Laboratory Revisions Physics 2010 and Physics 2020 modifications and studies of the laboratory sequence for introductory algebra-based physics N. Finkelstein and C. Keller 2003-2004

supported by:

AND The Department of Physics at the University of Colorado, Boulder

This document contains a description of the approach to laboratory revision, summary of evaluations of the labs, commentary on the labs and the latest versions of the labs for 2010 and 2020.

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PROJECT DESCRIPTION While undergraduate laboratories are considered an essential element of student learning in introductory physics, the laboratory experience remains a highly variable one. The efforts in the 2010 and 2020 sequence over the past year (2003-2004) have been directed at building on what is known from education research in physics1 and revising the labs to specifically promote the following goals: • promote student learning • increase student interest and engagement • model the process of experimental science The revisions of the 2020 labs (which include a more significant evaluation component described below) was supported by the LEAP initiative with a fractional time appointment of graduate student (Chris Keller). The approach we have taken in the re-write of the labs has been to appropriate some of the work of Rebecca Lippmann and Edward Redish at the University of Maryland.2 The Maryland labs simultaneously focus on students’ conceptual development, their laboratory skills, and views about physics (what it means to learn physics, conduct experiments, and justify findings). Simultaneously we attempted to reference real-world situations which were engaging and gender inclusive.3 Our emphasis on group consensus and epistemological development has been tempered by pragmatic concerns about maintaining the actual physical equipment from prior years, making sure that TA’s could conduct these labs, and insuring continuity with the rest of the course (and the existing traditions from prior years). In short, we attempted to move the labs from labs of verification to labs of discovery and inquiry. Such a procedure also follows work from the chemistry community in the last few years.4

LABORATORY REVISION PROCEEDURE The first drafts of the 2020 labs were composed by Chris Keller. These labs were based on the previous Physics 2020 labs (by Michael Dubson), labs used at UCSD by Noah Finkelstein, and the labs developed at U Maryland. The drafts were then reviewed by Finkelstein, and tested in the actual laboratories by the students and teaching assistants. The 2010 labs were revised by Finkelstein building on the earlier versions created by Dubson. Constant feedback from the TAs was collected throughout the semester, and a more detailed evaluation was conducted at the end 1

E. F. Redish, Teaching Physics with Physics Suite, Wiley 2003. R. Lippmann, Students' understanding of measurement and uncertainty in the physics laboratory: Social construction, underlying concepts, and quantitative analysis, doctoral thesis, University of Maryland 2003. Available at: http://www.physics.umd.edu/rgroups/ripe/perg/dissertations/ 3 Rosser, S. V. (Ed.), (1995) Teaching the majority: Breaking the gender barrier in science, mathematics, and engineering (pp. 220-229). New York: Teachers College Press. 4 E. Lewis, "Multi-Initiative Dissemination Project,(2004) http://www.cchem.berkeley.edu/~midp/ 2

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of the course. After reviewing over TA evaluations, we have made further changes and modifications to the lab write-ups.

QUANTITATIVE DATA The quantitative data collected from the TAs is shown below. Three different characteristics are used to describe the labs: learning experience for the students, student enjoyment and improvement from the previous labs. The scores are the average responses from all the TAs on a 4-point scale (4=good, 0=poor). TA Perception of Labs 4

Learn Enjoy Improve

Rating

3

2

1

0 1

2

3

4

5

6

Lab #

A few notes about the above data are in order. We were generally satisfied with the ratings of learning experience and student enjoyment. The improvement ratings may seem low, but that is the nature of the rating system—anything positive is considered good. In addition, since our inquiry theme for these labs may seem rather different and unfamiliar to the TAs, their perception of the improvement may be lower than expected. However, the real test is whether or not these students were able to learn more physics concepts and develop vital laboratory and critical thinking skills, compared to students from previous semesters. Both anecdotal evidence and learning gains on some of the materials presented in the class suggest so. However, a controlled test of this sort was not feasible, given our resources and timing. One could perform this task, but that was not the goal of this particular project.

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COMMENTS AND NOTES ON NEW PHYSICS 2020 LABS The following is a detailed description of the new labs. Learning goals, common misconceptions, pitfalls and precautions are all described to the best of our knowledge. It is highly recommended that the instructor and TAs read these notes prior to running the labs with the students. LAB #1: Fun with Electrostatics For the first lab of the semester, the students get to experience and see the behaviors of electrostatics. They have 6 plastic rods, various pieces of cloth and an electroscope to get a visual idea of how electric charges interact. PRECAUTIONS: Make sure the students do not tear or rip the gold leaves in the electroscope, by either tilting the electroscope or bring a charged object near the side of the electroscope. They are very thin and expensive. PRE-LAB: The pre-lab is suppose to get them thinking about something they all have experienced—getting shocked. This example is to help them start thinking about what is going on during that process. There is a corny online simulation that they can play around with that will allow them to see what is going on deep down. PART I: The first goal of this lab is to get them to figure out how to properly use an electroscope. There are some hints and suggestions on how to figure this out, but we want them to discover on their own how this thing works. Also, many students get confused and think that you can immediately measure the sign of the charge. You can do this only if you know the sign of the charge of the object you are measuring first. We don’t tell the student the sign of the rods or the cloth until later in the lab, so make sure they understand this. PART II: In the second portion of the lab, they develop a sense of what electron affinity is and what it means. Each rod has a different electron affinity, and therefore it can hold a different amount of charge compared to the others. The long, white Teflon rod has the greatest electron affinity (don’t tell your students this). Some students get confused on how exactly to set up the experiment. They need to compare each rod to every other rod, and making a table/matrix is often the easiest way to do this. Some groups will forget to discharge the rods and make sure they are neutralized before they rub them together. They will get confusing and contradictory data, and they may have to redo the whole experiment. This is perfectly fine—the lab is designed so they have enough time to redo it if necessary, and they will definitely learn from their mistakes. PART III: The last part of the lab allows them to be creative and have fun as well. They have to race aluminum cans across a table using a charged plastic rod(s). There are many tricks you can use to do this, but it may help if you charge up the can with positive charge.

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LAB #2: Fun with DC Circuits The second lab focuses on developing a deep understanding of basic DC circuits. They also get to learn how to use a DMM and a simple power supply as well. PRECAUTIONS: Since the students are still learning about current and voltage, they will inevitably burn up a few resistors. If something smells funny in the lab, find out which group it is and explain to them what happened. PRE-LAB: The pre-lab is designed to get them thinking about how current and voltage behave. We have found that many students still have a difficult time with questions 3 and 4. It might be a good idea to go over this part before proceeding with the lab. Also, the answer is “yes” to question 2—it’s tricky and some professors get it wrong. In addition, there is another online simulation called the Circuit Construction Kit (CCK). You may want your students to play around with this simulation before class as part of the pre-lab if you wish. http://www.colorado.edu/physics/phet/simulation-pages/electricity-simulations.htm PART I: The first part of the lab allows the students to play around with the DMM to get a feeling of how to measure resistance. Also, they can combine various resistors together, predict the equivalent resistance and measure it to see if their prediction was correct. PART II: This portion of the lab uses a very simple circuit that allows the students to immediately see if their prediction is correct. Again, it may be tempting to have the students build a more complex circuit and analyze it; however, students in this class will never need that level of sophistication. We’re only striving for an understanding of the basic underlying concepts and to develop critical thinking skills. PART III: The trick that the students have to realize is that you can calculate the resistance by using Ohm’s law. The dials on the power supply give them the current and voltage values they need. LAB #3: Fun with AC Circuits The third lab focuses on the students developing a deep conceptual understanding of AC circuits. This lab has two parts: the first uses a make-shift EKG machine that allows the students to measure the voltage difference (from their heart) between their hands. The second part has the students build an electromagnet that they can turn into a transformer. PRECAUTIONS: Be sure to do a quick run through this lab before running it with your students. It can be difficult to get a nice display of your pulse on the oscilloscope. Students may get frustrated with this part; have Jerry Leigh come in and help you if many of the students are having trouble.

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PART I: Once students can get a nice display of their pulse on the oscilloscope, most of them find this one of the most interesting labs of the semester, especially the pre-meds. There are lots of other experiments that can be done, such as squeezing the electrodes, having multiple people touch the electrodes in various positions, etc. PART II: As an introduction to transformers, students first make an electromagnet. This does not involve AC current, but nevertheless it’s a good precursor to transformers. Constantly remind students not to leave the batteries connected to the coil for too long. This quickly drains the batteries and other students may get confused when their electromagnet doesn’t work. Also, the trick to the second part is to somehow create an AC signal from a battery. All you have to do is rapidly touch the wire to the battery terminal and you now have an AC voltage. Some students don’t realize that batteries produce a constant voltage and may ask, “Is this an AC or DC battery?” Stress the points that batteries produce constant voltages, and that transformers only work for AC voltages. LAB #4: Fun with Light and Lasers The fourth lab allows the students to see diffraction and interference effects firsthand using a He-Ne laser and a Cornell plate. The students also have the opportunity to flex their lab muscles a little more in this lab because they have to setup their own experiments and be able to interpret their results. PRECAUTIONS: This goes without saying, but make sure the students do not look into the laser beam or reflect it off a metallic object and shine it around the classroom. PART I: The students made predictions as part of their pre-lab as to how the intensity pattern changes if you change one aspect of the experiment. They have to figure out a way to test these predictions. We know that you cannot test the 4th prediction, but we want the students to realize this for themselves. PART II: This part tends to be somewhat difficult for the students. They may not have seen combined interference and diffraction effects in lecture. We want the students to realize the similarities between the pairs of slits that they have to compare. They may need some more assistance from the TAs on what exactly to look for in this part. Have the students trace out the intensity patterns on a sheet of paper so that they can visually see the similarities and differences. Also, note that the Cornell plates are not perfect and the slit width and separation numbers quoted on the lab report are approximate. Thus, the intensity patterns will not match up exactly like one would expect. PART III: Again, the students have to devise their own experiment to accomplish this part. There are many ways this can be done, and most methods will yield a good answer. We don’t ask them to give their uncertainty in their measurement because they haven’t leaned about error and uncertainty yet in this course.

