The following instructional plan is part of a GaDOE collection of Unit Frameworks, Performance Tasks, examples of Student Work, and Teacher Commentary. Many more GaDOE approved instructional plans are available by using the Search Standards feature located on GeorgiaStandards.Org. Unit One Organizer: Kinematics (Approximate Time 7 weeks) OVERVIEW: This unit introduces students to the topic of motion in one and two dimensions. All motion must be compared to a frame of reference. After learning the difference between vector and scalar quantities, the students will learn about how to describe the motion of an object in terms of its position, velocity, and acceleration. Furthermore, they will understand how to use past or present information about the motion of an object to predict future trends. The students will also learn to draw and interpret graphs of displacement vs. time, velocity vs. time, and acceleration vs. time. The law of conservation of energy is reviewed in this unit, and the concept of momentum is introduced. Gravitational acceleration is also introduced and demonstrated in this unit. The unit begins with the introduction of motion compared to a frame of reference, and finishes with a phenomenological introduction to Einstein s theory of relativity and Heisenburg s uncertainty principle reinforcing the importance of the frame of reference for an observer to interpret motion. STANDARDS ADDRESSED IN THIS UNIT Focus Standard: SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. a. Calculate average velocity, instantaneous velocity, and acceleration in a given frame of reference. b. Compare and contrast scalar and vector quantities. c. Compare graphically and algebraically the relationships among position, velocity, acceleration, and time. f. Measure and calculate two-dimensional motion (projectile and circular) by using component vectors. Supporting Standards: SP3. Students will evaluate the forms and transformations of energy. a. Analyze, evaluate, and apply the principle of conservation of energy. b. Measure and calculate the vector nature of momentum. c. Compare and contrast elastic and inelastic collisions. October 2006 Page 1 of 11
Supporting Standards (continuation) One Stop Shop For Educators SP6. The student will describe the corrections to Newtonian physics given by quantum mechanics and relativity when matter is very small, moving fast compared to the speed of light, or very large. b. Describe the Uncertainty Principle. c. Explain the differences in time, space, and mass measurements by two observers when one is in a frame of reference moving at constant velocity parallel to one of the coordinate axes of the other observer s frame of reference if the constant velocity is greater than one tenth the speed of light. Characteristics of Science Standards SCSh1. Students will evaluate the importance of curiosity, honesty, openness, and skepticism in science. a. Exhibit the above traits in their own scientific activities. b. Recognize that different explanations often can be given for the same evidence. c. Explain that further understanding of scientific problems relies on the design and execution of new experiments which may reinforce or weaken opposing explanations SCSh2. Students will use standard safety practices for all classroom laboratory and field investigations. a. Follow correct procedures for use of scientific apparatus. b. Demonstrate appropriate technique in all laboratory situations. c. Follow correct protocol for identifying and reporting safety problems and violations. SCSh3. Students will identify and investigate problems scientifically. a. Suggest reasonable hypotheses for identified problems. b. Develop procedures for solving scientific problems. c. Collect, organize and record appropriate data. d. Graphically compare and analyze data points and/or summary statistics. e. Develop reasonable conclusions based on data collected. f. Evaluate whether conclusions are reasonable by reviewing the process and checking against other available information. October 2006 Page 2 of 11
Supporting Standards (continuation) One Stop Shop For Educators SCSh4. Students will use tools and instruments for observing, measuring, and manipulating scientific equipment and materials. a. Develop and use systematic procedures for recording and organizing information. b. Use technology to produce tables and graphs. c. Use technology to develop, test, and revise experimental or mathematical models. SCSh5. Students will demonstrate the computation and estimation skills necessary for analyzing data and developing reasonable scientific explanations. a. Trace the source on any large disparity between estimated and calculated answers to problems. b. Consider possible effects of measurement errors on calculations. c. Recognize the relationship between accuracy and precision. d. Express appropriate numbers of significant figures for calculated data, using scientific notation where appropriate. e. Solve scientific problems by substituting quantitative values, using dimensional analysis and/or simple algebraic formulas as appropriate. SCSh6. Students will communicate scientific investigations and information clearly. a. Write clear, coherent laboratory reports related to scientific investigations. b. Write clear, coherent accounts of current scientific issues, including possible