Unit Lesson Plan – Dynamics 2D Teacher: Grade: <Teacher> Time Frame: 11, 12 School: Subject: AP Physics C Standards: <School> PSI AP Physics C NGSS DCI: 8 days HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration. HS-PS2-4. Use mathematical representations of Newton’s Law of Gravitation to describe and predict the gravitational and electrostatic forces between objects. B. Newton’s laws of motion 1. Static equilibrium (first law) Students should be able to analyze situations in which a particle remains at rest, or moves with constant velocity, under the influence of several forces. 2. Dynamics of a single particle (second law) a) Students should understand the relation between the force that acts on an object and the resulting change in the object’s velocity, so they can: (1) Calculate, for an object moving in one dimension, the velocity change that results when a constant force F acts over a specified time interval. (2) Calculate, for an object moving in one dimension, the velocity change that results when a force F(t) acts over a specified time interval. (3) Determine, for an object moving in a plane whose velocity vector undergoes a specified change over a specified time interval, the average force that acted on the object. b) Students should understand how Newton’s Second Law, , applies to an object subject to forces such as gravity, the pull of strings, or contact forces, so they can: Â = F Fnet = ma (1) Draw a well-labeled, free-body diagram showing all real forces that act on the object. (2) Write down the vector equation that results from applying Newton’s Second Law to the object, and take components of this equation along appropriate axes. c) Students should be able to analyze situations in which an object moves with specified acceleration under the influence of one or more forces so they can determine the magnitude and direction of the net force, or of one of the forces that makes up the net force, such as motion up or down with constant acceleration d) Students should understand the significance of the coefficient of friction, so they can: (1) Write down the relationship between the normal and frictional forces on a surface. (2) Analyze situations in which an object moves along a rough inclined plane or horizontal surface. (3) Analyze under what circumstances an object will start to slip, or Note that this exact Smart Notebook presentation has not been used in the classroom, although all of the material has. The pacing below is approximate based on a 40-45 minute class period. Feel free to adjust as necessary and please provide your feedback! to calculate the magnitude of the force of static friction. e) Students should understand the effect of drag forces on the motion of an object, so they can: (1) Find the terminal velocity of an object moving vertically under the influence of a retarding force dependent on velocity. (2) Describe qualitatively, with the aid of graphs, the acceleration, velocity, and displacement of such a particle when it is released from rest or is projected vertically with specified initial velocity. (3) Use Newton's Second Law to write a differential equation for the velocity of the object as a function of time. (4) Use the method of separation of variables to derive the equation for the velocity as a function of time from the differential equation that follows from Newton's Second Law. (5) Derive an expression for the acceleration as a function of time for an object falling under the influence of drag forces. 3. Systems of two or more objects (third law) a) Students should understand Newton’s Third Law so that, for a given system, they can identify the force pairs and the objects on which they act, and state the magnitude and direction of each force. b) Students should be able to apply Newton’s Third Law in analyzing the force of contact between two objects that accelerate together along a horizontal or vertical line, or between two surfaces that slide across one another. c) Students should know that the tension is constant in a light string that passes over a massless pulley and should be able to use this fact in analyzing the motion of a system of two objects joined by a string. d) Students should be able to solve problems in which application of Newton’s laws leads to two or three simultaneous linear equations involving unknown forces or accelerations. Essential Questions (What questions will the student be able to answer as a result of the instruction?) 1. How can an object be made to accelerate? 2. How do forces interact? 3. How do objects respond to multiple forces acting on them? 4. How can you use Newton’s Laws of Motion to predict the behavior of objects? 5. How can free body or force diagrams be used to analyze interactions between objects? 6. Why can’t an object exert a force on itself? 7. How can resistive forces change when an object is in motion? Knowledge & Skills (What skills are needed to achieve the desired results?) By the end of this unit, students will know: How to apply the concept of inertia to determine the motion of an object experiencing a net force and zero net force. How to solve problems specifically by first sketching the setup, drawing a free body By the end of this unit, students will be able to: Describe inertia using Newton’s First Law. Relate force, mass and acceleration using Newton’s Second Law. Solve problems in 1 and 2 dimensions using diagram, determining the forces present, aligning coordinate axes, solving the equation for the variable needed, inserting numbers into the equation, and finally performing calculations with a scientific calculator. Newton’s Second Law. Describe inertial reference frames. Differentiate between weight and mass. Describe weight as a force in terms of mass and gravitational acceleration. Describe the normal force and understand the conditions in which it exists. How apply Newton’s Third Law (for every action force, there is an equal and opposite reaction force) to determine action/reaction pairs. Identify a reaction force if given an action force. Determine whether a frictional force is kinetic (moving) or static (not moving). How to identify when friction must be considered in a problem and when it can be ignored, determine the type of friction present, and the point at which the static friction is overcome to result in kinetic friction. Solve problems in 1 and 2 dimensions involving static and kinetic friction. Identify and solve for tension force. Draw free body diagrams in 1 and 2 dimensions. How to identify all the different types of force present in a problem. They will draw the relative magnitudes and directions of the forces on a free body diagram and note the direction of acceleration Solve problems in 1 and 2 dimensions involving multiple forces and accelerations not restricted to one axis of motion. How to, after drawing a free body diagram, students will apply Newton’s Second Law to a problem, determining the net force acting on an object. They will solve for net forces and forces specific to the problem. How to identify the following forces and illustrate their relative magnitudes and directions when problem solving: How to determine the weight of objects in settings with vertical accelerations and determine the difference between true weight and apparent weight (normal force). o Applied Force o Normal Force o Weight (Gravitational Force) o Apparent Weight o Tension o Friction (Kinetic and Static) How to solve air resistance problems Assessment (What is acceptable evidence to show desired results (rubrics, exam, etc.)? Attach Copy During the Smart Notebook lesson designed to introduce concepts, students will be continually questioned on these concepts using a combination of class work/homework questions and the SMART Response system. Classwork and Homework questions will be discussed as a class and misconceptions will be addressed by the teacher prior to the formal evaluations listed below. Dynamics 2D Test Note that this exact Smart Notebook presentation has not been used in the classroom, although all of the material has. The pacing below is approximate based on a 40-45 minute class period. Feel free to adjust as necessary and please provide your feedback! Other assessments on the NJCTL website are optional and can be used as needed. (What is the sequence of activities, learning experiences, etc, that will lead to desired results (the plan)? Topic Classwork Homework** 1 Review of 1D Dynamics & Resolving Forces Presentation slides 1-71 MC 1 - 10 & FR 1 - 4 2 Two Dimensional Forces Presentation slides 72-135 MC 11 - 20 & FR 11, 12, 13, 14 3 Static Equilibrium and Tension Force Presentation slides 136168 Extra AP problems*** & MC 20-30 4 Air resistance Separate presentation slides 123-130 MC 31-40 & FR 6 - 10 5 Air Resistance Lab Lab Finish Lab 6 Review MC Review HW: FR 5 & Extra AP Problems 7 Review & Quiz Quiz on AP Problems & Review for test Study for test 8 Dynamics 2D Test Test Review next unit Day * It may not be possible to complete labs in the order stated due to lab schedules. Other labs on the NJCTL website are option and can be used as needed. **HW Problems are currently not scaffolded from least to most difficult, but are instead listed in order of topic. Teacher should pay special attention at the end of each class period when assigning HW so that only problems related to the topic that was taught are being assigned. *** Students should be given 5-10 AP problems from previous years’ AP exams regarding dynamics.