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However, if time permits you can ask the students which method might result in a smaller uncertainty. LAB #5: Fun with Optics The fifth lab allows the students to see how converging lenses behave and how their focal lengths can be measured. At the end of the lab, the students get to make and use their own telescope. PRECAUTIONS: Everything is fairly safe in this lab. If their light source is battery powered, remind them to shut it off when not in use. Sometimes the images projected on the frosted screen will be difficult to see with the room lights on, so advise them to pull down the curtains on their lab station. PART I: The first part of the lab should be fairly straight forward. PART II: There are basically two methods that the students can use to measure the focal length. If you set up the light source, lens and screen so that you have a clear image, all you have to do is measure the i and o and plug them into the lens equation. The other method involves a collimated beam—if the light source is at the lens’ focal point, you can produce a collimated beam and directly measure the focal length. Do not tell your students the two methods right away; remind them of pre-lab question 3 and hopefully the gears will start turning. PART III: This portion allows the students to apply their knowledge of optics to the real world and analyze a slide projector. The students have to figure out why all the major components are oriented the way they are. In addition, they have to figure out what type of lens is being used and why. The slide projectors are not standard lab equipment for this lab, so be sure to ask Jerry Leigh for them and track down some slides that the students can use. PART IV: The last part of the lab has the students build their own telescope and test it out to measure the angular magnification. This part relies on the students having read the appropriate section in their book on telescopes so they have an idea of where to begin. If students are initially stuck, tell them to consult their text book first. If time permits, the students can try to build a three-lens telescope. It is difficult to set up, so keep that in mind. LAB #6: Fun with Atoms The last lab allows the students to explore the various emission spectra from different atoms. They also get to use a prefabricated spectrometer to observe the different wavelengths of light, in addition to making their own spectrometer to see how the instrument actually works. PRECAUTIONS: The discharge tubes and diffraction gratings are both fragile, so make sure your students handle them carefully.

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PART I: In the first part of the lab, students get to play around with the prefabricated spectrometer. Make sure that they calibrate the spectrometer, as noted in the lab. By observing the emission spectrum from the discharge tube, the students have to figure out what they are looking at. The tube is actually filled with Hydrogen, but don’t tell them this right away. PART II: In order to get a feel for how a simple spectrometer works, the students have to build their own from a meter stick and a diffraction grating. Some groups may find this rather difficult and will get stuck when trying to observe the spectrum. Make sure that you attempt to set up the spectrometer yourself before having the students do the lab themselves. The students also have to figure out how to calculate the wavelengths of the light they observe. Some students may find this challenging, but remind them of what variables they already know (or can easily measure). This portion of the lab usually takes the longest to do. There are also a few questions about the uncertainty of their spectrometer, and which one is more accurate. We are looking for some qualitative reasoning and explanations for these questions. Remember, most of them have no formal knowledge of error and uncertainty, but you can definitely get them thinking about these aspects of the experiment. PART III: The most important aspect in this part is the last question: why do the light bulb and fluorescent light both appear white when we know they are composed of different wavelengths of light? Try to get them thinking deeply about this question and about how our eyes interpret various colors. PART IV: If there is enough time, have the students figure out the composition of the mystery substances. Talk to Jerry Leigh about this and make sure you know what is in each discharge tube. Some students have gotten conflicting data from the giant wall chart in the lab, so make sure you have an up-to-date version somewhere for the students to look at. If there is even more time remaining, you can give a better explanation as to how discharge tubes work.

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Physics 2010 Labs

2010 Lab 1: Motion and Gravity: aka floating on air In this you will be working with air tracks, messing about in a scientific way to discover some properties of motion, acceleration, and effects of gravity. Your first priority in any lab is safety. The good news is that there are relatively few ways to hurt yourself or others in this lab. Still, pay attention at all times to what you and your lab mates are doing. Your next priority is to treat the equipment safely and respectfully. DO NOT BREAK THE EQUIPMENT. They are cool instruments … and they are sensitive. Do not elevate the air tracks past approximately 10 degrees. Have fun and learn some physics. There is a challenge at the end of this lab. So, if you wish to be deemed MASTERS of the LABORATORY pay close attention (plus it may well help your grade). Lastly, your PRE-LAB HOMEWORK is embedded in these lab instructions. YOU MUST TURN THOSE IN ON A SEPARATE PIECE OF PAPER at the beginning of lab. You should also have a copy in your lab notebook. (It is okay if you print out copies of your prelab and tape one in your book). Activity I: Pre-amble to the lab: (15 minutes) a. Turn on the air tracks (get instructions from the TA) photogates

card glider

air track

b. Level your track -- With the air on, place a glider on the track, and adjust the track's feet until the glider can remain stationary on the track, not sliding one way or the other. c. Place ONE glider on the track, and mess around in order to: i. get a feel for how the cart moves ii. how the timers work (ask the TA for help if you are stuck) The speed of the glider on the track will be measured with photogate timers. A card 10.0cm long, placed on top of the glider interrupts a light beam in the photogate and triggers a timer. The photogate timer can be used to measure either the time for the glider to travel between two gates (when the timer control is set to PULSE mode) or the time for the card to pass through one gate (when set to GATE mode). The timer can be set to read either milliseconds (msec) or 0.1 msec. With 0.1 msec resolution, the timer will count up to a maximum of 2 sec, before overflow. 2010 Lab 1 Fall '03 ©PER@C (NF) UC Boulder

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d. In your lab notebook describe or sketch the set-up and answer the following questions: i. How are the air track / glider different from objects you normally encounter? ii. Why do we have them in lab (instead of pushing a block on a table for instance)? e. Make a couple of measurements of how long it takes for a glider to pass through a gate when you push it. Note the times in your lab books. In your groups discuss the following and answer in your notebooks: i. Are the measurements always the same? ii. What is the best method to get the most accurate measure the time it takes for a glider to pass through a gate. Take any measurement? Average all measurements? Take the middle-most measurement? Activity II. Instantaneous versus Average Velocity (10 min) Using the setups you have, play with the timers in the pulse mode and the gate mode. Note the differences in your lab books. How can you measure average velocity? How can you approximately measure instantaneous velocity? (hints: consider the definitions of instantaneous and average velocity. Which equations describe each?) Convince your lab partners of your answers to Prelab Ic (below). Collectively agree on good examples and write them in your notebook. Prelab work I: (completed PRIOR to attending lab) a. Describe the difference between average velocity and instantaneous velocity. b. If you take the average velocity over some time (say 1 hour on a car trip), is it possible that average velocity is ever larger the instantaneous velocity (at any given time during the trip)? c. What are some real world conditions where you measure instantaneous velocity, what about average velocity? Activity III. Measuring gravity part I --- preparation for a challenge. (50 min) Galileo figured out you could thin out gravity by placing an object on a slope -- that is by only having a portion of the earth's gravity pulling in the direction of motion along an incline plane. Play around with the air tracks by raising one end and placing a block under it. NEVER INCLINE THE TRACK MORE THAN 10 degrees. i. Convince yourself (make measurements) that an object accelerates faster when the track is steeper. Log your findings in your notebook. Compare each of these results to an object (not the

2010 Lab 1 Fall '03 ©PER@C (NF) UC Boulder

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glider!) that you drop straight down from the same height. (You need not measure the time of free-fall (falling straight down), but note whether the glider or object falls faster in each case). ii. Let's get quantitative. Fix your angle of incline for the track. Make it somewhere between 5 and 10 degrees. a. Measure your angle (use either a protractor or better yet measure distances and use trigonometry … See Prelab section III) b. Take measurements of how long it takes to travel different distances. Note that it will be very important to start measuring the glider from rest. What is the best way to do this? i. Measure how long it takes the glider to travel from rest to 0.25m away Do this several times and take the averages of all reasonable measurements. (Recall your work on making a measurement in Activity I --- if you have questions ask the TA). Looks like you better record these data in your lab book ii. Pick three other distances each successively further away and measure the time it takes to travel from rest to each of these distances. Do you need to make more than one measurement of each of these distances? iii. Make a table of the distance traveled (x- xo) versus time. Do you see a pattern? (No is an acceptable answer provided that you justify it) iv. Add another column to your table t2 (squaring the time). Do you see a relation between (x- xo) and t2? Try a plot of (x- xo) and t2 Make sure to label your axes, title, and use units. v. Solve for acceleration using your data and or graph. (Note: use Prelab work II below) Is this more or less than the acceleration due to gravity? Does this make sense? (why?) Prelab work II: (completed PRIOR to attending lab) 1. Solve for acceleration: Note that the equation of motion for constant acceleration is: x = xo + vo t + 1/2 a t2 (1) Now, vo = 0 (you start from rest). Solve for the quantity x - xo Solve for acceleration, a, in terms of (x - xo ) & t. 2. Given a graph plot of distance versus (time)2, which feature of the graph represents acceleration? c. Now change the incline angle of your ramp. i. Make it approximately 1/2 the height you just had. ii. Calculate the acceleration the glider experiences using the above technique. That is, if you are confident in your measurement skills you can just use one length (fix x- xo) and

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average the times for several trials. Use equation for acceleration from your Prelab II above to solve for acceleration. iii. Is this larger or smaller than the previous round? Does this make sense? Why? Prelab work III: (completed PRIOR to attending lab) 1. Trig refresher: If your track is inclined as follows: L h θ

What is θ in terms of h and L (use sine, cosine, tangent,etc)? 2. Note that if you know the angle you could calculate the acceleration of the glider, by noting that only a faction of g is in the direction of the air track and hence, g is diluted or thinned out. If you precisely know the angle you can figure out the acceleration, a, using a little trigonometry: a = gsin(θ)

(2)

What happens if θ = 0? What situation is this? What if θ is 90? What situation is this? Activity IV: CHALLENGE: (25 min) Your TA will setup an air-track at a fixed angle that only (s)he knows. You are only allowed to measure distances along the air track (only L, not vertically or horizontally). Your team will be able to make one measurement of the glider running down an air track. Based on that single measurement, predict what the angle of inclination is. Note that you have to think about a lot of experimental issues: where to place the gates, when / where / how to let the glider go, etc. You only get one shot at this so make sure it is right. If you foul up, you get a job for NASA trying to land a spacecraft on Mars. In the last 10 min of lab, each team will present their measurement of the angle with reasoning and estimated uncertainty. The team with the most accurate answer (and best est. of uncertainty) will be crowned LAB MASTERS and be so recognized in next week's recitation section.

