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Transcript
Unit 6: Circular Motion and Torque Lesson 1 - Circular Motion READ Chapter 9 Take NOTES Concept Development 9-2 Problems Solving 6-1 1.1 Web Walk - Understanding and Applying Circular Motion 1.2 Lab Activity – Going In Circles In class 1.3 Online Problem Solving 1.4 Quiz – Circular Motion Lesson 2 - Center of Gravity READ 10 Take NOTES Concept Development 10-1 Problems Solving 6-2 2.1 Lab Activity - Center of Gravity 2.2 Practice Online Quiz - Center of Gravity 2.3 Center of Gravity Demonstrations and Review 2.4 Quiz – Center of Gravity Lesson 3 - Rotational Mechanics READ Chapter 11 Take NOTES Concept Development 11-1 and 11-2 Problems Solving 6-3 3.1 Virtual Lab – Torque 3.2 Lab Activity – Rotational Derby 3.3 Online Concept/Problem Review 3.4 Lesson Wrap Up – Physics Thoughts for Discussion 3.5 Knowledge Check Lesson 4 - Unit Assessment Review Data sheet Take unit test By the end of this unit, you will be able to: distinguish between rotate and revolve distinguish between linear and rotational speed describe the velocity of an object moving in uniform circular motion at any point in that motion demonstrate that the acceleration of an object may result in a change in direction with no change in speed define centripetal acceleration define centripetal force explain why centrifugal force is “fictitious” solve problems involving: centripetal force, centripetal acceleration, speed, radius of revolution, period of revolution, object's mass analyze and describe the forces acting on common objects in circular motion define center of gravity , give examples of how center of gravity affects objects and people, and describe how to find its location of irregularly shaped objects distinguish between stable, unstable, and neutral equilibrium define torque and identify situations involving the application of torque solve problems involving: torque, force, lever arm define angular velocity define angular acceleration define angular momentum and describe the conditions under which it changes and remains the same define rotational inertia and describe what rotational inertia depends on Our scenario for this unit will be to apply the kinematics concepts and motion principles will be to the motion of objects in circles and then extended to analyze the motion of such objects as roller coaster cars, a football player making a circular turn, and a planet orbiting the sun. We will see that the beauty and power of physics lies in the fact that a few simple concepts and principles can be used to explain the mechanics of everyday situations. When riding an amusement park ride, you feel as if a force is pushing you against the side or pulling you in a direction away from the center. This is commonly called “centrifugal force” (a fictitious force), however; it is actually the result of inertia that causes you to maintain the motion in a straight line path. The effects of this “fictitious force” are everywhere. For example, when you punch the accelerator of your car, you feel as if you are being pushed back into the seat, but there is no force pushing you backward. You feel pushed backward due to inertia because you are in your original state of motion and the car is accelerating. Circular motion is similar to linear motion except that the object is rotating rather than moving in a straight line. The concepts and variables of linear (translational) motion have analogs in rotational motion. The important concept in circular motion is that while you are traveling in a circular path at a constant speed you are accelerating. This acceleration is called centripetal acceleration and points toward the center. The force keeping an object in a circular path is called centripetal force or the center seeking force. Some of the questions that will be answered in this unit are: Why do quarterbacks spiral the ball when they throw a pass? Why are the starting positions on a racetrack staggered? Why do tall chimneys break near the middle as they topple? How do you stay in amusement park rides that go upside down? Why are curved roadways/racetracks banked? Why are there so many pieces of truck tire tread lying on the interstate highways? How are ice skaters able to spin so fast? Why are divers, cheerleaders, and/or gymnasts able to do more rotations in the tuck position than the layout position? Why is it difficult to open a door when you push on the side near the hinges? Lesson 1: Circular Motion In this lesson, our study will begin with the development of kinematic and dynamic ideas can be used to describe and explain the motion of objects in circles. Newton 's laws of motion and kinematics principles are applied to describe and explain the motion of objects moving in circles; specific applications are made to roller coasters and athletics. Check it Out! Hand tossed or regular crust? Ride more merry-go-rounds! DVDs! Does it rotate or revolve? A football spirals when released by the quarterback – why? A popular demonstration of many physics teachers is to swing a bucket of water around in a vertical circle fast enough so that the water doesn’t spill out when the pail is upside down. How is this possible? Circular motion is everywhere in our real lives from pizza spinning and rotating restaurants to skaters and divers to amusement park rides and NASCAR racing to throwing a shot put at a track meet. How are these events related to each other? 