alternative interpretations of the data c. Use data as evidence to support scientific arguments and claims in written or oral presentations. d. Participate in group discussions of scientific investigation and current scientific issues. Nature of Science Standards SCSh7. Students will analyze how scientific knowledge is developed. b. Universal principles are discovered through observation and experimental verification. e. Testing, revising, and occasionally rejecting new and old theories never ends. SCSh8. Students will understand important features of the process of scientific inquiry. a. Scientific investigators control the conditions of their experiments in order to produce valuable data. b. Scientific researchers are expected to critically assess the quality of data including possible sources of bias in their investigations hypotheses, observations, data analyses, and interpretations. e. The ultimate goal of science is to develop an understanding of the natural universe which is free of biases. October 2006 Page 3 of 11
Reading Standard SCSh9. Students will enhance reading in all curriculum areas by: a. Reading in all curriculum areas Read technical texts related to various subject areas. c. Building vocabulary knowledge Demonstrate an understanding of contextual vocabulary in various subjects. Use content vocabulary in writing and speaking. Explore understanding of new words found in subject area texts. d. Establishing context Explore life experiences related to subject area content. Determine strategies for finding content and contextual meaning for unknown words. ENDURING UNDERSTANDINGS 1. Vector quantities have magnitude (how large the vector quantity is) and direction, while scalar quantities have magnitude only. 2. All motion must be compared to a frame of reference. 3. Many quantities in physics are rates of change of other quantities. 4. Vectors are specified by magnitude and direction while scalars are magnitude only. 5. Velocity is a change of position. 6. Acceleration is the rate at which velocity changes. 7. In the absence of air resistance, all bodies fall with the same acceleration. 8. In elastic collisions objects bounce off each other. In inelastic collisions objects stick together. The total energy before an elastic collision is equal to the total energy after an elastic collision. 9. Simultaneous measurement of the momentum and position of a sub atomic particle is not possible. 10. As an object approaches the speed of light, the observation made by an observer at rest will be different (length appears to contract and time appears to dilate) from the observation made by another observer moving with the object. 11. The slope of a distance vs. time graph is velocity. 12. The slope of a velocity vs. time graph is acceleration. 13. Projectile motion has vertical and horizontal components and is motion under the influence of gravity. 14. Momentum is a measure of motion that depends of the mass of the object and its velocity. October 2006 Page 4 of 11
ESSENTIAL QUESTIONS: 1. Why is it important to use vector quantities and not just scalar quantities to describe the motion of an object? 2. How does the resultant of two vectors change as the angle between the two changes? 3. How does the shape of graphs representing the relationship between displacement, velocity, or acceleration vs. time offer information about the motion of an object? 4. How is the motion of an object affected by the acceleration of gravity? 5. How can velocity be negative? How can acceleration be negative? 6. Why is the initial acceleration of a sprint runner important in determining who will win the race? 7. How does the direction of the acceleration affect the direction of motion? 8. How is the distance a baseball travels before hitting the ground affected by the throwing conditions? 9. How does the description of motion of an object change depending of the reference frame used to describe it? 10. How can you prove that all objects fall at the same rate? 11. Why does a projectile make a parabolic path? 12. How do the characteristics (mass and velocity) of two objects affect the results of their collision? CONCEPTS: Free fall, gravity, force, mechanics, kinematics, dynamics, translational motion, frames of reference, position, distance, displacement, speed, velocity, acceleration, gravitational acceleration, rest, trajectory, parabolic motion, position, dependent variable, independent variable, scalar, vector, momentum, elastic collision, inelastic collision, conservation of energy, relativity (time/space), slope, mass. LANGUAGE: Final velocity, initial velocity, average velocity, instantaneous velocity, coordinate axes, x-axis, y-axis, significant figures, calculate, experiment, precision measure, accuracy, SI units, describe, scientific notation, conclusion, hypothesis, data, contrast, compare, variable, infer, analyze, predict, interpret, rate of change. October 2006 Page 5 of 11