2010 Lab 1 Fall '03 ©PER@C (NF) UC Boulder

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Lab II: Physicists Can Fix Anything Physics 2010 Fall 2003 You have come across an old grandfather clock that someone has discarded. It has a big brass pendulum that swings back and forth every second, making the clock tick forward once per swing. You are a group of artist-physicists and decide to build a new housing for the clock, decorate the face, and build a new pendulum out of materials from your studio. However, when you assemble the clock with the new pendulum, which is lighter, and longer, you notice that the clock no longer keeps the correct time. Before you rebuild the pendulum, you decide to figure out how the mass and length of the swing affect the time it takes to complete a swing (the period.) Then you can be sure you can build both an interesting and accurate clock.

Prelab 1: a) To measure the period of a pendulum, do you want to measure 1 time, 10 times, 100 times, 1000 times, 50,000,000 times? Explain why. b) What exactly is the length of a simple pendulum? Make a diagram to illustrate your answer. (Hint: In the figure of a pendulum at the end of this lab writeup, where precisely is the lower tip of the pendulum associated with length L?) c) What is the best way to measure Length, Mass and Period? (give a more detailed answer than, " a ruler, scale and watch." That is, consider parts a) and b) Pre-lab 2: For the experiment you will be doing in this lab, list two (or more) different reasons why your expect your measurements to vary and, hence, why your answers to the two lab questions may not be EXACTLY correct. Note: "Experimental error" or "human error" are not acceptable answers here, or at any time in your lab writeups! These phrases alone contain no useful or thoughtful information. Here is an example of an acceptable kind of answer: "Difficulty in using a flat ruler to estimate the radius of a spherical pendulum mass, which in turn means the measured value of L may be slightly off… " (Come up with at least two more such answers…) YOUR ENTIRE LAB: Answer the following questions experimentally and be prepared to defend your reasoning and results: 1. Does changing the mass of the object change the period? 2. Does changing the length of the string change the period?

LAB PROCEEDURE: In addition to filling out your lab notebook properly, you will have the following guidelines for lab: I. Prelab Homework Discussion: 5 min Whole Class Come into class ready to discuss your prelab … particularly Prelab 1c

II. Board Meeting: 15 min Groups of 4 Plan your experiment. Things to include: what is your goal? methods? what data will you collect? what form will your data take? how accurate are your measurements? how uncertain? Call the TA over when you feel you are ready to start taking data

III. Carrying out the Experiment 40 min Pairs Make sure you will be ready at the beginning of the second hour to present your experimental method, your data, and your conclusions about whether changing the mass or length affects the period. The goal of the presentation is to convince other students that your conclusions are correct. So, please put some thought into your presentation; it’s the main point of this lab. For instance, how will you convince a group whose measurements turned out very different from yours to believe your data? How will you convince a group that took similar data but still disagreed with your conclusions? During the Class Discussion, other students will have the opportunity to argue with your conclusions, so you’d better be ready for them!

IV. Class Discussion Whole Class 30 min Each group will present answers to at least one of these two questions. Be prepared to answer questions from fellow classmates and the TA.

V. Evaluate and Reconsider: Groups of 4 (15 min) How can you make your argument more convincing? Plan your revision. (You will not be actually doing this revised plan) Do you need a new experimental design? New data? New ways to analyze and present old data? New arguments in support of your conclusions? Call the TA over when your revised plan is ready and in your notebooks..

Warnings / Hints and other Useful Information: When you raise the pendulum for a swing, do not make it extend beyond 5 degrees.

Uncertainty: In cases where the total number of measurements is small (4 or less), then the uncertainty δT is roughly half the spread in values of T. However, if the number of measurements is large (10 or more), a more accurate estimate of the uncertainty is given by (half the spread) δT = , where N is the number of measurements. Note that, with this equation, N the greater the number of measurements, the smaller the value of δT.] €

Lab 3: energy and momentum NASA is considering hiring some grads from 2010 to design new space-suits for space-walks and work on the international space station. However, they are particularly concerned about making the suits light enough to send to space and robust enough to withstand the effects of collisions due to docking, bouncing into other space walkers, and catching flying objects in space. Thus, they have challenged you to sort our the parameters that seem to affect energy and momentum. The purpose of this lab is to study the conditions under which kinetic (or mechanical) energy is conserved, where that energy goes, and how this relates to momentum conservation. This lab will be much like the previous lab. You will be designing the experiments, conducting them, and presenting / justifying the results to the rest of the class. Note: throughout this lab you should be writing in your notebooks to turn in at the end of section. Prelab Homework: a. What does it mean for energy to be conserved? (Explain in terms of our everyday lives e.g. use an example that would make sense to someone at CU not in physics)? What about momentum conservation? In answering, consider the statements: You cannot create or destroy energy, you can only change it from one form to another [kinetic energy, potential energy, heat, acoustic energy (sound) etc.]. Likewise, you cannot create momentum out of nothing, nor can you get rid of it - you can only transfer it from one body to another. b. A 77 kg astronaut, freely floating at 6 m/s is hit by a large 36 kg lemon cream pie moving oppositely at 9 m/s. How much thermal energy is generated by the collision? [hint you have to first use conservation of momentum and THEN use conservation of energy -- It is important that you ATTEMPT this problem, but not necessary for you to complete it, if you have not covered the material in class]

Lab challenge: Using the air tracks, gliders, bumpers, wax cups, photogates, your lab notebooks and noggins, determine conditions under which kinetic energy is conserved. Your experimental evidence, reasoning and justification are far more important than the answer. (see part V for what you will be discussing / presenting).

Lab Procedure: I. Class Group discussion (10 min) Discuss your answers to Prelab a. II. Setup/ Measurement [Groups of 4] (15 min). In your teams, get a feel for the equipment you'll be using and what sorts of error you might encounter. Things to consider: - DO NOT let the equipment SLAM into anything or the track. - leveling the air track. - In this lab, you will be attaching various accessories to the ends of the Unfortunately, placing something on one side of a glider makes it unevenly weighted and causes the air cushion under the glider to be non-uniform-- the glider will slowly accelerate to one side, even though the track is perfectly level. Correct for this effect - you will probably want to use BOTH photogates if you are colliding two gliders. -- play around with the GATE mode and the READ button. These will have some sort of mathematical relation to the time in one photo sensor and the time in both photogates. - uncertainty. What are sources of measurement uncertainty? If a single cart passes through photogate one and then photogate two, should the amount of time it takes to pass differ? One way of measuring uncertainty is to consider fractional differences in time Δt 2 − Δt 1 . Repeat this experiment a few times and display your data in a table. The Δt 1 average value of

Δt 2 − Δt 1 Δt 1

is a good estimate of the fractional uncertainty of Δt avg .

III. Brainstorming (15 min) [Groups of 4] Place various accessories on the carts to get them to bounce off each other or to stick to one another. Play around with carts that are equally and unequally weighted. Can you find patterns of behavior? Do they change with initial velocity, mass, type of collision? Make a plan with your group and setup your lab notebooks to collect the data that are relevant to answering the lab question. Make sure you clearly list your research question and your experimental approach to answering it. [check out your plan with the TA]. IV. Experimental Measurements and prep for discussion ([Groups of 4] (30 min) Make your measurements and prepare to present/ justify your answers to the class. If you have sufficiently answered your research question (see topics for discussion in V), you can extend your inquiry to examine conditions under which momentum is conserved. V Class discussion / Presentations [25 min] Attend to the following: Does the mass make a difference? Does it's initial energy?

What are the most compelling forms of data? What is reasonable measurement uncertainty? (aka when are two measurements considered the same / repeatable?). Is it possible to not conserve momentum? total energy? What are factors that affect your experimental measurement? VI. Evaluate and reconsider (10 min) How can you make your argument more convincing? Plan your revision. (You will not be actually doing this revised plan) Do you need a new experimental design? New data? New ways to analyze and present old data? New arguments in support of your conclusions? Call the TA over when your revised plan is ready and in your notebooks..

gate 1

card glider 1

pin

gate 2

wax cup glider 2

air track

Flat metal contact Glider 1

Rubber band bumper

Glider 2

4.1

Physics 2010

Moment of Inertia

Experiment 4

note there are 5 pre-lab questions throughout this lab-writeup Prelab 1: When does a figure skater spin fastest, with hands out or hands in? Why? Which will win a race down a ramp: just the axle (in fig 2 or 3), the axle with the disk on it, or a frictionless cart (i.e. a glider on an airtrack)? Will mass matter? Prelab 2: Read the following background / setup, and fill in the 3 equations not yet completed (equations 4, 6, 8) Background / setup The moment of inertia I of a body is a measure of how hard it is to get it rotating about some axis. The moment I is to rotation as mass m is to translation. The larger the I, the more work required to get the object spinning, just as the larger the mass m, the more work required to get it moving in a straight line. Alloy rim wheels on bicycles have a lower moment of inertia I than steel rim wheels and so are easier to get spinning, making fast bicycle acceleration easier. The moment of inertia is always defined with reference to a particular axis of rotation — often a symmetry axis, but it can be any axis, even one that is outside the body. The moment of inertia of a body about a particular axis is defined as: I = Â m i ri2 i

where the sum is over all parts of the body (labeled with an index i), mi is the mass of part i, and ri is the distance from part i to the axis of rotation. Performing this sum is easy if the body consists of discrete point masses. But if the body is a continuous object of some arbitrary shape, then performing the sum requires the techniques of integral calculus. In this course, we simply tell you the answer for various shapes. For a disk with an axis through the center of symmetry, the moment of inertia is I disk =

1 M R2 . 2

(1)

4.2 axis of rotation R

Notice that the thickness of the disk does not enter into the expression for Idisk, which depends only on the radius and the total mass.

mass M

In this experiment you will measure I for a disk mounted on an axle. The axle can be thought of as a very thick disk and you can use the same expression to compute Idisk and Iaxle. The total I of the disk + axle is sum of these two.

