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Final project Newtonian Physics SME 401 Chris Armour Dominic Held SME 401 Our final project covers Newtonian physics. We decided to cover this topic for our final project because it is covered in EVERY high school physics class. This is usually the very first topic that is covered in any introductory class. It is the basis for all other physics and we felt it would be beneficial for ourselves as future teachers to investigate this topic since we will eventually one day be teaching it. This lab set is designed for an introductory or AP level high school physics class. The students will know relatively little about physics before we teach this unit. The labs are set up so that as you go through the unit and introduce a new topic in Newtonian physics then there is a lab for that topic. Therefore, these labs are not designed to be used as a unit in themselves, but are designed to be used over the course of a semester or even a year depending on how fast the class is moving and what topics the class talks about. Also, other activities can be used throughout the Newtonian Physics section of the class, but we felt like these were important or especially good labs for the students to perform. In researching these labs, most of them were labs that we either had while in high school, labs we have seen or have done in college, plus one found online. Most physics labs are universally known to be good and usually these labs are performed throughout most physics classes. Since most of the labs were ones we had experienced at some point, so we knew they were good experiments. Therefore, when we tested the labs to obtain sample data we had no trouble and did not really need to change very much of the labs procedure. The lab we found online was the one on projectile motion. This lab looked like it was high-quality so we decided to test it. Online it was primarily given as a demonstration so I adapted the ideas from the demonstration and applied them to create a 2 day lab for the students. When tested it worked reasonably well at showing projectile motion. This is a hard area in getting good experiments for students to conduct and I think I made a reasonably good experiment with very inexpensive materials. The only lab that might be difficult to recreate exactly in a classroom is the Force of Gravity lab. The apparatus is a little high tech and some classrooms might not be. Fortunately, you can adjust the lab to fit what you do have in the classroom, which is addressed in the teacher materials for that lab. In assessing the students, since this is not a short unit, and since the topic will be split up into smaller units each with its own exam, each lab will be assessed separately. For the most part the assessments will be done with follow-up questions and worksheets at the end of each lab. The labs will mostly be graded on these questions as well as finished data tables, complete graphs and calculations. The only exception is the mouse trap car lab. This lab will partly be assessed on how far the car goes compared to the rest of the class but will mainly be graded on a follow-up essay the students write. This essay is described further in the student materials for that lab. 2 Goals and Objectives Introduce the concepts of the semester/year. Spark students’ interest in physics and science in general. Give real experiences of Newton’s three laws. Have students reflect on observations. Incorporate velocity and acceleration into activities to help present their relation. Take measurements of the gravitational force on a mass. Plot data in a graph manually using graph paper and electronically using computer software. Gain experience interpreting graphs. Show how an object’s mass distribution affects angular momentum. Provide an opportunity for students to solve a problem incorporating the concepts of the unit with their creativity. 3 Activities/Table of Contents: Pages: 5–7 Magic of Physics Demonstration- This demonstration should be given at the beginning of the semester, possibly the first day. Topics that will be discussed throughout the semester will be introduced in an exciting way. (Time duration 1 day) 8 – 14 Motion Maps: Toy Car Lab- Using a motorized car, students will take measurements and calculate the car’s velocity in this activity. A long room or hallway will be necessary depending on the speed of the car. Students will then use computer software to plot distance vs. time and apply a best fit line to the plot. The slope of this line will equal the velocity of the car. (Time duration 2 days) 15 – 23 Force of Gravity (Measurement of g) - This activity is done to experimentally find the force of gravity of the earth. By timing how long a ball takes to fall a measured distance we can solve use a kinematic equation to solve for g. The goal of this lab is to show that gravity is caused by the mass of an object (the earth). (Time duration 1 day) 24 – 34 Projectile Motion (Motion in 2-D) - This lab demonstrates projectile motion by looking at how a dart is shot from a dart gun. Different parameters are changed like the angle the dart is shot from, the height above the ground the dart is shot from, and the mass of the dart to investigate how these will affect the horizontal distance the dart flies. (Time duration 2 days) 35 – 43 Rolling Cylinders and Angular Momentum- This activity displays the conversion of potential energy into kinetic energy of motion and kinetic energy of rotation through the use of ramps (inclines), balls and cylinders. It is a good introduction to rotational energy after inclines and pendulums have been discussed. (Time duration 2 days) 44 – 49 Mouse Trap Car – This activity would be preformed at the end of the whole Newtonian physics unit. The basic premise of this activity is to get the students to use all the knowledge they have gained throughout the unit/semester/year to build a mouse trap car. Not only do they have to build a working car but they need to write a paper that explains all the physics that is involved in their car. This is a good project to wrap up this topic. (Time duration 2 days) 4 Teacher Materials: Magic of Physics Demonstration (Time duration 1 day) Overview: This demonstration is dependent on the disposition of the presenter. You could really get into character with a cape, hat, and wand, or you could leave the magic part out and just give an interesting demonstration. Either way, you will be demonstrating topics that will be discussed throughout the semester. I chose to leave the depth of the magic show up to the presenter and have just given an outline of possible steps to follow. Teacher and Student Objectives: Excite students about physics and science. Introduce some of the topics that will be covered throughout the course. Begin thinking about the physics in our everyday lives. Who’s Being Taught? This demonstration is designed for an introductory high school physics class consisting of juniors and seniors. The table cloth and bed of cups tricks could be explained to younger students, but the rolling uphill and laser trick require a more experienced audience in order to give an explanation. Strengths of Exercise: 1. Visual performance that shows science can be fun. 2. Introduces the course in an exciting way; who wants to sit through another class reading rules and regulations on the first day of school? 3. The table cloth trick will lead directly into Newton’s laws. How to Assess: After the demonstration, ask for volunteers to explain each trick. Give an explanation to the aspects that the students have trouble explaining in terms of physics. What to Look Out For: Make sure that all of the demonstrations are setup in areas that will be in view of all of the students. As students enter your classroom, be mindful that they do not disturb the magic tricks. Make sure you have plenty of room when you pull out the table cloth. You do not want to hit a student when you pull it. All tricks should be tested and you should be confident they will work during the demonstration. Be sure to give an explanation of each magic trick. Technical Information: Table Cloth Trick: The dishes stay on the table because of Newton’s first law: A body at rest stays at rest unless acted upon by a force. Because the table cloth is so thin and slick, the force on the dishes when the tablecloth is removed is negligible. 5 Reflected Light Trick: The light is totally reflected by the mirrors, so the angle of incidence to the mirror is equal to the angle of reflection of the light. When the light from the laser is refracted by the grating, the interference pattern is projected on a screen. The interference pattern is caused by constructive and deconstructive interference brought about by the diffraction of the light. Constructive interference happens when wave the crest of waves add and deconstructive interference occurs when wave crests cancel each other out. Bed of Cups Trick: Pressure is equal to a force divided by an area. The area of a single cup is small so the force on the cup is large. The area of many cups is much larger so the force on the cups is much smaller. P = F/A Rolling Uphill Trick: The incline of the cones is greater than the incline of the meter sticks. As the meter sticks widen the center of mass of the cones is lower at the top of the slight incline made by the sticks. This is why the cones appear to roll upward. Materials: Table Cloth Trick: Heavy dishes with a low center of gravity Thin tablecloth made of slick material (nylon) Large flat surface at the front of the class. Reflected and Refracted Light Trick: Laser Mirrors Diffraction Grating Bed of Cups Trick: 30 cups 2 Trays or sheets of wood Rolling Uphill Trick: 2 Party Hats Tape 2 Meter Sticks Books Procedure: Table Cloth Trick: Before Class: 1. Set up dishes on top of the table cloth. 2. Make sure there is enough room to pull the table cloth out. During Class: 3. Make sure this is no students sitting close behind you. 4. Say the magic words to keep the dishes on the table. 5. With one quick motion pull the table cloth down and away. 6 Reflected Light Trick: Before Class: 1. Setup the laser and the mirrors so that the light is reflected from mirror to mirror and finally passing through the diffraction grating onto a screen. 2. Place something in front of the beam so it is blocked. During Class: 3. Inform the class that you are going to create a magical image on the screen. 4. Wave your wand and say the magic words while nonchalantly knocking aside the object that is blocking the laser beam. Bed of Cups Trick: Before Class: 1. Set up approximately 25 cups in a grid on a tray. 2. The cups should be pointed down. 3. Place the tray of cups and empty tray together behind the front desk. 4. Place 3 or 4 cups on your desk or another easy to reach area. During Class: 5. Take a single cup and ask the class what will happen if you step on it. 6. Take two or three cups and ask the class what will happen if you step on them. 7. Ask the class how many cups would be needed to hold you up. 8. Bring out the tray with cups and the empty tray. 9. Place the tray of cups on the ground and the empty tray on the cups. 10. Say the magic words and step on the tray. Rolling Uphill Trick: Before Class: 1. Tape together two identical cone shaped party hats. 2. Build a slight incline with the meter sticks and books. 