6.1.1 Understanding and Applying Circular Motion Web Walk It is important to go to the sites in order and follow the directions as given. If there is a related assignment, it will be clearly indicated. You may want to take notes as you move along the Web Walk. Go to http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Circular%20M otion/circular_motion_notes. View the powerpoint and take notes. Go to http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l1e.html (The Physics Classroom) “Applications of Circular Motion” for the connection of circular motion to the Laws of Motion. Note the suggested method for solving circular motion problems. You will be expected to solve circular motion problems and the method prescribed above will serve you well as you approach circular motion problems. “Check Your Understanding” is good practice in solving circular motion problems. Click “next” to go to Amusement Park Physics applications. Pay careful attention to the animations and sample problems. “Check Your Understanding” is good practice in solving circular motion problems. Click “next” to go Athletics and the applications of circular motion. Note how the sample problems are done and do the “Check You Understanding.” Respond to the following questions and submit your repsonses to your Notebook. 1. Many pizza places offer “hand tossed” pizza. Traditionally pizza makers form the crust by throwing the dough up in the air and spinning it. Why does this make the pizza crust larger? 2. An amusement park ride spins riders around on swings attached by cables from above. What causes the swings to move away from the center of the ride when the center column begins to turn? 3. Why would you weigh slightly less at the earth's equator than you would at the poles? 4. A girl at the state fair is spinning a ball attached to a string in a vertical circle. Is the force applied by the string greater than or equal to the weight of the ball at the bottom of the ball's path? 6.1.2 Lab Activity - Going In Circles Purpose: How does radius, mass and period influence centripetal force? Safety Note: Safety concerns are minimal; however, common sense should prevail while doing this activity. Eye protection is recommended. Materials : Ball point pen tube, 2 m of string, paper/plastic cup, paper clip, 30 metal washers, stop watch, tape, meter stick, candy (wrapped is better – in case you spill, you can still eat it without invoking the 5 second rule!) Submit your completed report to your lab notebook. Include the data collected, the graphs, and the interpretations/analysis. 6.1.3 Online Problem Solving Go to hyperphysics.phy-astr.gsu.edu/hbase/circ.html Circular Motion – Centripetal Acceleration Click “Calculation” and do some calculations for practice. Show at least 1 in your notebook. Click “Discussion of concept” for a review of centripetal force and centripetal acceleration. While you are on this page, click the “centripetal acceleration” link and practice a few centripetal acceleration calculations. When you have tried a few problems, click “go back” (lower right corner). Click Centripetal force on banked highway curve Study the problem and practice a few sample centripetal force calculations. do some calculations for practice. Show at least 1 in your notebook. Go to id.mind.net/~zona/mstm/physics/mechanics/curvedMotion/circularMotion /problems/cm0.htm (Zona Land Physics) Circular Motion Problems and solve problems 11, 14, 16, 17, 18, and 20. Note: You can use the help button as a self check. Show your work for problems 14,16, 18 and 20 in your notebook. Go to dept.physics.upenn.edu/courses/gladney/mathphys/hmwrk_week_4.html# prob_4_5 and solve problem 4.5 (PSYW). Submit your solution, with the work shown, to your notebook. 6.1.4 Quiz - Circular Motion To summarize, an object in uniform circular motion experiences an inward net force. This inward force is sometimes referred to as a centripetal force, where "centripetal" describes its direction. Without this centripetal force, an object could never alter its direction. The fact that the centripetal force is directed perpendicular to the tangential velocity means that the force can alter the direction of the object's velocity vector without altering its magnitude. Lesson 2: Center of Gravity In this lesson the following questions will be considered: Why doesn't the Leaning Tower of Pisa fall over? Why does the Hummer have such incredible maneuverability? How do tightrope walkers keep their balance? Why do they carry such long poles? How does learning physics help high jumpers set records? 6.2.1 Center of Gravity Lab Activity How were the massive trilithon stones of Stonehenge ever put into place? A Nova team investigated one possible method--shifting the stone's center of gravity to make it stand upright. Read the article, then find out how to recreate the Nova experiment using a cardboard model. Secrets of Lost Empires I—Stonehenge Ancient structures may generate awe and provide information about the people who built them, but they leave many questions unanswered: How were they constructed? What technologies were available to the builders? What tools did they use? Stonehenge Stonehenge distinctive feature of this stone site are the trilithons, which consist of two upright stones topped by a horizontal lintel stone. In this program, the NOVA team considers how to transport and raise the massive stones, as well as how to place the lintel stone on top. By comparing different strategies and adapting ramps, levers, and other tools that might have been available to the ancient builders, the team works to meet