R

=

+ m

axle

radius r

m disk

1 1 Itot = Idisk + Iaxle = mdisk R 2 + maxle r 2 2 2

(2)

In this experiment, you will determine I in two ways. First, you will measure the masses and radii † of disk and axle and then compute I from the formula above. Then you will compute I by timing the wheel as it rolls down inclined rails and using the principle of the conservation of energy. Consider the wheel, consisting of disk and axle, rolling down an inclined set of rails after starting from rest at the top, like so:

axle

w v

ho

(figure 3)

h

rails supporting axle

4.3 The total energy at any time is the sum of the translational kinetic energy, the rotational kinetic energy, and the gravitational potential energy. Energy = KE trans + KE rotational + PE =

1 1 Mv 2 + Iw 2 + Mgh . 2 2

(3)

Here, M is the total mass of disk+axle, v is its translational speed , w is its angular velocity, † and h is the height of the center of mass. Initially, the wheel is at rest at height ho, so its initial kinetic energy (both translational and rotational) is zero and its total energy is all potential. (4)

Energy initial = PE = ________ When the wheel reaches the bottom of the rails, h=0, and the energy is all kinetic: †

1 1 2 2 Mv f + Iw f 2 2 where vf is final translational speed and wf is the final angular speed.

(5)

Energy final = KE trans + KE rotational =

Because † the rolling friction is very small, we can assume that the total energy is constant as the disk rolls down the rails, and so the initial energy is equal to the final energy. .

(6)

=

For an axle or wheel that rolls without slipping, the angular velocity w and the translational speed v are related by † v w= (7) r Note that here and Eqn (8) below, r is the radius of the axle, NOT the radius of the big disk. † Using equations (6) and (7), one can find I in terms of M, r, g, vf, and ho.

I=

(8)

Prelab 3: Equation (8) involves g, the†acceleration of gravity. This seems to suggest that you would get a different value for I if you conducted the same experiment on the moon, where g is different. But the definition of I (Eqn (8)) does not depend on location. Like the mass m, the moment I of an object is the same on the moon as on the Earth or anywhere else. So how do you explain the presence of g in Eqn (8)?

4.4 You will use this expression to determine I using two different choices of the initial height ho, thus yielding two new values of I that you can compare with I calculated from Eqn (2). Prelab 4: Read the rest of this lab, and set-up tables for data collection. You should have sections on goals, experimental setup, and data collection tables already drawn coming into lab.

Part 0. Arriving in lab: Check off with your TA and with your lab partners the answers to pre-labs 1,2,3 10 minute class discussion on moment of inertia, spinning and energy Part 1. Measurement of I from dimensions and masses of disk and axle In this experiment, it is a good idea to use centimeters and grams, rather than meters and kilograms for all your measurements. This is because the moment of inertia of our disks turns out to be a very small number in MKS units (roughly 10-3 kg-m2) and it is a little awkward to work with small numbers. If you use cgs (centimeter-gram-second) units, you must be consistent and always use cgs units, so use g = 979.6 cm/s2 (not 9.796m/s2) Gently slide the axle out of the disk and weigh both separately to find their masses. Measure their diameters to find their radii, r for the axle and R for the disk. At this stage you do not need to know r very precisely, but you will in part 2, so measure the diameter of the axle very carefully three or four times with the calipers. Use the average of your measurements and estimate the uncertainty in r. (If you don't know how to use the calipers, ask your instructor.) Using Eqn (1), find I disk and Iaxle separately and then compute I = I disk + I axle . (Is Iaxle significant, compared to Idisk, or can it be ignored?) In using Eqn (1) to compute Idisk, we are making a small error by ignoring the hole in the center of the disk. Compare the "missing mass" of the hole to the mass of the axle to determine whether this omission is significant. Part 2. Measurement of I using energy conservation. One end of the rails can be raised and lowered to one of three positions. Place the rails in the lowest position, at which they are approximately level, and then using the adjustable screws in the base, make the rails exactly level. Use the bubble level to get a rough level and then place the wheel on the rails to get a precise level. (If the rails are exactly level, the wheel will not start rolling.)

4.5 Raise the movable end of the rails to one of the two upper positions and then fix the two starting blocks, one on each rail, at some convenient position near the top of the track. Make sure that the starting blocks are level with each other, so that the axle can be started resting against both blocks and will roll straight down the track when released. Using the meter stick attached to one rail, record the positions of the sharp tip of the axle in the starting and stopping positions and compute the distance d through which the wheel rolls. Leave the starting blocks fixed from now on, so that the value of d is the same for all timings. starting block

H2

stop H1

base adjustable feet

To determine the heights h1 and h2 through which the wheel descends, begin by measuring the height changes H1 and H2 of the end of the rail when it is raised from the level position to the two upper positions. H1 and H2 can be measured quite accurately by measuring the separations of the "notches" that hold up the end of the rail. Unfortunately, H1 and H2 are not the actual heights through which the wheel descends, since it does not roll the whole length of the rail. Instead, the situation is as shown below, where d is the distance traveled by the wheel, while D is the total length of the track (D is measured from the center of the pivot at the bottom to the center of the support at the h d top.) The two triangles shown are similar triangles, therefore = . Use this relation to H D calculate h1 and h2 from measured values of d, D, H1, and H2. †

4.6

D d H

h

Now use the stopwatch to measure the time t1 for the wheel to roll down the rail when it is in position 1 (height H1). This is best done with the same person operating the stopwatch and releasing the wheel. Make a few trial runs to determine the best procedure. Have each member of your team measure t1 a few times and record all values. From your measurements, determine an average value of t1 and estimate its uncertainty. Repeat this whole procedure for t2, measured when the rail is in position 2 (height H2). Now calculate the wheel's final speed v at the bottom of its travel for each of the two positions. Be careful! The quantity d/t is the average speed of the wheel. In the case of constant acceleration, the average speed is related to the final speed by v final = 2v average Prelab 5: Justify the above equation. [Hint consider the definition of average (using v- final and v(initial) = 0) … where † on the ramp is the velocity = average. velocity] Label the two final speeds v1 and v2. Finally, with all your measurements, using Eqn (8), compute I for each of the two positions of the rail. Be careful to display the correct number of significant figures in your final answers. Part 3: Display your three final values for I: your value from part 1 and your two values from part 2. If there is a large discrepancy among the values, comment on possible sources of experimental error. Part 4 (time permitting): As a class, using the notions of energy and conservation of energy, discuss, predict and experiment with Prelab 1 using equipment available.

Lab 5: Density, Dollars, and Detection Congratulations! You're a secret agent working for justice, truth, freedom and peace. You find yourself attempting to avoid the clutches of the evil Dr. Evil (no relation to any of your professors). You want to transport as much $$ value as possible. However Dr. Evil's stealthy agents are wary of your plans and looking for high density materials using fancy physics detectors. Thus, you wish to optimize your $$ / density ratio (by minimizing density and maximizing $). You can transport, quarters, dimes, nickels, or pennies. Which do you chose in order to maximize your $$/density? You will have access to beakers, triple beam balances, calipers (good rulers), water and string. Critically important will be for you to: a) measure the densities accurately b) know your uncertainty c) write out your experimental method d) document your results. e) present your answers to class

Pre-class challenge/homework: 0. Bring one penny, one nickel, one dime, and one quarter to section 1. Read the book (ha!) hint: issues of crowns on pg. 284 may be useful. 2. Come up with at least two ways of calculating $$/density ratio. Describe them. 3. Which will give you a more accurate measurement and why? Discuss uncertainties in each measurement you make and how they propagate through the equations you use in (2). E.g. if you measure the weight of an object W, you are not sure of this beyond a certain amount, ∂W (that is, I weigh 155 ± 0.5 lbs on a bathroom scale).

6.1 Physics 2010

Organ Recital

Experiment 6

Congratulations! You've just won yourself an audition at the world famous Juilliard School of Music. Of course, you'll be playing your favorite instrument, the organ. Unfortunately, shortly before your audition you find one of the organ pipes is broken and needs replacing. Fortunately, you recall some of your favorite days as a physics student in Boulder… You remember that the pitch (or frequency) of a standing wave in a tube is somehow related to tube itself. Being an experimentalist by nature (in addition to a world class organist) you decide to answer the following question: What are the conditions for resonance of a standing wave inside a closed tube? Being a perfectionist, and having an audition in a short two hours, you want to document your experiments, demonstrate your methodology, record measurements calculations, uncertainty and conclusions.

You

This is your lab for the day. The rest is detail.

Prelab review: (note that your pre-lab questions are at the end) Sound is a pressure wave in air. When we hear a sound, we are sensing a small variation in the pressure of the air near our ear In this experiment, we will be studying standing waves, which should not be confused with traveling waves. A traveling sinusoidal wave can be thought of as a sine (or cosine) curve that is rigidly moving to the right or to the left. The figure below shows a right-going traveling wave at two different times. The solid line is the wave at an A

l v

earlier time; the dashed curve is the wave at a slightly later time.

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6.2 A standing wave occurs when two travelling waves of the same wavelength l, the same frequency f, and the same amplitude A, but moving in opposite directions, pass through each other. The two traveling waves interfere, producing a standing wave which oscillates between large amplitude (when the two waves are in phase) and zero amplitude (when the waves are out of phase). Time 1

Time 2

+

+

=

= out of phase

in phase

One way to produce two travelling waves of identical l, f, and A, but moving in opposite directions, is to generate a travelling wave that reflects from a surface. The reflection, or echo, then combines with the original wave to produce a standing wave. The figure below shows a standing wave produced on a taut string which has its right end attached to a wall. (The amplitude of the string wave is greatly exaggerated for clarity.--you seem to recall this relates t your days as a rock guitarist) The figure shows snapshots of the standing wave at two different times; the solid curve is the wave at an instant when it has maximum amplitude; the dashed curve is the wave at an instant one half-period later. The standing wave oscillates between these two extremes. Points along the standing wave where the amplitude of motion is zero are called nodes; between the nodes are antinodes where the amplitude of the motion is a maximum reflecting wall

nodes

antinodes

l/2

l

A sound wave in air can produce a standing wave in a tube. In this experiment, a sinusoidal sound wave of variable frequency is generated by a speaker at one end of a ”University of Colorado at Boulder, 2000

6.3 tube. The sound wave bounces from the other, closed, end of the tube. As you will observe in this lab there are conditions when the tube is said to resonate, and a large amplitude standing wave forms in the tube. A movable microphone inside the tube allows us to measure the sound intensity in the tube and see where the nodes and antinodes are occurring. The figure above showing standing waves on a taut string is a plot of the displacement (y) as function of position (x) along the string. In our experiment, however, the microphone does not sense the displacement of the air; it senses the pressure of the air. So the oscilloscope will show you where pressure nodes and antinodes are occurring. One thing to verify in this lab is whether there is a node, antinode, or neither at the end of the tube when the sound resonates.

speaker

movable piston end movable microphone

tube length L Resonance occurs when L = N (l/2),

N=1, 2, 3,..