3. The meter sticks should be close together at the bottom of the incline and wider at the top. During Class: 4. Tell the class that you will make the connected cones roll uphill. 5. Say the magic words and release the cones at the bottom of the incline. Follow up: An introduction to Newton’s laws should follow this demonstration. Be sure to reference the table cloth trick when you talk about Newton’s 1st law. If this demonstration is used on the first day of school, an introduction to the class procedure could be incorporated into the show or given before or after the demonstration. Resources: Inspired by Merle Heideman, Fall 2006. 7 Motion Maps: Toy Car Lab Introduction: In this activity you will measure the distance traveled by a motorized car over several intervals of time. As we have discussed in class, velocity is the change in position of object over a period of time, or v = ∆x / s. On the first day you will collect data of your car. On the second day, you will use the data you collected on the first day to plot distance vs. time using computer software. By finding the slope of the best fit line to your data, you will have calculated the velocity of your car. Objectives: Take measurements of the distance traveled by a toy car over a period of time. Use computer software to make a graph of your data. Calculate the velocity of the car by finding the slope of your graph. Materials: Day 1: Toy Car Stop watch Dry Erase Marker Tape Measure Day 2: Data from day 1 Computer with graphing utility and printing capabilities Procedure: Day 1: 1. Find a long area that is free from obstructions. 2. Draw a starting line. 3. Start the car about a meter before the starting line. 4. When the front of the car reaches the starting line start the stopwatch. 5. Mark the front of the car every two seconds until you have six marks. 6. Measure the distance to each mark and record in the table provided. 7. Repeat for a second trial; don’t forget to erase the first marks. 8. Average the distances of the two trials and enter into the table. Day 2: 1. Each student will make their own graph. 2. Open Excel and create a new workbook. 8 3. In column A, enter the corresponding seconds to each distance. 4. In column B, enter the average distances. 5. Highlight the data in both columns. 6. Select “insert” from the tool bar and then select “chart.” 7. Select “xy (scatter)” and the scatter subtype and click “next”. 8. You should see a preview of the graph. There should be just points with no lines. 9. Make sure you have distance on the y axis and time on the x axis and click “next” 10. Under “Title” type in your name. 11. Under “Value x axis” type Time (s). 12. Under “Value y axis” type Distance (cm). 13. Click “finish”. A graph should appear in your table. 14. Right click any point in the graph and a menu will appear. 15. Select “Add Trendline.” 16. In the next menu the option marked “linear.” Should be highlighted. 17. Click on the options tab, at the bottom check the boxes for both “Display equation on chart” and “Display R squared value on chart” and click “ok.” 18. Your chart should now have a best fit line and an equation for that line. 19. Print your chart with your data and attach it to your lab report. Analysis: Position (cm) Time (s) Trial 1 Trial 2 Average 2 4 6 8 10 12 Assessment: Participation- Student is on task, working well with group. Instructor should not have to settle disputes between group members on how and who will complete the objectives of the exercise. Lab Report- This includes data for day 1 and the graph created on day 2. The graph must have both axes labeled correctly and the equation of the best fit line displayed Follow-up questions: Each student will submit their responses to the essay questions. Responses will be graded on completeness, thoughtfulness, grammar, punctuation, and spelling. Participation in Data Collection ---------------- 4 pts Data from day 1 ----------------------------------- 5 pts Graph from day 2 --------------------------------- 7 pts Follow-up Questions------------------------------ 9 pts Total------------------------------------------------ 25 pts Resources: Inspired by: Kartsounes, Andrew. Hartland High School “Toy Car Lab,” 2002 Mazar, Eric. 1997, Peer Instruction: A user’s manual. Prentice Hill, New Jersey 9 Follow-up: Match the following graphs to the correct description: (2 pts each) A. B. C. 1. Velocity is zero:__________ 2. Velocity is constant:_______ 3. Velocity is increasing:_____ 4. What is the velocity of the object represented in the graph above? (Include units - 3 pts) Object A Object B 5. In the motion map above, the position of object A and B is recorded every second. Between which time increment is there velocity the same? (Circle one - 3 pts) A. Between 1s and 2s B. At 3s C. Between 3s and 4s D. At 5s 6. Which object is accelerating? A. B. Which is not? A. B. (Circle one - 2 pts) 10 Teaching Materials: Motion Maps: Toy Car Lab (Time duration 2 days) Overview: In this activity, students will mark the distance traveled by a toy car at regular intervals. By measuring these marks and comparing these distances to time intervals, students will be able to calculate the velocity of the car. On the second day of the lab, students will use computer software to plot their data onto a graph. You should make sure you will have computers to accommodate your students. This activity should be completed during the first or second week of school, coinciding with Newton’s laws, and discussions on motion and velocity. It can also serve as a good introduction to the lab format and computer software that will be used throughout the year. Teacher and Student Objectives: Student Materials Take measurements of the position of a moving toy car over a period of time. Use computer software to make a graph of your data. Calculate the velocity of the car by finding the slope of your graph. Interpret graphical representations of distance vs. time to see trends in velocity. Teacher Materials Provide a visual representation of velocity using motion maps. Give students experience graphing with Excel, an important skill for college. Who’s Being Taught? This lab is designed for an introductory high school physics class consisting of juniors and seniors. If the class is advanced placement, you could add to the follow-up questions to increase the difficulty of the assignment. Groups should comprise of four students depending on the number of cars and space to take the measurements. For the second day, students will need access to computers. If computers are not available in your classroom or in a computer lab at your school, you could have the students plot on graph paper. How to Assess: Participation- Student is on task, working well with group. Instructor should not have to settle disputes between group members on how and who will complete the objectives of the exercise. Lab Report- This includes data for day 1 and the graph created on day 2. The graph must have both axes labeled correctly and the equation of the best fit line displayed Follow-up questions: Each student will submit their responses to the essay questions. Responses will be graded on completeness, thoughtfulness, grammar, punctuation, and spelling. Participation in Data Collection ---------------- 4 pts Data from day 1 ----------------------------------- 5 pts Graph from day 2 --------------------------------- 7 pts Follow-up Questions------------------------------ 9 pts Total------------------------------------------------ 25 pts 11 Strengths of Exercise: Taking measurements using a stopwatch and tape measure. Gain experience using Excel as a graphing utility. Correlation to the mathematical representation of a line; y = mx +b, where b is the slope of the line and in this case the velocity of the car. Discussion of possible causes of error. What to Look Out For: Your students should understand the difference between speed and velocity. You should complete this activity with each toy car so you know what range of velocity to expect for your car(s). You should compare the Excel instructions for day 2 with your version of Excel and make changes accordingly. The car’s velocity should be such that the students can keep up with it. If you plan on using a school computer lab for day 2, be sure to request the lab in advance. Technical Information: The toy cars can be inexpensive so that you can buy enough for each group. You really want them to be slow so the students can keep up with them. Having several types of cars would be ideal so groups would have different velocities. You also want to find a large area to perform this experiment. If your room is large enough you could push the desks aside and have some groups work in the classroom. You could have other groups in the hallway. If it’s nice enough outside, you could use chalk and run the experiment in the parking lot. Velocity (m/s) - The change of an object’s position over a period of time; basically speed with direction. Equation of a line- y = mx +b, where m is the slope and b is the y-intercept. Materials: Day 1: Toy Car (you will need several or only one group can work at a time) Stop watch Dry Erase Marker Tape Measure Day 2: Data from day 1 Computer with graphing utility and printing capabilities (instructions are for Excel) Procedure: Day 1: 1. Find a long area that is free from obstructions. 2. Draw a starting line. 3. Start the car about a meter before the starting line. 4. When the front of the car reaches the starting line start the stopwatch. 5. Mark the front of the car every two seconds until you have six marks. 12 6. Measure the distance to each mark and record in the table provided. 7. Repeat for a second trial; don’t forget to erase the first marks. 8. Average the distances of the two trials and enter into the table. Day 2: 1. Each student will make their own graph. 2. Open Excel and create a new workbook. 3. In column A, enter the corresponding seconds to each distance. 4. In column B, enter the average distances. 5. Highlight the data in both columns. 6. Select “insert” from the tool bar and then select “chart.” 7. Select “xy (scatter)” and the scatter subtype and click “next”. 8. You should see a preview of the graph. There should be just points with no lines. 9. Make sure you have distance on the y axis and time on the x axis and click “next” 10. Under “Title” type in your name. 11. Under “Value x axis” type Time (s). 12. Under “Value y axis” type Distance (cm). 13. Click “finish”. A graph should appear in your table. 14. Right click any point in the graph and a menu will appear. 15. Select “Add Trendline.” 16. In the next menu the option marked “linear.” Should be highlighted. 