velocity. 1. Students will be able to take a cross product of two vectors, finding magnitude and direction. 2. Students will be able to use the right hand rule to find the direction of a cross product. 3. Students will be able to take vecotr cross products using unit vector notation. 4. Students will be able to problem solve cross product questions. 5. Students will be able to find the magnitude of a torque using a cross product. 6. Students will do torque problem solving questions. 7. Students will be able to the magnitude of an abgular momentum vector using a cross product. 8. Students will do angular momentum problem solving questions. 9. Students will be able to find the direction of torques and angular momentum. 10. Students will be able to calculate the angular momentum of a rotating rigid body. 1. Use the tutorial at http://dev.physicslab.org/document.aspx?doctype=3&filename=rotarymotion_introangularmomentum.xml to experience and practice angular momentum. 2. Rotational Collisions - In this lab, we will verify the law of conservation of angular momentum by colliding a rotating disk with a stationary disk and a stationary rectangular object. In this lab, the disk and rectangular slab will rotate about their center of mass. 9
Unit 11 - SHM - Serway Chapter 15 (12 days) Content and/or Taught: 1. Define SHM. 2. Define restoring force. 3. Define amplitude, period, and frequency. 4. Analyze position vs time graphs. 5. Analyze the motion of a pendulum. 6. Analyze the motion of a mass vibrating on a spring. 7. Compare and contrast the pendulum to the vibrating mass. 8. Calculate the period of a pedulum. 1. Students will be able to recognize and define SHM. 2. Students will be able to measure and calculate the restoring force on the pendulum and a spring. 3. Students will be able measure and calculate amplitude, frequency, and period of SHM. 4. Students will be able to plot a position vs time for SHM. 5. Students will be able to derive the position time function for SHM. 6. Students will be able to calculate the period of motion for a mass vibrating on a vertical spring. 7. Students will be able to calculate the period of a pendulum. 1. Simulator Lab - Use the page http://www.hazelwood.k12.mo.us/~grichert/sciweb/shm.htm to view and analyze various SHM examples. 2. Hooke and SHM - The purpose of this lab experiment is to study the behavior of springs in static and dynamic situations. We will determine the spring constant,, for an individual spring using both Hooke s Law and the properties of an oscillating spring system. It is also possible to study the effects, if any, that amplitude has on the period of a body experiencing simple harmonic motion. 3. Pendululm - Build different pendulum to determine what factors the period of a pendulum depends on. 4. 10
Unit 12 - Gravity and Kepler - Serway Chapter 13 (10 days) Content and/or Taught: 1. Define the Universal Law of Gravity. 2. Determine the factors that affect the force of gravity between objects. What are the relationships? 3. Define and analyze Kepler s 3 Laws. 4. Connect the 3 Laws to the force of gravity. 5. Define a gravitational field. 1. Students will be able to calculate the force of gravity between point particles. 2. Students will be able to identify the variables that the force of gravity depends on and find the relationship for those variables. 3. Students will be able to add force vectors to find a net force. They will use the graphical method and unit vector notation. 4. Students will be able to determine the acceleration due to gravity on other planets and places away from the surface of the earth. 5. Students will be able to use Kepler s Laws to solve various problem sets. 6. Students will be able to determine the strength and direction of a gravitational field. 11
Student Prjoect (6 weeks mostly outside classwork). Content and/or Taught: 1. Students will be given 2 long questions to be answered. These questions are long answer questions that have numerous parts. 2. Students will answer these questions completely (showing work when appropriate). 1. Students will demonstrate the knowledge that they learned throughout the year. 2. Studetns will use the skill obtained throughout the year to answer questions about real work situations related to physics topics. 2. Students will demonstrate the proper use of techonology for the use to explore the answers to physics questions. 1. Students will be assessed by the written answers handed in. 2. Students will produce a poster that relates to the questions that were answered. 3. Students will present the answers orally to their classmates using any method they deem appropriate. They will present their poster to the class at that time and answer any questions that the class may have. Textbooks Title:Physics for Scientists and Engineers (with Physics Publisher: Brooks Cole Published Date: 21 July, 2003 Author: Raymond A. Serway Second Author: John W. Jewett Other Course Materials Material Type:Graphing Calculator TI-84+ Graphing Calculator Microsoft Office 2003 Software Package Material Type:Audiovisual Materials 12
Dell Latitude D610 Laptop w/ High Speed Internet Connection Material Type:Software Microsoft Office 2003 Software Package Websites URL:http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_ Video clip of astronauts on the moon showing free fall motion URL:http://galileo.phys.virginia.edu/classes/109N/more Projectile Motion applet used to test our theorectical calculations. URL:http://www.ph.utexas.edu/~phy-demo/resources/resou A list of various physics demonstrations. URL:http://sprott.physics.wisc.edu/demobook/intro.htm Various classroom demonstrations. URL:http://www.upscale.utoronto.ca/GeneralInterest/Har A list of physics animations used to connect lecture material to real world situations. URL:http://hyperphysics.phy-astr.gsu.edu/hbase/atwd.ht This link is used to assist in the Atwood s Machine Lab. URL:http://hyperphysics.phy-astr.gsu.edu/hbase/vect.ht The site is used for vector addition problem solving. 13