The speaker is driven by a signal generator which produces a sinusoidal voltage of adjustable frequency and amplitude. Note that there are both coarse and fine adjust knobs for the frequency.

AMPLITUDE

FREQUENCY

COARSE

OUTPUT

FINE

Function Generator

The microphone is hooked to an oscilloscope, which is a device that displays a graph of voltage vs. time, with voltage on the vertical axis and time on the horizontal axis. Your TA will introduce you to the use of the oscilloscope. If the voltage is DC, that is, constant in time, then the oscilloscope displays is a horizontal line. If the voltage is AC, that is, sinusoidal, then the oscilloscope will display a sinusoidal wave. The oscilloscope screen has 1 cm divisions on both axes. There is a volts per division (volts/div) knob, which sets the vertical (volts) scale and a seconds per division (sec/div) knob which sets the horizontal (time) scale. There are also knobs for setting the vertical

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6.4 and horizontal position of the display. There is small knob in the center of both the volts/div and time/div knobs, called the CAL or calibration knob. This should always be in the fully CW position in order for the volt/div and sec/div scale settings to be correct. Under the volts/div knob is a 3-position switch which reads (AC - ground - DC). This should always be in the DC position.

Oscilloscope Front Panel POSITION

POSITION

CH.1 VOLTS/DIV CH.2 VOLTS/DIV CAL

AC

GND

CAL

DC

AC

GND

POSITION

SEC/DIV CAL

DC

BNC connectors

Suggestions to help with your Experimental Procedure Part 0. Play around and familiarize yourself with the equipment Before starting, make sure that the two small holes in the top of the tube are covered with the sliding clips. Note that the way you will be able to tell that sound is resonant with the tube is that the microphone detects a maximal signal --- think about where the microphone should be placed. Play with the knobs and see what happens. Turn on the oscilloscope, the frequency generator, and the microphone. On the oscilloscope, turn the volts/div and sec/div knobs to see the effect on the display. Adjust the frequency and watch the signal from the microphone on the oscilloscope. Look for a maximum in the signal (resonance) when you move the piston end in or out or when you vary the frequency. If you listen carefully, you can hear when resonance is occurring; the sound from your tube will become louder (this might be difficult with several speakers on in the room). After adjusting the length and frequency for a maximum signal, move the microphone around in the tube and look for nodes and antinodes. (What can you do to make the total number of nodes in the tube larger or smaller?).

Part I. Fix the frequency and find the nodes with fixed tube length In this part, we will fix the length L and the frequency f at some resonance and then measure the positions of the nodes. At resonance, the signal on the oscilloscope screen will be a maximum. Adjust the piston so that the length L is large, and then fix the piston position with the clamp. With the microphone against the piston, set the frequency at a resonance so that there are several nodes (somewhere in the range 1500 to 2500 Hz) . Record the frequency f of the signal. Now slowly move the microphone from the piston ”University of Colorado at Boulder, 2000

6.5 end to the speaker end of the tube, while looking for nodes (signal minima) and antinodes(maxima) on the oscilloscope screen. Using the meter scale in the tube, record the microphone position x of every node. Compute the distance Dx between each adjacent pair of nodes. Does Dx change? What is the average Dx and uncertainty? Make sure you keep track of L, your frequency (f), and x for nodes and antinodes. D = N l/2

l/2=D/N

Part II. FOR THE SAME FREQUENCY, determine the effects of varying the tube length. Here we will fix f and vary L to find the resonant positions. Set the frequency as it was in part I. Start with the piston pulled all the way out (maximum L) and the microphone positioned against the piston. Slowly push the piston in, decreasing L, while keeping the mike against the piston. Record the positions x of the piston at which resonance occurs. Compute the distance Dx between each adjacent pair of resonant positions. Where are the resonances occurring?

Part III: Repeat Parts I and II for two other frequencies (in the range 1500-2500 Hz). What conditions remain the same, what change?

Part IV: Summarize your findings: If you haven't done so yet, identify what the relation between wavelength (l) and your Dx (the spacing between your nodes or spacing between your anti-nodes)? What happens to the node and anti-node spacing when you increase the frequency? What are the conditions for resonance (creating a standing wave)? Do they change with frequency?

Part V: When finished, please remember to turn off the microphone (or the battery dies). ”University of Colorado at Boulder, 2000

6.6 Appendix Pressure waves vs. Displacement waves When a sinusoidal sound wave passes through air, the air molecules are displaced from their original positions. The displacements of the air molecules at an instant in time are shown by the arrows in the figure below and by the dashed line in the bottom graph. Note that displacement to the right corresponds to a positive displacement on the graph, and displacement to the left is negative on the graph. Because of the sinusoidal displacement, there is a sinusoidal density and pressure variation. [Where density is high, pressure must be high, since p = (N/V)kT; that is, pressure p is proportional to density N/V, according to the ideal gas law.] The solid curve on the graph is a plot of the pressure vs. position. Note that the pressure peaks where the displacement is zero. Displacement nodes corresponds to pressure antinodes, and vice-versa.

Undisturbed air.

Air with sound wave present.

displacement

Solid line = pressure

Dashed line = displacement

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6.7 Prelab Questions 1. What is the relation between frequency and the sound you hear? How does wavelength figure into this? 2. What is the difference between a travelling wave and a standing wave? 3. In general, what is displayed on the screen of an oscilloscope? 4. In the figure at the end of Part I, how many nodes are there in the tube? 5. Dry lab. List out the tables you will need to collect data, your set-up and goals for the lab and any questions you have for the TA.

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Physics 2020 Labs

LAB #1: Fun with Electrostatics Physics 2020, Spring 2004 One of the downsides to living in Boulder is that annoying and painful electric shock you get when you touch a doorknob. If you’re not from around here, you may know that this doesn’t happen as often in other parts of the world. Why is this, and what physical process is going on when you get shocked? These are some of the questions you’ll discover and resolve in this lab on electrostatics. It’s always rewarding to have a solid understanding of these things we encounter everyday in our lives, and by the end of the lab, we should all have a better idea of what’s going on. In order to answer these questions, we will be using a variety of plastic rods that we can charge with a cloth (as seen in lecture). You will then figure out how to use a device called an electroscope, which will allow you to determine some of the properties of these charged plastic rods.

PRELAB QUESTIONS: (to be turned in on arriving at lab) 1) From your own experiences, describe under what conditions you tend to get shocked the most. (For example, when walking over hard wood floors, or carpet? In the summer or winter? In the morning or at night? Does it only happen when touching doorknobs?) 2) Can you think of ways that you’ve purposely tried to shock someone to annoy them? How did you do it, and did it work? 3) Go to the following link and play around with the computer simulation: http://www.colorado.edu/physics/phet/simulation-pages/electricitysimulations.htm Try the simulation called “John Travoltage.” (Move his arm and leg around and see what happens.) After playing with it, describe in your own words what you think is going on.

PRECAUTIONS & NOTES: The electroscope is a sensitive device and can be easily damaged. The small piece of gold colored foil inside is real gold! Be sure to follow these precautions during the lab: 1) Never tilt the electroscope or turn it upside down. This can tear the foil off. Just leave it on the table. 2) When you bring a charged object near the electroscope, do so from the top. Do not bring a charged object near the glass sides, as this can twist the gold foil and rip it off. 3) In order to ground the electroscope (that is, remove all the net charge from it so it’s neutral), touch the metal grounding plate to the metal ball on top of the electroscope. Touching your hand to the top of the electroscope can sometimes work, if you do not have any charge on your hands. 4) Before charging and testing the plastic rods, make sure that they are neutral first. You can ground the plastic rods by covering the metal grounding plate

with a damp towel and wipe the rods across the cloth. Always test the rod with the electroscope to make sure it is neutral first. 5) If you rub two objects together to test the charge on each, make sure you hold the side that was rubbed near the metal ball on the electroscope.

PART I: USING AN ELECTROSCOPE The questions to answer for part I of your lab are these: How does an electroscope work, and what is it good for? Imagine that at the end of this lab you have to describe how this thing works to a friend who has never seen an electroscope. Answer this question and be prepared to defend your explanation and reasoning. Here are some things to get you started: A. Take one of the plastic rods and charge it up by rubbing it with a piece of wool. Now take your charged rod and bring it near (but not touching) the ball of the electroscope. Observe what happens and explain in your own words what you think is going on. B. Now take a charged rod and touch it to the metal ball on the electroscope, then take the rod away. Again, observe what happens and record your results. C. After touching the metal ball with the charged rod, what happens when you bring another charged object towards the electroscope? Try to figure out why you would want to do this, and what information it can give you. Record your thoughts and observations. D. Try anything you like now and get a feel of how the electroscope is used. Figure out what this thing is useful for; that is, what can it measure, and what can it not measure? Can you measure the sign and magnitude of the charge? Do you think you can make any quantitative measurements?

PART II: WHICH ROD CAN HOLD THE MOST CHARGE? On your lab table, you should have about 6 different pieces of plastic. The shapes and colors of the rods all differ, but the important thing to know is that they are all composed of different materials. Therefore, they should behave differently when you try to charge up each rod. We already know that when rubbed with wool, the plastic become negatively charged (the plastic wants to hold these negative charges, so it takes them from the wool). However, what happens when you rub two neutral plastic rods together? Which one becomes negative and positive? The answer will depend on which rod wants to get those negative charges the most. So this is the goal of part II of your lab: figure out which rod can hold the most negative charge. Here are some ideas to get you started: A. Your group will need to devise a plan and procedure to test each pair of rods against each other to see which one in the pair can hold the most negative

charge. form?