17. Click on the options tab, at the bottom check the boxes for both “Display equation on chart” and “Display R squared value on chart” and click “ok.” 18. Your chart should now have a best fit line and an equation for that line. 19. Print your chart with your data and attach it to your lab report. Sample Data: Position (cm) Average Time (s) Trial 1 Trial 2 (cm) 2 82 81 81.5 4 170 186 178 6 286 290 288 8 395 382 388.5 10 497 479 488 12 583 574 578.5 700 600 y = 50.221x - 17.8 R2 = 0.9993 500 Distance (cm) 400 Series1 300 Linear (Series1) 200 100 0 0 5 10 15 Time (s) 13 Answer Hints Match the following graphs to the correct description: (2 pts each) A. B. C. 6. Velocity is zero:____B.______ 7. Velocity is constant:__A._____ 8. Velocity is increasing:_C.____ 9. What is the velocity of the object represented in the graph above? (Include units - 3 pts) y = 6/4x or 3/2x so v = 1.5 m/s Object A Object B 10. In the motion map above, the position of object A and B is recorded every second. Between which time increment is there velocity the same? (Circle one - 3 pts) A. Between 1s and 2s B. At 3s C. Between 3s and 4s D. At 5s 6. Which object is accelerating? A. B. Which is not? A. B. (Circle one - 2 pts) 14 Force of Gravity (Measurement of g) Introduction: Any two objects with mass exert a force on each other and are attracted. This fundamental force is called Gravitation. The attraction of two objects can be described by the Universal Law of Gravitation. It is F= [G*(m1*m2)]/r2 where G is the constant of proportionality (=6.67 e-11 N*m2/kg2), m1 and m2 are the masses of the two objects and r is the distance between them. Due to the constant of proportionality being so small the attractive force between you and every day objects on earth is so small you do not feel the force at all. But the earth is so much more massive that you do feel the attractive force between you and the earth, this is called gravity. The effects of gravity are felt everywhere. Every planetary body is surrounded by its own gravitational field, which exerts an attractive force on any object. Since the sun is so much more massive than the earth why are objects on earth not “pulled” of earth by the gravity of the sun? That’s because the sun is so much farther away that it is a much weaker force than the force of gravity from the earth. The gravitational force between the earth and sun causes the earth to orbit the sun. Since the earth is essentially a sphere the force of gravity is pretty much equal anywhere on the surface of the earth. The gravitational field is numerically equal to the acceleration of objects under its influence, and its value at the Earth’s surface g is approximately 9.81 m/s2. That means that an object falling freely near the earth’s surface increases in speed by 9.81 m/s for each second of descent, ignoring air resistance. This lab you will be performing a measurement of the earth’s gravity. If an object starts from rest and is allowed to fall freely toward the earth, the distance d it travels is a function of time t is given by the equation d=vot + gt2 /2 Since the object is falling from rest, there is no initial velocity vo so the equation can be given only as d= gt2 /2 (1) In this experiment you will use a precise timing device to measure the time it takes an object to fall a certain distance. Objectives: To determine the acceleration of gravity on the earth’s surface by measuring the free-fall time of an object. To compare their value of g to the theoretical value of 9.81 m/s2 Materials: Power Supply electromagnetic coil steel ball Control box (turns the coil on and off to drop ball) Timer “Catcher” switch meter stick Stand with movable clamp to hold coil at different heights Procedure: 1. The apparatus will already be hooked up for you (since it is complicated to set up, shown below). 15 (Figure adopted from ISP 209L, S. Tessmer) 2. Turn on power supply, and timer. 3. Put the control box to the hold position. The box in hold position completes a circuit so current from the power supply is going through the coil. As the current goes through the coil in creates a magnetic field which makes the steel ball “stick” to the coil. When the switch is flipped to the drop position the circuit is broke, the current stops flowing so the ball drops. When you flip the switch the ball will drop instantly and also the timer will start running. 4. Align the catcher switch under the ball so it will land on the switch which stops the timer. You may want to drop the ball to make sure the switch is directly under the ball. 5. Measure the distance from the top of the catcher switch to the bottom of the steel ball when stuck to the coil. 6. Flip the control switch to drop and record the time it took to fall. Record the distance and the time in Table 1. 7. Repeat for another 9 distances of your choice. You should range your distances from roughly 5-10cm up to 2 m if possible. The wider the range of data the better. Table 1 Trial # Distance (m) Time (s) g (m/s2) 1 2 3 4 5 16 6 7 8 9 10 average ----------------------- ------------------------ Calculations: 1. For each trial, using Eq. (1) calculate the value of g. 2. Find the average value of g for all of your trials Sample Calculations d= 1.91 m t=.625 s d= gt2/2 => g= 2*d/t2 = 2*(1.91)/(.625)2 = 9.78 m/s2 Average= sum of g for all trials / # of trials => 979/10 = 9.79 m/s2 3. Below show one sample calculation for finding the value of g and show work for finding the average value of g but completely fill out Table 1. 4. Plot d vs. t (distance vs. time) on the attached sheet. Label axis. Follow-up Questions: 1. Does the previously measured value of g= 9.81 m/s2 fall within the range of values which you measured? (2 pts) 2. Does your average result for g agree with the previously measured value of 9.81 m/s2? Show work. ( percent difference = abs(theoretical – experimental)/ theoretical. If this value is within 5% difference then they agree.) (3 pts) 3. Do the points on your graph of d vs. t fall in a straight line including the origin? If not what shape does the graph look like? What does this tell you about the motion of the falling ball? (3pts) 17 4. Why is it important to use a wide range of distances? (2 pts) 5. What is the source of uncertainty in measuring the distance related to the design of the catcher switch? Look carefully at how the catcher switch works. (2 pts) 6. If the earth were to suddenly start rotating twice as fast, would the value of g increase? Does the earth’s rotation cause gravity? (3pts) 7. In the introduction I stated that the force of gravity was 9.81 without air resistance. Give at least 3 reasons why in this lab set up we can say the ball is falling freely and can “ignore” air resistance. (3pts) Assessment: This lab is worth a total of 30 pts. I will be grading on the following areas. I will be looking at your data sheets to make sure they are fully completed (4 pts). I will look at your sample calculations. You need at least one sample calculation given for each calculation. You will be graded on whether they are calculated correctly, correct significant figures and units where applicable (4pts). I will be looking to make sure your graph is complete, and labeled your axis (4 pts). I will be grading your follow-up questions on correctness but also if ample thought and content was put into all the questions. The point values for each question are given above (18 pts). Total Points: 30 Resources: ISP 209L Course Pack, “Mystery of the Physical World Lab” FS. 2006. S. Tessmer 18 Distance vs. Time 19 Teacher Materials: Force of Gravity (Measurement of g) Overview: The basic principle being taught/shown in this lab is the force of gravity. The reason for the lab is to find the force of gravity experimentally and verify that it is 9.81 m/s2. This lab can be modified in numerous ways depending on the amount of resources that you have in the classroom. The basic setup only needs to consist of dropping a ball a known distance and recording the time it takes to fall that distance. If you do not have this high-tech of equipment then you can use a CBL with calculator programs to time the fall. If you do not have those then you can just use a hand timer, but this method will not give you as accurate of a g value. The major concepts that should be taught are the idea that gravity is a force between any two objects that have mass. Also, the earth’s gravity is caused by the mass of the earth and NOT by the earth rotating or by the earth orbiting the sun. These are some common misconceptions that students have and the goal of this lab is to make sure students understand that gravity is because of mass ONLY. Teacher and Student Objectives: Student Objectives: To determine the acceleration of gravity on the earth’s surface by measuring the free-fall time of an object. To compare their value of g to the theoretical value of 9.81 m/s2. Teacher Objectives: Stress the idea that gravity is due to the mass of objects ONLY and nothing else. This is a key idea in all of physics that students need to understand. If available, use computer software to graph data and analyze it with a computer. Who’s being taught? This lab is designed for use in a high school physics class consisting of juniors and seniors. Depending on whether it is a general class or advanced placement, you can tweak the follow-up questions. If it is an AP class then the questions should be more challenging, in depth, and more thought provoking. The preferred class size would be 20-30 students so that you can have groups of 4 students. With high school kids, these group sizes will still be able to work quickly and efficiently to finish the lab in a timely manner. These size groups are also very manageable for the teacher. How to assess students? I would grade this lab out of 30 points. I would grade on the following items. Look at the data sheets and make sure they are fully completed (4 pts). I would look at the sample calculations. I recommend AT LEAST one sample calculation given for each calculation. Students should be graded on whether they were calculated correctly with correct significant figures and units (4 pts). 20 Also I would make sure that they correctly labeled and made the graph of distance vs. time and that it correctly looks quadratic or one sided parabola (4pts). I would then grade the follow-up questions primarily on correctness but also if ample thought and content was put into all the questions (18 pts). Answer hints 1. Should be yes. 2. It should agree within 5% if using this set-up. Depending on if you have to alter the set- up depending on the materials you have in the classroom you can change the % to a higher value if the experiment can not be as accurate as this set-up. 3. No. Parabolic/quadratic. It shows that since the slope of the line is changing that the object is accelerating as it falls. 