EVIDENCE OF LEARNING: By the conclusion of this unit, students should be able to demonstrate the following competencies: Culminating Activity: Space Race The idea for this activity is taken from an Article Note written by Michael Vinson in The Physics Teacher Newsletter. Name: Culminating Performance Assessment Traveling in Outer Space Based on Michael Vinson s Space Race: A Game of Physics Adventure Instructions: Is the year 2345 and you are the pilot of the news space rescue ship stationed on Earth. Your base has received a distress signal from a group of miners on the asteroid 2004 XP14. There has been an accident and you must go there and bring back the injured miner. You must pilot your ship to their location, but need to be extremely careful as there are a number of asteroids between you and the miners. (See Interstellar Map). To pilot your ship, you must follow the laws of physics. The rules are: 1. You begin with zero velocity. 2. Each time that you move represents 1 minute and each square in your graph represent 10 km. 3. Your ship is capable of an acceleration of 10 km/min 2 every time that you accelerate or decelerate using your engines. 4. You can accelerate along the X direction only, the Y direction only, or both (the diagonal). 5. Your starting location is the space station orbiting Earth. To keep track of your movements you need to fill out your flying log (see Flying Log). Your teacher would further demonstrate for you how you can fly your space ship. Pay attention because if you collide with an asteroid on your way to rescue the miners, you will die, and so will the injured miner. Completion Instructions: After successfully completing your mission write a short report describing how you managed to accomplish your mission. You can talk about things that you have learned in this unit, and those lessons allowed you to rescue the injure miner. Attach your interstellar map and flying log to your reflection piece and turn them to your teacher. Date: October 2006 Page 6 of 11
Flying Log Name: 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 Turn Initial Position Initial Velocity Date X acceleration Y acceleration Final Position Final Velocity October 2006 Page 7 of 11
Interstellar Map You Miners location (0, 0) October 2006 Page 8 of 11
MISCONCEPTIONS AND PROPER CONCEPTIONS MISCONCEPTIONS Two objects traveling side-by-side must have the same speed. Velocity is always positive. Acceleration and velocity travel in the same direction. Velocity is classified as a force. If velocity is zero, then the acceleration must be zero also. A positive slope for a negative velocity indicates that the object is speeding up. The position vs. time graph and velocity vs. time graph plot the path of an object. PROPER CONCEPTIONS The objects traveling side-by-side do note always have the same speed. An example of this is two objects traveling in a circle can be side-by-side yet traveling at different speeds. Velocity is a vector quantity, the negative or positive sign of the velocity is related to the direction of motion. Acceleration and velocity not always point in the same direction. The vectors themselves do not travel; they describe a rate of change in a direction. An example of acceleration and velocity in different directions is when an object is decelerating. An object that is decelerating (negative acceleration) has acceleration in the opposite direction of the velocity. Velocity is not a force. Force is measured in Newtons (N), and velocity is measured in m/s (distance/ time) When an object changes direction by 180º will reach an instant velocity of zero but will also experience acceleration in the opposite direction of its original motion. An example of this is when an object is thrown upward and reaches its maximum high, its velocity is zero. However, it is being accelerated downwards with an acceleration of 9.8m /s 2. In a graph of velocity vs. time, the positive slope of a negative velocity implies that the object is slowing down. The position vs. time graph indicates the velocity of an object and its distance from the origin, not its path. The velocity vs. time graph indicates the acceleration of an object. October 2006 Page 9 of 11
MISCONCEPTIONS AND PROPER CONCEPTIONS (continuation) MISCONCEPTIONS Heavier objects fall faster than lighter objects. The acceleration of an object falling downward depends upon its mass. Acceleration and velocity are the same. Freely falling bodies only move downward. (ex. satellites) Gravity does not exist in a vacuum. Gravity is only present when objects are falling. When an object is traveling with a horizontal velocity, and is thrown upward, the path the object follows is along a line. PROPER CONCEPTIONS All objects fall at the same rate neglecting air resistance. The acceleration of a falling object is independent of mass. The acceleration of a falling object depends of the magnitude of the gravitational acceleration acting upon it. Acceleration is the rate of change of velocity. Freely falling bodies such as a satellite fall toward the earth, creating a circular orbit rather than falling downward. Gravitational force is caused by mass. Planets, stars and even you produce gravitational fields. Gravity is always present. The acceleration of gravity is the result of the gravitational force exerted by the presence of mass. When an object is traveling with a horizontal velocity, and is thrown upward, the object actually makes a parabolic path. October 2006 Page 10 of 11
TASKS The collection of the following tasks represents the level of depth, rigor and complexity expected of all students to demonstrate evidence of learning. Task: Description: Discussion, Suggestions for use: Possible Solution : SAMPLE OF STUDENT WORK October 2006 Page 11 of 11