If there are 6 plastic pieces in all, how many different pairs can you

B. First charge the electroscope with some charge, either negative or positive—it’s your decision. C. Take a pair of plastic rods and make sure they are neutral first. Rub the two rods together to charge up each one, and test each with the electroscope. Can you tell which one is positive and which one is negative? Be careful to record all your findings clearly so that both you and your TA know exactly what you did. Also make sure you understand the whole procedure clearly. Be sure to answer the following: Why do we start with a charged electroscope instead of a neutral one for these tests? Why can’t we charge up each rod and compare all of them at once with the electroscope?

PART III: ALUMINUM CAN RACE And now for the fun part. Once you have determined which plastic rod can hold the most negative charge, challenge another group to a race. Here’s how the race goes: if you lay a soda can on its side, you can get the can to roll towards your charged rod. Try it! Line up 2 soda cans and see which one of you can get the can across the table the fastest without touching the can with the rod. You are allowed to use any tricks and insights that you learned from the lab to make your can go faster, including “preparing” the can before the race. However, once the race starts, you cannot touch the can or blow on it. Betting on the race is not required, although it is highly encouraged.

LAB #2: Fun with DC Circuits Physics 2020, Spring 2004 The field of electronics has revolutionized the way we live and what we do. We can find circuits everywhere—from our cell phones, digital watches, calculators, televisions, computers, etc. Understanding how these things work is interesting in their own right, but from this we can figure out how to do more practical things, like design and install our own car stereo system or make sure that we do not electrocute ourselves. In this lab, we will first look at a few simple DC circuits that will give us an idea of how these things work in the first place. We will learn how to use a DC power supply and an electrician’s best friend—a digital multimeter (DMM).

PRELAB QUESTIONS: (to be turned in on arriving at lab) 1) Read the lab thoroughly and chapters 19.1 to 19.5 of your text. 2) Thought experiment: Can you use a single light bulb, a single battery and a single wire to light the light bulb? Draw a diagram if it can be done. 3) For the circuits below, rank the brightness of the bulbs from brightest to dimmest. Note all batteries are identical and ideal. All light bulbs are identical and ideal. Note also that bulb brightness reflects the power dissipated in the bulb and that the bulb is just like a resistor.

4) In 50 words or more describe why the bulbs are ranked as they are. Present your reasoning in every day language so that a friend who has never taken physics would understand your reasoning for why you ranked the bulbs as you did (you can use words like voltage difference, current, energy, etc, but no explicit formulas). 5) Look at the picture on the following page. Select the schematic diagram for the resistors and power supply shown in the picture.

voltage source -->

wire --> resistor -->

(A) (B)

(D)

(C)

(E)

PRECAUTIONS & NOTES: The two instruments you will use in this lab are a DC power supply and a digital multimeter. The DC power supply produces a constant voltage, which voltage can be adjusted anywhere from zero to 30 volts coarse with the voltage knobs (coarse and fine) on the voltage front panel. The power supply has three output fine terminals: plus (red), minus (black) and ground (green). The ground terminal is always at zero volts. In this experiment, the ground and minus current terminals are tied together by a metal connector current so the minus terminal is also at zero volts. Both the current and voltage produced by the power + supply can be read on meters on the front panel. Also on the front panel is a current-limit knob, which can be adjusted to limit the maximum metal connector output current, to prevent damage to sensitive circuits. In this lab, the current knob has been set and clamped in place so the power supply cannot produce more than about 0.6 amps.

DC Power Supply

-

The hand-held digital multimeter (DMM) is a wonderful little device which can be used to measure the voltage difference between any two points in a circuit, the current, and the resistance or capacitance of any circuit component(s). In this lab, we will use the DMM to measure both resistances and DC voltage differences. There are 2 wires attached to the DMM. One of the two wires always goes to the COM (common) terminal. To measure either the voltage difference or the resistance, the second wire is attached to the “VΩ” input. In this lab, all our measurements will be DC, so the DC/AC switch (upper right) should always be in the DC position. The DMM has an alarm; it rings if you have wires plugged into positions which conflict with the central knob’s position. The 2 wires attached to the DMM are called "needle probes". You can quickly measure the change in voltage between any two points in a circuit by touching the points with the needle probes. When measuring a resistance with a DMM, you must disconnect the source

V

Measuring a resistance with the DMM.

DC DC AC

V DMM Ω com VΩ needle probes

of the resistance from any other devices, such as power supplies. measure the resistance of a resistor while it is still in a circuit.

Never try to

PART I: MEASURING RESISTANCE Your goal of this part of the lab is the following: Figure out how to measure the resistance of various things using the DMM. At your table, you should have 5 resistors: one 15Ω, one 40Ω, one 1500Ω, and two 3000Ω resistors. These values are given by the manufacturer and are approximate. Each resistor is mounted in a double-banana plug connector. Carefully measure the resistance of each resistor with your DMM and record your measured resistances. You should also have two light bulbs at your table. Use the DMM to measure the resistance of each light bulb filament, and record your results. What is the resistance of other things around you? The tabletop, your hands, your lab partner, your lab book, etc. Explore. Are these consistent with how well these materials conduct electricity? It is up to your lab group to create 2 different resistor combinations using some (not all) of the 5 resistors. Create circuits that have both parallel and series combinations in them. Draw a picture of each combo of resistors in your lab book, and predict the equivalent resistance of that combo. Then measure the resistance of the combo and see if your prediction matches—does it?

PART II: CIRCUIT BEHAVIOR Now that you understand how to use the DMM, you will now build a circuit and investigate its behavior. Construct the circuit shown below, consisting of two light bulbs in series with the power supply. (The resistor R will be added later). Slowly increase the voltage until the bulbs are glowing, but not too bright. Predict what will happen to the brightness of the bulbs when you place a R = 40Ω resistor in parallel with bulb #2 as shown in the schematic. Go ahead and add in the resistor, and describe in your own words what happened and why. Measure the voltage across the light bulbs and resistor and verify that they match your prediction (i.e., if you know the power supply voltage and all the resistances, do the other voltages make sense?).

R

V

1

2

Do the same thing for 2 other resistor values and describe what happens in each case.

PART III: MEASURING RESISTANCE IN MULTIPLE WAYS In Part I of this lab, you learned how to measure the resistance using the resistance feature on your DMM. Go back to one of the circuits that you built in Part II and measure the resistance of the resistor in parallel with bulb #2 without using the resistance setting on your DMM. Your group will have to figure out a clever way to do this using the power supply and the other features of your DMM. Describe in detail how you were able to accomplish this. Note: Besides not being able to use the resistance feature on your DMM, make sure that the light bulbs are still glowing when you take any measurements.

LAB #3: Fun with AC Circuits Physics 2020, Spring 2004 In the previous lab, we studied some simple DC circuits, where all the voltages and currents did not change with time. What happens when the voltages and currents do change with time? It turns out that we live in a world where most circuits are in fact AC instead of DC. In this lab, we will explore two different applications of AC circuits—electrical impulses from our own hearts and transformers. Feel free to ask your TA why we have AC circuits rather than DC.

PRELAB QUESTIONS: (there are more pre-lab questions on p. 3) 0) Read the entire lab. 1) The picture to the right is a typical display you may see on an oscilloscope. What are the period, frequency and amplitude of this voltage signal? Assume that the volts/div setting is 50 V/div and the time/div setting is 5 msec/div.

NOTES AND PRECAUTIONS: 1) In all your measurements and observations, include a careful picture of the display, and be sure to indicate the horizontal and vertical scales (in SEC/DIV and VOLTS/DIV, respectively). 2) In Part II of the lab, only connect the battery to the coil when you are testing it. Immediately disconnect the battery when you are not using the coil. This will drain the battery, and guess who will have to pay for a new one? 3) Be sure to listen to your TA for other precautions.

PART I: MEASURING SIGNALS FROM YOUR HEART (45 mins) Every living person's heart produces electrical signals that can be measured on the surface of the skin. An EKG (electrocardiograph) is an instrument that can measure these signals and produce a visual image (and sometimes an audible sound, as in the "beep . . . beep . . . beep . . .” you hear in movies) of the signal your heart produces. Your goal for this lab is to obtain an accurate recording of this voltage signal from one of your lab mates, and to determine what things affect this signal. Why the acronym “EKG” instead of “ECG”? Actually, both are used, but “EKG” comes from the German word "Elektrokardiogram." It has stuck around and is used more often for historical reasons. Our makeshift electrocardiograph is made from an oscilloscope, which is a very useful tool for measuring voltages that are changing in time. Think of the oscilloscope just like the DMM we used in the last lab—it measures voltage, but now it maps it out in time. The screen on the scope displays voltage vs. time (voltage

on the vertical axis and time on the horizontal axis). The grid that you see on the screen is used to measure the voltage and time of your signal—think of it like graph paper. Each little box on the grid is called a division, and you can adjust the scale of the voltage and time axes with the volts/div and the sec/div knobs, respectively. For example, if the volts/div knob is set to "5", this means that each box on the grid is equal to 5 volts. These are just the basics on what this device is used for, but your TA will give you a short intro on how to properly use an oscilloscope. Your heart is a complicated electrochemical machine that produces time-varying voltages as it beats. These heart voltages produce small voltage differences between points on your skin that can be measured and used to diagnose the condition of your heart. Usually, nine electrodes, positioned at various points of the patient's body, are used when recording a full electrocardiogram. However, in this lab, we will only use two electrodes to measure the voltage between your right and left hands.

A typical plot of voltage difference between two points on the human body vs. time is shown above. The P deflection corresponds to the contraction of the atria at the start of the heart beat. The QRS group corresponds to the contraction of the ventricles. The T deflection corresponds to a recovery (or re-polarization) of the heart cells in preparation for the next beat. Every heart pattern is slightly different, and the interpretation of an EKG requires experience with many patients. The EKG apparatus that you will use consists of two electrodes, an amplifier, and a storage oscilloscope. Signals travel from the hands, one placed on each electrode, to the EKG amplifier and then on to the oscilloscope. The voltage that is measured is the potential difference between the two electrodes. However, the voltage difference between your hands is inconveniently small to measure directly. To compensate for this, the signal from the electrodes is given a boost by the amplifier. Enough talk for know...let's get to business: A. You should have a battery at your lab station. Play around with the battery and make sure you understand how to measure its voltage correctly using the oscilloscope. B. The voltage displayed on the oscilloscope differs from the input voltage of your hands by an amplification factor. To find this factor, switch the amplifier mode

switch to "calibrate" and then press the red button—this produces an input voltage whose peak (positive) value is 1 mV = 10-3 volts. Measure the voltage on the oscilloscope, and determine the amplification factor of your amplifier. C. Have one person in your group sit down in front of the electrode assembly with his or her hands wrapped gently around the electrodes, palms down. Adjust the settings on the oscilloscope until you can see a full EKG signal on the screen (this may take awhile to get a nice picture on the screen). Draw a picture of the EKG in your lab notebook and record any specific details of the signal that you can measure. Using the amplification factor, what is the actual voltage produced by your lab mate’s heart? D. Now grab and squeeze the electrodes with your hands. voltage signal, and what could explain this?