4. So you can see the data forms a parabolic line from the origin. If you only use far distance and not short distances it may look straight which would tell you that the ball is not accelerating which is not true. 5. The gap in the catcher switch between where the ball hits the switch and where the switch actually closes and the timer is stopped. 6. No. NO, the whole underlying point of this lab is for students to realize that gravity in no way is created by the earth rotating but is due to mass only. 7. Ball is small so small area for air to resist it, it is smooth so low drag on it, and the ball falls a short distance so short time for air to affect it falling. (these are the more common answers but any answer that makes sense can be accepted). Strengths of Exercise: This exercise is very good at showing the students the force of gravity by measuring it very accurately. Also, the greatest advantage is that the object is actually falling and the students see this. Other experiments can solve for the force of gravity by using rolling balls, or masses and spring scales but they do not actually show an object falling freely. I think that since the students see the ball fall under the force of gravity that they believe it more then if solving for in another lab. It is a very accurate lab and the data is very good which is good for the students to see. What to look out for: For the most part this lab is easy to control. The instructor and walk around to each group to make sure they are on task. The data is easy to acquire and it is very accurate. But the only disadvantage is that if you do not have access to this technically advanced apparatus then it could be hard to do. Depending on how accurate of other types of timing devices you have the lab will need to be altered and tested to make sure that the experiment can be completed accurately with the materials you have in your room. A hand timer could be hard to use because you would not be able to do relatively short distances accurately. You would need to test to see what the shortest possible distance that can be measured relatively accurate is and whether the lab is still worthwhile with the data that you are obtaining. 21 Sample Data: Trial # Distance (m) Time (t) g (m/s2) 1 1.91 .625 9.78 2 1.71 .589 9.85 3 1.45 .543 9.76 4 1.25 .505 9.80 5 1.04 .460 9.83 6 0.82 .409 9.80 7 0.58 .343 9.85 8 0.32 .256 9.77 9 0.15 .175 9.79 10 0.06 .111 9.74 average ----------------------- ------------------------ 9.79 Technical Information: I would set up the apparatus for the students ahead of time because it is a more complicated set up then other labs. Like I have stated before, if your lab equipment won’t let you follow this write up explicitly you can alter it in anyways necessary so that it will be feasible for you to perform in your classroom. Also, if you have the ability to use computer software to analyze and graph the data I would encourage you to have to students do the lab that way instead of graphing it by hand. It will be valuable experience in using computer software which will be needed in other classes, college especially. 22 Distance vs. Time 23 Projectile Motion (Motion in 2-D) Introduction: Projectile Motion When you throw a ball into the air it will unavoidably fall back to the ground. Newton’s first law says that once the ball is in motion then it will travel in a straight line forever unless acted on by an outside force. Therefore a force is acting on the ball and that force is gravity. The force of gravity causes rising objects to slow down by applying a negative acceleration and eventually begin to accelerate towards the earth. But objects don’t only move vertically but can also move in a 2-dimensional path. This path is called the trajectory and it follows a parabolic path which is shown below. Figure adopted from http://cnx.org/content/m13847/latest/ In this lab you will be looking at the trajectory of a dart shot from a toy gun. The main forces that are affecting the projectile are the force of gravity and air resistance. Immediately after the dart is shot the force of gravity acts on the dart and begins to pull the dart downward. This is what causes the parabolic path of the dart. The distance that the dart travels depends on the initial speed of the dart, mass, height it is fired from and angle it is initially shot at. The initial speed of the dart is constant because you can not change the force applied to the dart to make it fly so the initial velocity is always constant. The height that the dart is fired from and the mass of the dart are changeable but will stay constant during different parts of the experiment. Therefore, the initial angle that the dart is being shot is what you will be analyzing. In this experiment we will be looking at 3 different scenarios of projectile motion. The first part you will be firing the dart from ground level, varying the angle of the dart by 150 from 00 to 900 and recording the horizontal distance the dart flies. The second part of the lab is to fire the dart from 2 heights above ground level (i.e. 70 cm and 120 cm) and record the horizontal distance the dart goes. The third part is adding mass to the dart by taping a dime to the front of the dart and seeing how far it flies now with added weight but with the same amount of initial force propelling the dart. 24 Objectives: To look at how objects move in a 2-Dimensional path (vertically and horizontally) and how different factors such as initial angle of firing, differences in initial height above the ground, mass of the object, and air resistance affect the horizontal distance the dart travels. To predict the best angle for firing any object to maximize the horizontal distance it can travel. Materials: Dart Tech Dart gun with dart meter stick or metric measuring tape protractor dime tape Procedure: Part 1- Firing the gun from ground level 1. Mark where the gun is going to be initially shot from. This will be the point you measure from when measuring the horizontal distance. 2. If you have a measuring tape, lay it out along the ground in the direction of where the dart will be fired at. If only have a meter stick then use a “marker” to mark where the dart initially lands. 3. Shoot the dart first at an initial angle of 00 using the protractor. Measure the horizontal distance the dart flies from the initial point of firing to the spot where the dart initially hits the ground first and NOT to where it finally stops at. 4. Repeat this 2 times at 00 for a total of 3 trials and record in Table 1. 5. Repeat for angles varying by 150 up to 900. Do 3 trials for each angle and record in table 1. Part 2- Firing gun from 2 different heights 1. Place the gun higher than ground level. The height of a desk or table top approximately 70 cm high will work. Measure the exact height he gun is above the ground and record at the top of table 2. 2. Mark where the dart is initially being fired from on the ground directly below the gun. This is the point where you will measure from when measuring the horizontal distance. 3. Repeat the experiment just like in part A by firing the dart at varying angles of 150 from 00 to 900 recording the horizontal distance the dart flies in Table 3. 4. Repeat again for another height approximately 120 cm which is the gun at chest high and record in table 4. Part 3- Changing mass of the dart 1. Once again repeat the experiment at ground level for a dart of a different mass by taping a dime to the front of the dart where the suction cup is at. Record data in Table 3. Table 1: Distances traveled (cm) by dart at ground level (h0) Trials 0 deg 15 deg 30 deg 45 deg 60 deg 75 deg 90 deg 1 2 3 Avg. Dis. (cm) 25 Table 2: Distance traveled (cm) by dart initially height h1= _____cm above ground Trials 0 deg 15 deg 30 deg 45 deg 60 deg 75 deg 90 deg 1 2 3 Avg. Dis. (cm) Table 3: Distance traveled (cm) by dart initially height h2=_____cm above ground Trials 0 deg 15 deg 30 deg 45 deg 60 deg 75 deg 90 deg 1 2 3 Avg. Dis. (cm) Table 4: Distance traveled (cm) by weighted dart height h=____cm above ground Trials 0 deg 15 deg 30 deg 45 deg 60 deg 75 deg 90 deg 1 2 3 Avg. Dis. (cm) Calculations: 1. Calculate the average values of the distance traveled for each angle in each table (Sample calculation needed). 2. For each table graph average distance traveled vs. angle fired. Make a legend to differentiate between the 4 different tables. Graph paper attached. Follow-up Questions: 26 1. At what initial angle at ground level (h0) did the dart that was being shot travel the furthest? The shortest? Why do you think this happened? Use your graph to help you. What shape do the points from Table 1 make on your graph? (5pts) 2. Did you notice anything different about the horizontal distances when you fired the dart from the first height (h1) above the ground (h0) compared to the ground distances? At what angle did the dart travel the furthest? Explain why. What shape do the points from Table 2 make on your graph? (5pts) 3. Did you notice anything different about the horizontal distances when you fired the dart from the second height (h2) compared to h1 (specifically looking at angles 15, 30, 45, and 60 degrees)? Explain what you think happened to support your data. (6 pts) 4. What happened to the dart when you added more mass? What did the new path look like? Did it travel farther or shorter? Explain why (Hint: use Newton’s 2nd law to help you explain it). (6pts) 5. Let’s say you hypothetically cut off the suction cup of the dart, how do you think this would affect the flight of the dart, thinking about distance traveled and trajectory? (Under the premises that the dart will still fly correctly) Hint: think about air resistance and weight (5pts). 