the challenge. http://www.pbs.org/wgbh/nova/teachers/activities/2403_sle1ston.html For Activity 6.2.1 "The Great Trilithion Balancing Act", you will need the following: student handout (print from the web site), string, 15 cm (6 in.) long, washer, cardboard (about .1 mm, or 1/32 in., thick), scissors, several large paper clips, pencil with flat eraser, hole puncher, and a ruler. Submit Answers to your Notebook 6.2.2 Center of Gravity Practice Quiz Go to www.batesville.k12.in.us/physics/PhyNet/Mechanics/CenterOfMass/Cen_Mass_Quiz.ht ml click on the practice quiz and answer the questions for a review of Center of gravity. Submit your score to your Notebook 6.2.3 Center of Gravity Demonstrations and Review Join me for demonstrations and discussion of center of gravity, center of mass, and toppling. During the demonstrations and discussion consider the following questions to ponder: Why is the middle or aisle seat in a bus or airplane the most comfortable when the road or air is bumpy? How is a baseball bat standing on its handle or on its head be likened to the different centers of gravity in women and men? If you are sitting in a chair, why is it not possible to stand up without putting your feet under the chair? Why can't you touch your toes if you are standing with your heels against the wall? You are standing on the edge of a cliff and a friend nudges you from behind. Describe the reaction of your body in terms of motion and center of gravity. At the conclusion of the Center of Gravity demonstrations, complete the Question/s to ponder and submit your answers to your notebook. 6.2.4 Quiz – Center of Gravity Check it Out! At this point you should have an understanding of and be able to apply the concepts of toppling, stability, center of gravity, and center of mass to many everyday events. The center of gravity and the center of mass are important concepts in the study of circular motion. They not only are applicable to everyday situations, but also are a key to understanding rotational mechanics, the next lesson in this unit. Lesson 3: Rotational Mechanics Everyone enjoys watching an ice skater finishing a performance with a spin. The impressive skill demonstrated along with some interesting physics makes for quite a sight! Skaters may not understand the physics involved, but they are very good at applying it! Rotational dynamics (and kinematics!) concepts and variables are very similar to translational (linear) dynamics (and kinematics!). In this lesson we will consider the dynamic variables that are analogs to linear dynamics quantities. Some questions to ponder during this lesson are: Why do quarterbacks spiral the ball when they throw it? Why are there so many pieces of truck tire tread lying on the interstate highways? How are ice skaters able to spin so fast? Why are divers, cheerleaders, and/or gymnasts able to do more rotations in the tuck position than the layout position? 6.3.1 Virtual Lab – Torque Purpose: What is the relationship between forces and distances from the fulcrum for a balanced see-saw? Discussion: An object at rest is in equilibrium and the sum of the forces acting on it is zero. Because the object has no rotation, the sum of the torques is zero. When a force causes an object to start turning or rotating, a nonzero net torque is present. Suppose that you are an animal trainer and you want to balance a 600 kg gorilla on a see-saw using only your own body weight. If your mass is 50 kg and the gorilla is 2.0 m from the fulcrum, how far from the fulcrum must you sit on the other side to balance the gorilla? OBTAIN LAB FROM INSTRUCTOR 6.3.2 Rotational Derby Lab Purpose: How does the rotational inertia affect the rate of rotation? OBTAIN LAB FROM INSTRUCTOR 6.3.3 Online Concept/Problem Review Go to btc.montana.edu/olympics/physbio/biomechanics/cam02.html ( University of Montana ) Conservation of Angular Momentum. Review the animations. Go to www.nasaexplores.com/show_912_student_st.php?id=04021991438 (NASA Explores) Angular Momentum. Solve the problems. Click “Go to teacher sheet” and scroll down to check your answers. Go to www.batesville.k12.in.us/physics/PhyNet/Mechanics/RotMechanics/Rot_ Mech_Quiz.html Practice Quiz. Do the practice quiz and submit your score to your notebook. 6.3.4 Lesson Wrap Up – Physics Thoughts for Discussion Answer the questions and Respond to at least 2 other persons with a thoughtful comment to your notebook 1. Which will roll with a greater acceleration down an incline, a can filled with water or a can full of frozen water? 2. A basketball player wishes to balance a ball on his/her finger tip. Will he/she be more successful with a spinning ball or a stationary ball? What physics supports your answer? 3. Why is it incorrect to say that when a cheerleader executes a somersault and pulls her arms and legs inward, her angular momentum increased? Knowledge Check Figure Skater Spins Everyone has seen the classic spin in figure skating, where the skater draws her arms and a leg in and speeds up tremendously. This is the result of conservation of angular momentum : as the skater reduces her rotational inertia by pulling her arms and leg in, her rotation speed must increase to maintain constant angular momentum. Angular momentum conservation plays an important role in all figure skating routines. Watch the video clips of skaters spinning. Why do they spin faster when they pull their arms inward? www.bsharp.org/physics/stuff/skater.html The Physics of Everyday Stuff Lesson 4: Unit Wrap Up Unit Assessment