What happens to the

E. Now adjust the oscilloscope so that you can see at least 2 peaks on the screen, and record your observations. Figure out a way to measure the pulse rate of your lab partner from this data. F. After everyone in your lab group feels they have a solid understanding of what you are measuring and how you exactly do it, predict what would happen if two people holding hands were to touch the electrodes (that is, on person grabs it with their right hand and the other person grabs the other electrode with their left hand). Record your prediction and test it to see if you’re right.

PART II: ELECTROMAGNETS AND TRANSFORMERS (45 mins) PRELAB QUESTIONS: 2) What do transformers do, and why are they useful? 3) Does a transformer work for DC or AC current? What would the transformer do if you plugged it into a DC circuit? Why? Simply put, an electromagnet is just a coil of wire. That’s it—just a bunch of wire. You may think that this will be the most boring lab in the world because you’re going to play around with a bunch of wire, right? Well, it turns out that electromagnets are extremely interesting and are found all over the place—electric motors, speakers, your car, etc. Your goal in this part of the lab is to figure out what makes electromagnets stronger and weaker, and to figure out how electromagnets and transformers are related. A. First, build an electromagnet. Take a 3 ft. long piece of wire and wrap it around one of the rods you have (wood, iron or aluminum) and secure the ends with electrical tape (see figure below). Count and take note of the number of turns of wire that are wrapped around the rod. Draw a picture of it in your lab notebook.

B. Connect your coil of wire to a battery and see how your electromagnet works. Can you pick up small metal objects with it? If so, how many? C. Now make another electromagnet with the same number of turns, but with a different rod this time. Is the electromagnet stronger or weaker? Use all 3 materials and rank them on how strong they make your electromagnet. D. Reduce the number of turns by one-half. Did this strengthen or weaken your electromagnet? E. Reflect on these observations—given what you know about magnetism, do your observations make any sense at all? F. Now you will build a transformer (as shown in the figure below). For the primary coil, it is best to combine two of the 3 foot wires into one long wire and wrap them on the iron coil. Now take one of your longer 12 foot wires and wind it over the top of the primary coil as shown in the figure below. Count the number of turns as you wind. This will serve as your secondary coil. Secure both ends with electrical tape. Is this a step-up or step-down transformer, and what does this mean?

G. Hook up the primary coil (your original electromagnet) to the battery. Does the LED light? Remember, the battery provides a DC current. In your report, describe under which conditions you can light the LED and be sure to explain its behavior.

H. Find out what happens if you reduce the number of turns of the secondary coil. (You may have to change it by quite a bit to see a substantial effect.) Describe and explain what goes on in your lab report.

LAB #4: Fun with Light and Lasers Physics 2020, Spring 2004 For quite some time, scientists believed that light was composed of tiny particles that carried energy. It wasn’t until the early 19th century that people started to view light as a wave instead of a constant stream of mysterious particles. In this lab, we’ll explore some of these early experiments that convinced scientists of the wave-properties of light, and how they can be useful.

PRELAB QUESTIONS: 0) Read chapter 24 of your text. 1) On p. 729 in your text, Fig. 24-10 shows the intensity pattern from interference on a distant screen produced by light going through a screen with a double slit. Suppose that a single change were made to this configuration. In each case, determine how the resulting intensity pattern would change (draw a picture and describe how the pattern changes): A. The width of each slit is decreased (while keeping the distance between the slits constant) B. The distance between the slits is increased (while keeping the width of the slits constant) C. The screen is moved closer to the double slits D. The wavelength of the incoming light is decreased

PRECAUTIONS & NOTES: 1) 2) 3) 4)

Do not look into the laser beam. Do not move the laser. Do not put your head near the laser beam. Last but not least, do not look into the laser beam.

PART I: Interference From a Double Slit Experiment Before you begin taking any data or observations, play around with the equipment in order to get a feel of how you set things up and what kind of light patterns the various slits produce.

1 1.43 _ 1 0.755

1 0.345

1 0.195

1

15 0.05 0.176

1 0.05 _

1 0.107 _

30 0.05 0.088

2 0.05 0.132

2 0.10 0.175

3

75 0.01 0.034

0.05 0.132

2 0.10 0.35

37 0.027 0.066

4 0.05 0.132

2 0.10 0.70

20

10 0.05 0.132

2 0.10 1.40

Now go back to your predictions you made in pre-lab question #1. Make sure all your lab mates agree on what s h o u l d happen and why. With the available equipment you have, determine which predictions you can test, and which ones you cannot. For the changes that you can make, set up an experiment to test these changes. Record in your lab notebook a picture of the setup, what you did, how you did it and what the results were. If any of your predictions are incorrect, you’ll have to determine if your experiment or your original prediction itself is wrong.

The diagram on the left is a picture of the mask containing all the slits that 0.088 you will use for this experiment. The mask consists of an opaque photographic negative, containing several single, double and multiple slits. This particular plate is often called a Cornell Plate, since apertures of this kind where first used at Cornell University. Next to each set of slits, you will see 3 numbers. The top number indicates the number of slits, the middle number is the width of the slit(s) and the bottom number is the distance between the slits (in millimeters). 0.108

0.044

PART II: Interference and Diffraction Combined So far, you have learned what an interference pattern looks like and what a diffraction pattern looks like. The diffraction pattern arises because of the behavior of light as it passes through a single narrow slit. For the interference pattern, we also have light passing through narrow slits. So, shouldn’t we get some sort of diffraction effect with a double slit, in addition to the interference effect? This is the question you’ll be addressing in Part II of the lab. Here are some things to get you started: A. Use the single (D=0.107 mm) slit to create a pattern on the screen. Take note of the bright and dark spots from this pattern. B. Now compare that pattern to the one produced by the double slits (D=0.10 mm, d=0.175 mm). What are the similarities and differences between the two different patterns? Do the two have anything in common? Again, trace out a few diagrams of the patterns so that you can compare them. (Notice that both the single slit and the double slits all have the same slit width, D.) C. After you feel comfortable with parts A and B, compare the single slit (D=0.345 mm) to the double slit (D=0.10 mm, d=0.35 mm) pattern. Again, what are the similarities and differences between the two patterns?

D. Can you say anything in general about what the intensity pattern will look like for a double slit? (i.e., where will the bright and dark spots be?)

PART III: Measuring the Wavelength of Light The laser you are using is a He-Ne laser (He-Ne stands for helium-neon, which are the two elements inside a glass tube that makes up the heart of your laser). We know the laser light is red, and that the light is monochromatic (meaning only one wavelength is produced). But what is this wavelength? Figure out a way to measure the wavelength of the light from your laser using all the lab equipment you have. Once you obtain an answer, make sure it makes sense. Compare your answer to other groups in the class and see how can get the most accurate result.

LAB #5: Fun with Optics Physics 2020, Spring 2004 Although it may not be obvious at first, we all heavily rely on optics everyday. Many of us wear corrective lenses or contacts to see—in fact, our eyes themselves contain lenses. There is an array of other fields, from photography to communications, that all take advantage of optics. In this lab we will study converging lenses and discover some of their useful properties.

PRE-LAB QUESTIONS: 0) Read chapters 23 and 25 of your text. 1) In your own words, what is so special about the focal point of a converging lens? 2) Imagine that have just made an image with a lens. Predict what would happen to the image if you covered the top-half of the lens with a piece of paper. Justify your reasoning. 3) What does it mean for a beam to be collimated? Using a point source of light and a single converging lens, how could you produce a collimated beam? Before diving into the experiment, let’s review over a few concepts that we have learned so far. When a bundle of parallel light rays enters a converging lens, the rays are focused at a point in space a distance f (the focal length) from the lens. A converging lens is convex in shape (it’s thick in the middle and thin at the edges). A diverging lens is concave in shape (it’s thin in the middle and thicker near the edges).

f

f

Converging lens, convex

Diverging lens, concave

A converging lens can be used to form an image of an object on a screen. The lens equation relates the focal length f of a lens, the object distance do and the image distance di ,

1 f

=

1 do

+

1 . di

(1)

(This equation can used for both converging and diverging lens; the only difference is that the focal length f is positive for converging lenses and negative for diverging lenses.)

do ho

F object

image

F

hi

optic axis

di

In the diagram above, the points labeled “F” are the focal points of the lens. The lateral magnification m of the image is defined as m= one can show that m can also be written as m=

hi . From the diagram above, ho

di . do

PART I: Verify Pre-lab Question #2 (20 min) In this lab, you will use an optics bench, which is simply a rail, on which lenses are placed, with a ruler on the side for measuring distances. The other equipment includes a bright light source, which acts nearly like a point source, and two converging lenses labeled A and B. There is a frosted glass screen, labeled "I", on which you can view images. Finally, there is a metal plate with a hole in the shape of an arrow. The hole is covered with scotch tape. When this aperture is placed in front of the light source, it forms a convenient object for image-forming experiments. Play around with the equipment for awhile to get a feel of how things work and how the different lenses affect the image. Now test your prediction from pre-lab question #2 by covering half of the lens. What happens to the image? If your prediction is wrong, try to figure out what is going on.

PART II: Measuring Focal Lengths (10 min) Now figure out how to measure the focal lengths of both lenses. Record your procedure and results in your lab note book. (NOTE: there is more than one way to measure the focal length)

PART III: Slide Projector (30 min) With the popularity of digital photography, slide projectors are slowly becoming a thing of the past. However, some photographers still prefer to use them because of

their ability to produce a large image of a slide. Your TA has a couple of slide projectors that you can use to analyze. Here are some things to get you started: A.