27 Assessment: This lab is worth a total of 45 points. I will be grading on the following items. I will be looking at your data tables to make sure they are fully completed and correct (7pts). The graph you construct will be graded on neatness, if the axes are labeled correctly, if it correctly matches your data, and if it has a proper legend to distinguish the different data sets (8 pts). I will look at your sample calculations. You will need at least one sample calculation given. You will be graded on whether they are calculated correctly, correct significant figures and units where applicable (3pts). I will be grading your follow-up questions for correctness but mainly on if your answer to each part of each question contains ample thought and content. The point values for each question are given above (27pts total). Total Points: 45 Resources: Idea adopted from http://swift.sonoma.edu/education/newton/newton_2/nlawprt2.PDF Figure adopted from http://cnx.org/content/m13847/latest/ 28 Distance Traveled vs. Angle Fired 29 Teacher Materials: Projectile Motion (Time duration 2 days) Overview: The basic concept behind this lab is to show the idea behind 2-Dimensional motion. Projectile motion is a complicated and hard lab to show in a lab setting. Initially when the dart is shot a force is applied which propels the dart out of the gun at an initial velocity. Now instantly after this force is applied the only force acting on the dart is the force of gravity (ignoring air resistance). Therefore the dart is immediately being accelerated toward the earth and therefore the dart will follow and parabolic trajectory path. Depending on the initial force applied, a higher force will make the dart fly farther. Also, the angle the dart is being shot at effects the distance it travels. If it is shot at 00 then the dart only has a force in the horizontal distance and therefore will hit the ground soon into its trajectory and skip along the ground. But if a dart is shot at 900 then it only has velocity in the vertical direction so it will not move any distance in the horizontal distance. Therefore there should be a distance in between 00 and 900 that can maximize the amount of initial velocity given to the dart in the horizontal direction but also give enough velocity in the vertical direction so it will stay in the air long enough to maximize the energy in the horizontal direction so it does not hit the ground too soon. This is the idea that the students will be looking at in this lab. In this experiment, students will need to work in groups of 3 or 4 at the minimum because it is a labor intensive lab. One or two students will be needed to fire the gun at the correct angle, one to spot where the dart initially lands, and one to measure and record the data. There are multiple parts of the experiment that look at the dart being shot from ground level, two varying heights (h1 and h2) above the ground and a dart that has added mass to it. The ideas that you want students to understand are the optimum angle to shoot the dart to obtain the greatest horizontal distance. Also that if you shoot a dart above ground level it will travel farther horizontally then at ground level. At the same time they hopefully are going to notice that the distance the dart travels for 30, 45, and 60 degrees do not really change between h1 and h2 because of air resistance. Finally they should be able to see that since the force the gun shoots the dart at is constant so changing the mass will effect how far the dart travels. I would recommend doing this lab over a 2 day period of time due to the amount of variations in the experiment. Because the setup is minimal there is no set place the students need to be at or stop at the end of the 1st day. I would guess at most they will get through the h1 table. But if you only have 1 day you should be able to alter this lab so that it will fit in that time period and still be able to get across all the main ideas. Teacher and Student Objectives: Student Materials: To look at how objects move in a 2-Dimensional path (vertically and horizontally) and how different factors such as initial angle of firing, differences in initial height above the ground, mass of the object, and air resistance affect the horizontal distance the dart travels. To predict the best angle for firing any object to maximize the horizontal distance it can travel. 30 Teacher Materials: To learn the basic ideas behind projectile motion. To learn the optimum angle of firing to maximize horizontal distance is 450. To learn that the initial height of the projectile will affect the distance it will travel but once you reach a certain height and above the dart will no longer increase its’ horizontal distance because of air resistance To understand the idea behind Newton’s equation F=ma and that if you change the mass of the projectile, if the initial force stays constant they can predict how the dart will fly. Who’s being taught? This lab is designed for an introductory high school physics class consisting of juniors and seniors. Depending on if the class was advanced placement you could alter the experiment for that class. The questions would be sufficient for an AP class but I would add to them and also have them figure out what the initial velocity the dart is leaving the gun at and other harder calculations maybe including air resistance that can not be done in an introductory class. The preferred class size would be 20-30 students so the students could work in small groups. These group sizes are needed for the students to be able to perform the experiment in an efficient and timely manner due to it being so labor intensive. These size groups are also manageable for the teacher so they can walk around the room helping each group and making sure the students understand the concepts and the material. How to assess students? I would grade this lab out of 45 points. I would grade on the following items. I would look at the data tables to make sure they are fully completed and correct (7pts). The graph the students construct will be graded on neatness, if the axes are labeled correctly, if it correctly matches your data, and if it has a proper legend to distinguish the different data sets (8 pts). I would look at the sample calculations. They should least have one sample calculation given and it should be graded on whether they are calculated correctly, correct significant figures and units where applicable (3pts). I would grade the follow-up questions for correctness but mainly on if the answers to each part of each question contain ample thought and content. The point values for each question are given above (27pts total). Answer Hints: 1. Furthest- 450, maximizes the horizontal and vertical components from the force of the gun. Shortest- 900, no horizontal distance to the dart only moves vertically. Parabola. 2. They got larger; the dart traveled a further horizontal distance. 450 still produced the largest horizontal displacement b/c it still maximizes the components of the force to produce the largest displacement. The way the energy is used doesn’t change since the gun is moved vertically so the angle still holds. Parabola. 3. You would expect to see an increase in the horizontal distance but there is relatively none. This is due to air resistance. The horizontal component of velocity goes to 0 in the air and so the dart falls only under the force of gravity. Since the force is always constant the horizontal component of velocity goes to 0 at relatively the same point so it will only go so far no matter how high you shoot the dart initially from. 4. The new path still looks like a parabola but it travels much shorter (no matter what height you shoot it from). Newton’s law is F=ma and since the force is constant, when you 31 increase the mass you will decrease the initial acceleration of the dart which will decrease the initial velocity of the dart so it will not go as far. 5. It would travel farther horizontally in any case we tested. By cutting the suction off you will drastically reduce the air resistance of the dart but you also will make it less massive. The mass will increase the overall velocity of the dart and less air resistance will increase the amount of energy in flight so it will fly farther. These answers are only guides. If you want the students to answer more in depth then you can change the questions for that purpose. Also, the data should come out correct for the students but if the data is wrong but they answer the questions correctly from their data then they should receive full credit. Strengths of Exercise: This is a good, practical exercise to show students projectile motion in a classroom. It is relatively cheap and easy to complete (I bought my Dart Tech Dart gun from Meijer for only $1.99 so it is conceivable to buy a set for a classroom). It has relatively no safety concerns. It is a good lab that teaches students to work in groups and also team work in completing a task. What to “look out for”: One problem with this lab is if the data is hard to obtain. When I did the experiment, it worked relatively well so I believe it will work for the students AS LONG AS they are careful and precise in measuring, marking the initial hit of the dart, and the angle they shoot it at. Also students getting rowdy with shooting at each other instead of doing the lab could be a problem. But the gun bought from Meijer only shoots up to 10 feet so that will definitely help keep students under control. Part 3 of the experiment could be a problem if the gun is not powerful enough to shoot the dart with the added weight. You will need to make sure that the weight the students put on the suction cup is not large enough so the gun barley shoots. Sample Data: Table 1: Distances traveled (cm) by dart at ground level (h0) Trials 0 deg 15 deg 30 deg 45 deg 60 deg 75 deg 90 deg 1 101.2 206.7 259.1 292.1 233.7 149.9 0.0 2 108.3 209.4 261.4 295.3 231.2 147.8 0.0 3 98.8 201.1 262.9 290.9 232.4 146.5 0.0 Avg. Dis. 102.8 205.7 261.1 292.8 232.4 148.1 0.0 (cm) Table 2: Distance traveled (cm) by dart initially height h1= _72_cm above ground Trials 0 deg 15 deg 30 deg 45 deg 60 deg 75 deg 90 deg 1 241.3 337.7 359.8 363.2 274.3 208.3 0.0 2 237.7 339.8 356.2 361.8 275.4 207.3 0.0 3 240.8 334.1 360.9 362.9 276.1 209.5 0.0 Avg. Dis. 239.9 337.2 358.9 362.6 275.3 208.4 0.0 (cm) 32 Table 3: Distance traveled (cm) by dart initially height h2=_122_cm above ground Trials 0 deg 15 deg 30 deg 45 deg 60 deg 75 deg 90 deg 1 292.1 340.4 360.7 362.5 259.1 ------- -------- 2 294.6 339.7 361.8 363.4 261.4 ------ --------- 3 290.5 342.1 360.2 361.7 260.2 -------- -------- Avg. Dis. 292.4 340.7 360.9 362.5 260.2 --------- ---------- (cm) (for 75 and 90 degrees the dart would hit the ceiling) Table 4: Distance traveled (cm) by weighted dart height h=____cm above ground Trials 0 deg 15 deg 30 deg 45 deg 60 deg 75 deg 90 deg 1 2 3 Avg. Dis. (cm) (Because the gun was not very powerful I could not get any useful data. The exercise will work depending on the gun and the mass) Technical Information: The dart gun needs to be chosen correctly. I found the gun I bought from Meijer for only $1.99 to be a good choice. One, because it is inexpensive it is very easy to buy a set for an experiment. Two, because since it is not a really powerful gun, the dart only travels 10-12 feet so it is a lab that can easily be done in a classroom. Other guns are so powerful you would not be able to use or test all the set-ups that are in this experiment. The one downfall is that since the gun is not very powerful it is hard to do the last part of the experiment with attaching a mass to the dart because the dart will barely fly. Also, depending on if the students are having trouble with getting the launch angle; students might want to create their own “large” protractor from cardboard if they feel like it is necessary. I found the easiest way to get the angle was by propping the protractor off the ground so it was along the barrel of the gun so you can get a more correct angle measurement. Or another good method is to actually invert the gun so the barrel is on the ground and you just rotate the tip of the barrel up. It is easier to find the angle by doing this method also because you do not have to prop up the protractor up. Also if computer graphing capabilities is available I would recommend the students use that to analyze data instead of doing it by hand. 33 Distance Traveled vs. Angle Fired 34 Rolling Cylinders and Angular Momentum Introduction: Rolling Cylinders In this qualitative activity, you will observe the conversion of potential energy into kinetic energy of motion and kinetic energy of rotation through the use of ramps, balls and cylinders. We will consider how the variables mass, radius, release height, and distribution of mass affect the period and velocity of a rolling cylinder or sphere. Recall from our discussion on pendulums, the potential energy (mg∆h) of the initial height of the mass is transformed entirely into kinetic energy of rotation (Erot) at the bottom of its swing. Also recall from our discussion on inclines, that the potential energy of the initial height of the mass is transformed entirely into kinetic energy (½mv2) of motion at the bottom of the incline. In this case, conservation of energy gives ½mv2 + Erot = mg∆h. Note that as the rotational energy increases, the velocity must decrease. A cylinder rolling down a ramp has the same rotational energy as if it were rotating in place about its center of mass. The rotational energy can be found by considering the cylinder to be made of little pieces of mass mi and by calculating the kinetic energy of each little mass according to Ei = ½miv2 . The mass points farther from the rotational axis have a greater velocity than ones closer because they travel through a larger circumference with each revolution, which makes their kinetic energy bigger. Adding up all the kinetic energies of these little masses and averaging them gives the rotational energy of the rolling object. This concept may help you in this activity. Angular Momentum Linear Rotational Position Angle Velocity Angular Velocity Force Torque Mass Moment of inertia Momentum Angular momentum Acceleration Angular acceleration There is a simple correspondence between linear motion and rotational motion. The table above gives the corresponding quantities of the two types of motion. Newton’s second law, f = ma, says that force equals the rate of change of momentum. In a rotational system, Torque would correspond to a force. A torque applied to a body changes the angular momentum of a body. Torque can be thought of a twisting force, like the force used to turn a screwdriver. When a force is applied to a body at rest, we can observe the acceleration of the body as its speed increases in the direction of the applied force. If a force is applied to a body already in motion, the same thing is observed. If, however the force is always directed at a right angle to the velocity, the change of momentum observed is a change in direction, not the size of the momentum. When a torque is applied to a body to a body at rest, we observe its effect as an increasingly rapid rotational motion. This is an increase of the angular momentum of the body. For a body already spinning, an applied torque can increase or decrease the spinning depending on the direction of the spinning with respect to the applied torque. If a torque is applied at right angles to the angular momentum, it can leave the rate of angular momentum unchanged; only affecting the direction of the angular momentum of the body. 35 Objectives: Determine what influences rotational energy Observe how the height a cylinder is released at affects a rolling cylinder’s period. Observe how mass affects a rolling cylinder’s period and velocity. Observe how the radius of a cylinder affects that cylinder’s period and velocity. Observe how the distribution of mass affects a cylinder’s period and velocity. Materials: Ramp with two sides Steel and billiard ball with identical radii but different masses. Cylinders: 2 identical A cylinders B cylinder larger than A C cylinder with empty center Large D cylinder with small diameter Angular Momentum: Bike wheel with handles on axle (Figure adopted from ISP 209L, S. Tessmer) Swiveling stool Batons of equal mass Procedure: Note: You may notice that if you put the cylinders too high on the ramp they will tend to fall off very quickly. The trick is to start them out at a position about half way up from the bottom. Fill out the worksheet as you complete each step. 1. Place the two A cylinders at the same height h on each ramp and release them simultaneously. The cylinders are identical so the cylinders should roll back and forth with the same period. 2. Now place the identical cylinders at different heights on the ramps and release them simultaneously. Observe the period and velocity of each cylinder. 3. Work with another group for this step. Place your ramp side by side with the other group’s ramp. Place the billiard ball and steel ball at the same height on each ramp. Use the side with the slot so the balls stay on their ramp. Observe the balls’ period and velocity. 36 4. Using cylinders A and B, place them at the same height and again release them simultaneously. Observe the period and velocity of both cylinders. 5. Repeat again for cylinders B and C. Notice that C has no center. This means that the mass of C is further away from its axis of rotation than B’s mass is from B’s axis of rotation. Do you observe any differences in the period and velocity of cylinders B and C. 6. Now compare the velocity of D with respect to B and C. Practice rolling D until you get it to roll without sliding or rubbing against the ramp. Record your observations on the worksheet. The following should be completed when the wheel and stool or batons are available: 7. Examine the batons, do they weigh the same? Try to rotate the batons, why is one harder to rotate than the other? Record your observations. 8. Hold the handles of the wheel and have someone get the wheel spinning. Now try to twist the wheel in several directions. Record your observations. 9. Sit on the swiveling stool with your arms outstretched. Have your partner get you spinning. What happens when you quickly bring your arms close to your body? 10. While sitting on the swiveling stool, quickly turn the spinning wheel over. The handle that was pointing up should now be pointing down. Record what happens to the stool. Calculations: Although this lab is qualitative, the following equations may be helpful: Frictionless incline: potential energy = energy of motion Pendulum: potential energy = kinetic energy kinetic of rotation Cylinder: potential energy = energy of motion + kinetic energy of rotation Force parallel = (mass) x (gravity) x (sin θ) Follow-up: See attached worksheet. Resources: ISP 209L Course Pack, “Mystery of the Physical World Lab” FS. 2006. S. Tessmer 37 Rolling Cylinders and Angular Momentum Worksheet 1. When using identical cylinders, was the period the same for the different heights? _________ Are the velocities the same? (If not which is faster? – 1 pt) 2. When using the balls with different masses, explain how their periods and velocities related to one another. (1 pt) 3. When using cylinders with different radii, explain how their periods and velocities related to one another. (1 pt) 4. How are your answers in the questions above related to pendulums? (Include mass, length of string, and height of release point. – 2 pts) 5. What did you observe when you compared the periods and velocities of B, C, and D? (2 pts) 6. Draw the forces acting upon the cylinder as it is released. (3 pts) 7. When you rotated the batons, one was more difficult to turn than the other. Give an explanation of what might be causing this. (1 pt) 8. What happened when you twisted the axle of the rotating wheel? (1 pt) 9. What happened when you brought your arms closer to your body when you were spinning on the stool? Why? (2 pts) 10. What happened to the swiveling chair when you flipped the wheel over? (1 pt) 38 Assessment: Participation: Student is on task, working well with group. Instructor should not have to settle disputes between group members on how and who will complete the objectives of the exercise. Short Answer work sheet: This includes your observations and answers to questions. Responses should be written in complete sentences. Participation in Data Collection ----------------- 5 pts Lab Report ---------------------------------------- 15 pts Total------------------------------------------------20 pts 39 Teacher Materials: Rolling Cylinders and Angular Momentum (Time duration – 2 days) Overview: This activity covers many different elements of physics and should be performed after inclines and pendulums have been discussed. Friction can also be discussed depending on what has been discussed prior to this activity. Students will not be taking measurements, so they will be expected to give detailed explanations of their observations. Teacher and Student Objectives: Student Materials Determine what influences rotational energy Observe how the height a cylinder is released at affects a rolling cylinder’s period. Observe how mass affects a rolling cylinder’s period and velocity. Observe how the radius of a cylinder affects that cylinder’s period and velocity. Observe how the distribution of mass affects a cylinder’s period and velocity. Teacher Materials Connect students’ knowledge of inclines and pendulums to angular momentum. Demonstrate that only the distribution of mass affects a cylinder’s period. Who’s Being Taught: High school Physics 10-12 grade 20-25 students Groups of 2-3 students Students should be instructed on where to find the materials needed to complete this activity How to Assess: Participation: Student is on task, working well with group. Instructor should not have to settle disputes between group members on how and who will complete the objectives of the exercise. Short Answer work sheet: This includes the student’s observations and answers to the short answer questions. Responses should be written in complete sentences. Participation in Data Collection ----------------- 5 pts Lab Report ---------------------------------------- 15 pts Total------------------------------------------------20 pts Strengths of Exercise: Combines inclines and pendulums to help students understand the conversion of potential energy into rotational and translational kinetic energy. Gives insights on a hard to explain and understand topic. 40 What to look out for: Cylinders should be released halfway up the ramp. If you notice students are having difficulty keeping their cylinders on their ramp, they are probably releasing them too high. Make sure students have plenty of room to spin batons. Students should not fool around with batons. (sword-fighting, etc) Technical Information: The materials in this activity are fairly common in physics experiments. If your school does not have any of these materials you should be able to obtain them from any physics supplier. The batons can be made from equal lengths of conduit and masses positioned at the center or ends. Materials: Ramp with two sides Steel and billiard ball with identical radii but different masses. Cylinders: 2 identical A cylinders B cylinder larger than A C cylinder with empty center Large D cylinder with small diameter Angular Momentum: Bike wheel with handles on axle Swiveling stool Batons of equal mass Procedure: Note: You may notice that if you put the cylinders too high on the ramp they will tend to fall off very quickly. The trick is to start them out at a position about half way up from the bottom. Fill out the worksheet as you complete each step. 1. Place the two A cylinders at the same height h on each ramp and release them simultaneously. The cylinders are identical so the cylinders should roll back and forth with the same period. 