After playing around with the slide projector, draw a picture of its major components (lens, slide, screen and light source). Explain in your own words why they are set up in this orientation (i.e., why is the slide always on one particular side of the lens, and not the other?)

B.

What is going on when you focus the image of the slide? change the focus?

C.

Is there one unique configuration of the light, slide, lens and screen, or are there multiple configurations that produce a clear image?

D.

Figure out a way to measure the focal length of the lens and what type of lens is being used for the slide projector. Is it a converging or diverging lens? Does this make sense for what it is being used for?

Why does this

Be sure to describe in detail where everything is located in your slide projector and why it’s located there. Make a nice diagram in your lab notebook.

PART IV: Making a Telescope (30 min) In this part of the lab, you will make a telescope. What are you waiting for? Get going! Try to make a telescope (using both lenses) with the largest angular magnification possible. As usual, describe in detail how you set up your telescope. Now aim your telescope at the wall and look at the picture with an arrow and a graduated scale. You should already have calculated the angular magnification of your telescope, but now try to use the picture on the wall to estimate and measure the angular magnification. A. Do the two different measurements agree? B. With just the two lenses you have, is it possible to make a different telescope with a different angular magnification? C. Determine the critical factors in designing a telescope. diameter? Focal length? etc.

What matters?

Lens

D. If your TA has access to a third lens, get one, measure its focal length and determine whether or not you can improve your telescope with this new lens. Note: the more you prepare in your lab notebook in advance, the more thorough and easier your lab write-up will be in section.

LAB #6: Fun with Atoms Physics 2020, Spring 2004 If we were to give you a solid block of material, you could probably find out what it was made of. You could measure its density, see if it conducted electricity, whether it could hold charges, etc. and compare that info to existing data. However, what if we gave you a tube filled with gas? How would you determine what type of gas is inside? It seems a little harder to analyze this. However, there are other properties of atoms that we can look at—the way atoms emit and absorb light is very unique, which gives rise to a unique spectral signature or "fingerprint." In this lab, we will use a spectrum analyzer to see what colors of light atoms emit, and from that information, determine what flavor of atoms we are looking at.

PRELAB QUESTIONS: 0) Read chapter 27 of your text (you may not have covered this in class yet, but that’s okay). 1) From the Bohr model of the hydrogen atom, calculate the minimum amount of energy (in eV) an electron in the lowest orbital (ground state) would need to free itself from the proton. This is what is meant by “ionizing” the atom. How is this problem similar to calculating the escape velocity of a mass from the gravitational effects of a larger mass (for example, a rocket being launched from Earth into space)? 2) The colors of the four lines of the hydrogen spectrum are: red, blue-green, and two shades of violet. Which initial states ni = 3, 4, 5, or 6 correspond to these colors? 3) The grating equation (d sin θ = mλ) tells you at what angles different colors of light will appear. Make a sketch based on the figure below to show a beam of white light shining onto a grating with line separation, d = 1500 nm. Show the angles for red and blue light for m = 0, +1 and –1. You can find the approximate wavelengths for red and blue light in your book.

Show on your figure each of the places where you could place your eye if you wanted to view red light. (Draw an eyeball in the appropriate place and label the rays). What color would you see if viewed the m = 0 beam?

PRECAUTIONS & NOTES: 1) Be careful with the discharge tubes. It’s best not to touch the glass tubes. 2) Do not drop the diffraction gratings. DIFFRACTION GRATINGS A diffraction grating is simply a piece of glass or plastic which has a series of very fine scratches or grooves cut in its surface. The grooves are perfectly straight and parallel and are equally spaced so that there are a fixed number of grooves per millimeter, typically around 500 grooves/mm. A grating behaves essentially like a screen with a bunch of equally spaced slits. If the number of slits per length is n (grooves per mm), then the separation between adjacent slits is d = 1/n (mm per line or simply, mm). Consider what happens when a beam of monochromatic (single wavelength) light strikes a grating at normal incidence, as shown below. Each slit scatters the light in all forward directions. However, in only certain directions will the light scattered from different grooves interfere constructively, producing a bright beam. This is just like the single & double slit diffraction you have done.

to observer scattered light θ d d sinθ

d incident beam wavelengthλ

grating

The diagram (above, right) shows two light rays emerging from adjacent slits in the grating and heading toward an observer (or a point on a screen) at an angle θ from the normal (perpendicular) direction. In traveling to the observer, the ray from the lower slit has to travel an extra path distance; this path difference is d sin θ . The two rays will interfere constructively only if the path difference is an integer number of wavelengths: (1)

d sin θ = mλ

where λ is the wavelength of the light and m is any integer. At only those special angles corresponding to integer m's (m = 0, 1, 2,...) will the rays from all the slits

interfere constructively, producing a bright beam in that direction. The integer m is called the order of the diffraction. An incident light beam made of several different wavelengths will be split by the grating into separate wavelengths, with each separate wavelength heading in different directions, determined by equation (1) above. In this way, the various wavelengths can be determined by measuring the angles. BOHR MODEL OF THE ATOM In the 19th century, it was known that hydrogen gas, when made to glow in an electrical discharge tube, emitted light at four particular visible wavelengths. In 1885, a Swiss high school teacher named Balmer discovered that the four wavelengths (here labeled λ i where i = 1, 2, 3 & 4) precisely obeyed the mathematical relation:

1 1 1 = R − λi  4 ni2

(2)

  

where R is a constant, and ni = 3, 4, 5 & 6. The four wavelengths (or "lines") were henceforth called the Balmer lines. Why hydrogen emitted only those visible wavelengths and why the wavelengths obeyed the Balmer formula was a complete mystery. The mystery was solved in 1913 by the Danish physicist Niels Bohr. According to the Bohr model, the electron orbiting the proton in a hydrogen atom can only exist in certain orbital states labeled with a quantum number, n (n=1, 2, 3, 4...). When the electron is in orbit “n”, the total energy of the hydrogen atom is given by the formula: (3)

E n =−

Rhc 13.6eV =− , n2 n2

where c is the speed of light, h is Plank’s constant and R is a number predicted by the Bohr model called the Rydberg constant. The different energies En correspond to different orbital states of the electron. Smaller-radius orbits correspond to lower values of n and lower, more negative, energies. The n=1 state is the lowest possible energy state and is called the ground state. When an electron makes a transition from an initial state of higher energy Ei to a final state of lower energy Ef , the atom emits a photon of energy

(4)

E γ = hf = h

c = Ei − Ef λ

Here we have used the expression for the energy of a single photon: E = hf, where h is Planck's constant and f is the frequency of the light. From equations (3) and

(4), the wavelengths of the emitted photon are related to the initial and final quantum numbers like so:

(5)

 1 hc 1 = E i − E f = − R hc  2 − 2  λ  ni n f 

,

 1 1 1 = R 2 − 2 λ  nf n i  .

This is none other than Balmer's formula! Transitions between any pair of states such that ni > nf produces a photon; however, only the Balmer lines produce photons in the visible range of wavelengths.

PART I: Using a Spectrometer For this lab, you will be using a simple spectrometer that separates light into its individual components. Point the spectrometer at the fluorescent lights on the ceiling and look through the diffraction grating. You should see a scale that is used to represent the wavelength (in nanometers) and a series of colored lines on the scale. We can now see that the white light is actually composed of a couple of different, yet distinct, wavelengths of light. These are the wavelengths of light emitted by the atoms in the fluorescent tube. Let all the group members play around with the spectrometer and get a feel for how it’s used. A. You will have to calibrate your spectrometer by carefully moving the scale (black strip of plastic) either back or forth so that the green line observed from the fluorescent lights is at the known value of 546 nm. What are the other wavelengths you see? What colors are they? Does this make sense? Why does your eye see white light if you directly look at the fluorescent lights? B. You should have another light source (aka discharge tube) at your lab table. Turn it on and view its light with your spectrometer. Record the wavelengths of light you observe as accurately as possible. Around the corner from the lab (ask you TA), there is a large poster of pictures of known spectrums of various substances. Compare what you observed with what is given on the poster, and try to determine what type of gas is inside the discharge tube. Are you sure this is the correct gas? Why or why not?

PART II: Making Your Own Spectrometer Now you will make your own (and more precise) spectrometer using a diffraction grating and a meter stick. This should give you some insight as to how a spectrometer works. Observe the hydrogen source through the grating provided. In the first order spectrum (m=1, the first peaks of each color), you should clearly see three lines: red, blue-green, and violet (some people can see a second violet line, if the room is dark.)

Arrange the hydrogen lamp and the diffraction grating on your lab bench, as shown

meter stick grating L

eye

H-lamp

θ x

position of a Balmer line

images of Balmer lines

below. Set them on supports to place them at a convenient height for your eye. Position the grating exactly L=1.00m from the lamp and orient the grating so that it is perpendicular to the line from the lamp (that is, have the grating squarely face the lamp). Place your eye very close to the grating and look through it toward the hydrogen lamp. On both sides of the lamp (above and below), you should clearly see the images of the first-order Balmer lines. (Be careful to keep the grating facing the lamp. Move your eye position, not the grating, to see the lines to the side of the lamp.) With a meter stick as close as possible to the lamp, as shown, measure the xpositions (on both sides of the central position) of each of the three lines as accurately as possible. With your measured L and x's, compute the angle θ of each of the first-order Balmer lines. (Hint: use tanθ = x/L) Make a table of your results in your lab book. Leave space for extra columns to add other calculations. Now that you understand what you’re looking at, try to compute the wavelengths of each of the (three or four) Balmer lines that you observe. Include a rough estimate of the uncertainty of your wavelengths (i.e., what part of your experiment may be inaccurate?). Record your method and results in your lab notebook. Which spectrometer is more accurate? Why?

PART III: Everyday Substances Using the same procedure as above, observe the light from the fluorescent lights on the ceiling. Make a careful drawing of the spectrum lines and their measured wavelengths in your lab notebook. Now do the same thing for the incandescent light bulb at your lab table. Both of these appear white(-ish). What is the difference between them?

PART IV: Mystery Substances (time permitting) At the front of the lab, there should be a variety of mystery sources (in discharge tubes). Use either the “meter stick spectrometer” you just made, or use the small, blue, plastic one. Record the emission lines you observe and try to figure out what elements you are looking at. You may consult the poster or your textbook to figure this one out