2. Now place the identical cylinders at different heights on the ramps and release them simultaneously. Observe the period and velocity of each cylinder. 41 3. Work with another group for this step. Place your ramp side by side with the other group’s ramp. Place the billiard ball and steel ball at the same height on each ramp. Use the side with the slot so the balls stay on their ramp. Observe the balls’ period and velocity. 4. Using cylinders A and B, place them at the same height and again release them simultaneously. Observe the period and velocity of both cylinders. 5. Repeat again for cylinders B and C. Notice that C has no center. This means that the mass of C is further away from its axis of rotation than B’s mass is from B’s axis of rotation. Do you observe any differences in the period and velocity of cylinders B and C. 6. Now compare the velocity of D with respect to B and C. Practice rolling D until you get it to roll without sliding or rubbing against the ramp. Record your observations on the worksheet. The following should be completed when the wheel and stool or batons are available: 7. Examine the batons, do they weigh the same? Try to rotate the batons, why is one harder to rotate than the other? Record your observations. 8. Hold the handles of the wheel and have someone get the wheel spinning. Now try to twist the wheel in several directions. Record your observations. 9. Sit on the swiveling stool with your arms outstretched. Have your partner get you spinning. What happens when you quickly bring your arms close to your body? 10. While sitting on the swiveling stool, quickly turn the spinning wheel over. The handle that was pointing up should now be pointing down. Record what happens to the stool. Calculations: Although this lab is qualitative, the following equations may be helpful: Frictionless incline: potential energy = energy of motion Pendulum: potential energy = kinetic energy kinetic of rotation Cylinder: potential energy = energy of motion + kinetic energy of rotation Force parallel = (mass) x (gravity) x (sin θ) Follow-up/Sample Data: Answer Hints: 1. When using identical cylinders, was the period the same for the different heights? _________ Are the velocities the same? (If not which height is faster?) Periods are the same, the cylinder released at a higher height has a larger velocity. 2. When using the balls with different masses, explain how their periods and velocities related to one another. Periods and velocities are the same. 42 3. When using cylinders with different radii, explain how their periods and velocities related to one another. Periods and velocities are the same. 4. How are your answers in the questions above related to pendulums? (Include mass, length of string, and height of release point. Mass of cylinder or ball does not affect period or velocity- same for the mass of a pendulum. Radius of cylinder does not affect period or velocity- same for the length of a pendulum’s string. Height of release does not affect period but does affect velocity- same for the release point of a pendulum. 5. What did you observe when you compared the periods and velocities of B, C, and D? Explain your observations. D was slower and has the longest period because it has the most mass away from the axis of rotation. C was the second slowest and has the second longest period because it has more mass away from the axis of rotation than B, but less than D. 6. Draw the forces acting upon the cylinder as it is released. 7. When you turned the batons, one was more difficult to turn than the other. Give an explanation of what might be causing this. The mass is concentrated at the center of the baton that is easier to rotate. The mass is concentrated at the ends of the baton that is harder to rotate. 8. What happened when you twisted the axle of the rotating wheel? The resistance to the axial rotation is felt. 9. What happened when you brought your arms closer to your body when you were spinning on the stool? Why? When arms are outstretched, more mass is away from the axis of rotation, so the angular momentum decreases, and when they are brought in close the angular momentum increases. 10. What happened to the swiveling chair when you flipped the wheel over? The swivel chair should rotate in the opposite direction of the spinning wheel when it is flipped over. 43 Mouse Trap Car Introduction: In this activity you will be working in groups to construct and build a mouse trap car. A mouse trap-powered car is a vehicle that is powered by the energy of a wound mousetrap spring. Some mouse trap cars have been known to travel over 100 meters or can travel at very high speeds like 5 meters in under a second. In order to construct a successful car you must learn about different variables that will affect the performance of the car and apply you knowledge of physics from this class to reduce factors that hurt your car. There is no right or wrong way to build this car. The best approach is to apply your best understanding of the laws of physics you have learned in this class but to not focus mainly on once concept and ignore others. Do not be fooled into thinking there is only one way to build the winning car and try to copy the ideas of fellow classmates or of ideas from the internet. But instead use these to help get your own ideas flowing and thinking on how to improve, change, and create a better method to improve the performance in your own car. Be willing to try something original, test it out and see if it works. If not then go back to the drawing board or try to improve the original design. Building mousetrap cars is a simple process of brainstorming, building it, test it, experiment with different changes, test to see if they work and you keep doing it over and over again until you create the best car you can. A basic design that most students will start out with is tying one end of a piece of string to the mouse trap lever and rapping the other end around the axle of the rear wheels. As the string is wound around the axle by turning the rear wheels the lever is pulled closer to the drive axle causing the mousetrap spring to store energy by “winding up”. When the wheels are released, the string is pulled off the axle causing the wheels to rotate. Now this design is a good start but by no means is this where YOU need to start building your car from. This is only meant to get you to start thinking about different designs. Different external forces that you will want to think about when designing and building your car might include friction, gravity, inertia (weight), rotational inertia, and drag. These will be the major factors that will affect your car in a negative way. There are some basic physic concepts that are related to the motion of your car. First is that the energy from the spring is what is making the car move. This energy will apply a force causing the car to move. The force changes the potential energy into kinetic energy of motion of the car. The importance of transferring energy from a potential state to a kinetic state is of great importance in this activity. Since energy is conserved the system will only have as much energy as the spring potentially has. Once the maximum velocity is reached constant external forces will eventually cause the car to lose kinetic energy and slow down (decelerate). Also think about Newton’s laws and how they can help you create a better car that utilizes the potential energy in the best possible way. Eventually you are going to have a mouse trap car that travels down the track. Some cars will travel faster then others but might not go as far. Others will travel farther but not as fast. There are a lot of external forces that you will have to overcome in order to get your mouse trap car to be successful. Understanding the constraints; resources, external forces, and the dynamics of your car, will ultimately help you build a more successful car. Most of this activity will be done outside of class time. You will need to finish designing, build, and test the car outside of class time. Therefore the day that we “race” your cars will be 2 weeks from today. In the time from now till then, if we end class early for any reason you will be able to use that time for this project. 44 Objectives: To build a mouse trap car powered solely by the energy of one standard-sized unaltered mouse trap that will travel the greatest linear distance. You will rely/use the concepts taught in class to help create the best possible car you can. Guidelines/Rules: Each team will build a vehicle whose sole source of mechanical power is the spring of a single standard mousetrap. The spring must be the only source of stored energy for the vehicle, no batteries or electricity will be allowed. Also no form of elastic or rubber bands can be used in place of string or fishing line. Also, no fishing poles are allowed to be used as arm rods since they can add more energy to the system. By definition, a vehicle is a device with wheels or runners used to carry something (i.e. car, bus, bike, sled, etc.). Therefore, launching a ball from the mousetrap will be ruled illegal. Regulations 1. The device must be powered by a single Victor brand mouse trap (1 3/4" X 3 7/8"). Other brands may be used if permitted and approved by instructor. 2. The mousetrap can not be physically altered except for the following: 4 holes can be drilled only to mount the mousetrap to the frame or can be connected in another fashion as long as spring is not altered 3. The device cannot have any additional potential or kinetic energy at the start other than what can be stored in the mousetrap's spring itself. (This also means that you cannot push start your vehicle.) 4. The spring from the mousetrap cannot be altered or heat treated. 5. The spring cannot be wound more than its normal travel distance or 180 degrees. 6. Vehicles must be self-starting. Vehicles may not receive a push in the forward direction or side direction. 7. The vehicle must steer itself. Measurements of distance will not measure the total distance traveled only the displacement distance. 8. Distance will be measured from the front of the tape at the starting line to the point of the vehicle that was closest to the start line at the time of release. 9. You CAN NOT buy a car kit online; you must build the car yourself from scratch. If you want to get ideas from kits online that is ok. Materials: One standard mouse trap (unaltered) Any other materials you want you use. (Ex: cd’s, records, bearings, bushings, string/fishing line, wood). Besides the mouse trap you are allowed to use any materials that you can find around your house, classroom, or buy from hardware store that you need. Procedure: 1. You will work in groups of 2 or 3 in designing and building a mouse trap car. 2. You will have 2 weeks from the day the project is assigned to design, build and test your car. 2 weeks from today we will “race” the cars in class against each other. 3. On race day you will be given at least 3 runs (more if time allows). The farthest distance will be the only one that is used to for you grade and for finding the class average. 45 4. You should recall all the ideas learned from Newtonian physics in order to design your car so it performs well. Some ideas you might want to consider and friction, inertia (weight), rotational inertia (resistance to rolling), drag, torque, Newton’s Laws, etc. Thinking about these ideas and where they are being applied to your car will help you engineer ways to reduce these effects so your car travels farther. 5. You will need to create an ORIGINAL design of your car and indicate where areas of physics (examples listed above) are affecting the car and if it is a positive or negative way. 6. Once final car is built that you are going to “race” you need to draw a FINAL design for your car just like you did for the original car. 7. Finally, you need to write a write-up/follow-up (which will be discussed in further detail later). Follow-up: The major follow-up to this activity is that you will be comparing and contrasting you original design and your final design. You will be writing a paper that explains the original physics concepts you saw in your original design, what those concepts were and how they would positively or negatively effect your car and if negative how you were planning on designing the car to help limit these effects. Then you need to do the same thing with your final design but you will also need to explain what changes you made to the original design to get to the final design and why you made them. Throughout all parts of this paper you are trying to justify to me (the instructor) why and how you made these changes and what physics idea led you to believe that it would help in the end. If in the end your car barely works, you can discuss what physics ideas are hurting your car and what ideas you have to improve the car in the future. This paper is to show me that you fully understand that physics concepts behind a mouse trap car. This paper is fairly open for writing it however you want as long as it shows me that you fully understand the physics involved in this whole activity. Be creative, it will make it more enjoyable for me to read your papers. There is not length requirement, but you should not need to write more then 4 pages (if you do that is ok, you will not be penalized). Assessment: Since your objective was to build a working mouse trap car you will be awarded points for how far your car goes. It will be based on overall performance of the class and the grades will be fit around the average distance the class goes. Basically if you attempt to build a working car you will be given 15 of 30 points. From there depending on how far it goes compared to the average you will be award more points, up to 30. The group that goes the farthest will be awarded 5 extra credit points. (30 pts, potential for 5ec) The second part is when grading the follow-up essay. I stated above what I am looking for. This will be worth 50 pts. Even though your task is to build a working mouse trap car, your ability to understand and explain the physics involved will be worth more in your grade. Therefore, as long as you understand the physics, even if you can not build a good car will not severely hurt your grade. (50 pts) Total points: 80 pts 46 Teacher Materials: Mouse Trap Car (Time duration – 2 days) Overview: In this activity students will be working in groups of 2 or 3 to build a mouse trap car using the knowledge of physics they have learned throughout the year. The basic idea of the cars is simple. The spring of the mouse trap has only a certain amount of stored or potential energy. Therefore the system has a set amount that it can initially have. The goal is to transfer as much energy from potential energy to kinetic energy while at the same time limiting dissipating effects such as friction, drag/air resistance, inertia, rotational inertia, etc., so that the car will go the farthest distance. This activity will be done at the end of the semester or year once students have covered all of Newtonian physics and Rotational physics. I would recommend this be a two day lab. Day 1: You will want to introduce this lab to the students. You will want them to read over the lab and split up into their groups. I would then hold a group discussion for the remainder of class. This is an example of how I might hold the discussion. Once the students are broken up into their groups I would tell them that for 5-10 minutes they should start brainstorming and begin designing their car. I would then call the class back together and would then go around the room and ask the students to explain what the initial design is. As the instructor I would ask them questions why they decided to design it that way and what physics idea/concept made them do that. After everyone talks I would perform a couple small demonstrations of different major physics concepts that all students will have on their cars. These demos could be showing friction on the axel which will hurt the car but also show good friction needed on the drive tires so the car will move. Also, you could show torque by showing that for the least amount of energy you get the maximum amount of force if your torque is perpendicular. Also you can show the idea of gear ratios and showing the benefit of having smaller or larger drive tires. There are many more concepts you can demo but after each demo you should engage the class and ask what they saw, how it would hurt/help the car, and how to improve/fix it if it had a negative effect. Then I would have the students get back together in there groups for the rest of the hour and have them improve their original design or create a completely new design all together. Day 2: The second day of the activity would be held roughly 2 weeks later. You can change the exact length but you should give the students enough time to be able to meet outside of class to finish designing, building, and testing their car. One the second day of the lab you will be “racing” the students cars. This can be done in any smooth floored area. I would recommend a long hallway or a gym if it is open. This day is for running the cars and the students really enjoy seeing how their cars compare to the others in the class. Teacher and Student Objectives: Student Materials: To build a mouse trap car powered solely by the energy of one standard-sized unaltered mouse trap that will travel the greatest linear distance. You will rely/use the concepts taught in class to help create the best possible car you can. 47 Teacher Materials: For students to be able to work cooperatively in groups and as a team construct a working mouse trap car. Students be able to use physics concepts learned in class to help design a better car. Also, for them to be able to write a clear paper describing their understanding of these physics concepts; how they affect the car and what ways they can help fix these problems. Who is being taught? This activity is geared towards a high school physics class, consisting of usually juniors and seniors. This activity would be good for both an introductory class but also and AP class. The preferred class size would be 20-30 students so that you can have multiple groups and have a wider range of design ideas for the whole class to see. Most of the time is outside of class so this activity is more put on the students to get it done and meet with their partners. The students could get kind of rowdy and loud when running the cars so a hallway away from a lot of classrooms would be ideal incase the class does get load. How to assess students? Their objective was to build a working mouse trap car so I recommend basing some points off of how well the car performs (30 pts). If the student attempts to build a car then they should get 15 points. From there I would give the class points depending on how they ran compared to the class average and how the distribution looks. The group that goes the farthest I think should be awarded 5 extra credit points (30 pts, potential for 5ec) The second part is grading the follow-up essay. The requirements are stated in the follow-up section of the student materials. Basically it is to see the students ability to understand and explain the physics involved with the car. This section will be worth more points then the actual car because the physics concepts are more important. (50 pts) Strengths of exercise: This is a very good exercise to examine the students overall understanding of Newtonian physics. It is a great activity because the students are applying ideas learned in the classroom to real world areas (engineering). This activity promotes team work in completing a task which is an essential skill needed when working in the real world. Students will find this activity engaging and fun because it is not your typical lab. What to “look out for”: The only problem with this lab is that it is primarily done outside of the classroom. Therefore it is harder for the instructor to keep an eye on the progress of the students. But it will also teach the students responsibility of finishing a project on time and keeping themselves accountable. Because it is primarily out of class, this activity needs to be done with upperclassman. They will have driver’s licenses and access to cars so they will be able to meet easier. The only safety concern is with students hurting themselves with tools when constructing these cars. They should be told that if they do not feel comfortable with the tools they are using to construct the car they should have an adult do it or find another way to construct it. 48 Sample Data: There is no real sample data for this activity. If you would want to construct your own car and show the students you could do that. Technical Information: This activity is basically for the students to explore themselves without a lot of guidance. There are a lot of websites that have good information for teachers. If you want to buy a teachers guide to mouse trap cars you can find one at http://www.mousetrap- cars.com/mousetrap/books_plans.htm. This could be helpful to have a couple books for students to look in for ideas also. Resources: Parts adapted from http://www.docfizzix.com Parts adapted from http://www.gatortrax.eng.ufl.edu/mousetrap_lesson1.pdf Rules taken from http://www.mousetrap-cars.com/rules.htm; Official rules many organizations, teachers and competitions (also I modified them slightly). 49