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Laboratory RevisionsPhysics 2010

andPhysics 2020

modifications and studies of the laboratory sequence forintroductory algebra-based physics

N. Finkelstein and C. Keller2003-2004

supported by:

ANDThe Department of Physics

at theUniversity 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 latestversions of the labs for 2010 and 2020.

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PROJECT DESCRIPTION

While undergraduate laboratories are considered an essential element of studentlearning in introductory physics, the laboratory experience remains a highly variableone. 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 inphysics1 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 evaluationcomponent described below) was supported by the LEAP initiative with a fractionaltime appointment of graduate student (Chris Keller).

The approach we have taken in the re-write of the labs has been to appropriatesome of the work of Rebecca Lippmann and Edward Redish at the University ofMaryland.2 The Maryland labs simultaneously focus on students’ conceptualdevelopment, their laboratory skills, and views about physics (what it means tolearn physics, conduct experiments, and justify findings). Simultaneously weattempted to reference real-world situations which were engaging and genderinclusive.3 Our emphasis on group consensus and epistemological development hasbeen tempered by pragmatic concerns about maintaining the actual physicalequipment from prior years, making sure that TA’s could conduct these labs, andinsuring continuity with the rest of the course (and the existing traditions from prioryears). In short, we attempted to move the labs from labs of verification to labs ofdiscovery and inquiry. Such a procedure also follows work from the chemistrycommunity in the last few years.4

LABORATORY REVISION PROCEEDURE

The first drafts of the 2020 labs were composed by Chris Keller. These labs werebased on the previous Physics 2020 labs (by Michael Dubson), labs used at UCSDby Noah Finkelstein, and the labs developed at U Maryland. The drafts were thenreviewed by Finkelstein, and tested in the actual laboratories by the students andteaching assistants. The 2010 labs were revised by Finkelstein building on theearlier versions created by Dubson. Constant feedback from the TAs was collectedthroughout the semester, and a more detailed evaluation was conducted at the end

1 E. F. Redish, Teaching Physics with Physics Suite, Wiley 2003.2 R. Lippmann, Students' understanding of measurement and uncertainty in the physicslaboratory: 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/

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

QUANTITATIVE DATA

The quantitative data collected from the TAs is shown below. Three differentcharacteristics are used to describe the labs: learning experience for the students,student enjoyment and improvement from the previous labs. The scores are theaverage responses from all the TAs on a 4-point scale (4=good, 0=poor).

TA Perception of Labs

0

1

2

3

4

1 2 3 4 5 6

Lab #

Rati

ng

Learn

Enjoy

Improve

A few notes about the above data are in order. We were generally satisfied withthe ratings of learning experience and student enjoyment. The improvementratings may seem low, but that is the nature of the rating system—anythingpositive is considered good. In addition, since our inquiry theme for these labs mayseem rather different and unfamiliar to the TAs, their perception of theimprovement may be lower than expected. However, the real test is whether ornot these students were able to learn more physics concepts and develop vitallaboratory and critical thinking skills, compared to students from previoussemesters. Both anecdotal evidence and learning gains on some of the materialspresented in the class suggest so. However, a controlled test of this sort was notfeasible, given our resources and timing. One could perform this task, but that wasnot 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, commonmisconceptions, pitfalls and precautions are all described to the best of ourknowledge. It is highly recommended that the instructor and TAs read these notesprior to running the labs with the students.

LAB #1: Fun with ElectrostaticsFor the first lab of the semester, the students get to experience and see thebehaviors of electrostatics. They have 6 plastic rods, various pieces of cloth and anelectroscope to get a visual idea of how electric charges interact.

PRECAUTIONS: Make sure the students do not tear or rip the gold leaves in theelectroscope, by either tilting the electroscope or bring a charged object near theside of the electroscope. They are very thin and expensive.

PRE-LAB: The pre-lab is suppose to get them thinking about something they allhave experienced—getting shocked. This example is to help them start thinkingabout what is going on during that process. There is a corny online simulation thatthey 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 anelectroscope. There are some hints and suggestions on how to figure this out, butwe want them to discover on their own how this thing works. Also, many studentsget 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 aremeasuring first. We don’t tell the student the sign of the rods or the cloth untillater in the lab, so make sure they understand this.

PART II: In the second portion of the lab, they develop a sense of what electronaffinity is and what it means. Each rod has a different electron affinity, andtherefore it can hold a different amount of charge compared to the others. Thelong, white Teflon rod has the greatest electron affinity (don’t tell your studentsthis). Some students get confused on how exactly to set up the experiment. Theyneed to compare each rod to every other rod, and making a table/matrix is oftenthe easiest way to do this.

Some groups will forget to discharge the rods and make sure they are neutralizedbefore they rub them together. They will get confusing and contradictory data, andthey may have to redo the whole experiment. This is perfectly fine—the lab isdesigned so they have enough time to redo it if necessary, and they will definitelylearn 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 thecan with positive charge.

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LAB #2: Fun with DC CircuitsThe 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 andvoltage behave. We have found that many students still have a difficult time withquestions 3 and 4. It might be a good idea to go over this part before proceedingwith the lab. Also, the answer is “yes” to question 2—it’s tricky and someprofessors 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 beforeclass 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 DMMto get a feeling of how to measure resistance. Also, they can combine variousresistors together, predict the equivalent resistance and measure it to see if theirprediction was correct.

PART II: This portion of the lab uses a very simple circuit that allows the studentsto immediately see if their prediction is correct. Again, it may be tempting to havethe students build a more complex circuit and analyze it; however, students in thisclass will never need that level of sophistication. We’re only striving for anunderstanding of the basic underlying concepts and to develop critical thinkingskills.

PART III: The trick that the students have to realize is that you can calculate theresistance by using Ohm’s law. The dials on the power supply give them thecurrent and voltage values they need.

LAB #3: Fun with AC CircuitsThe third lab focuses on the students developing a deep conceptual understandingof AC circuits. This lab has two parts: the first uses a make-shift EKG machine thatallows the students to measure the voltage difference (from their heart) betweentheir hands. The second part has the students build an electromagnet that theycan turn into a transformer.

PRECAUTIONS: Be sure to do a quick run through this lab before running it withyour students. It can be difficult to get a nice display of your pulse on theoscilloscope. Students may get frustrated with this part; have Jerry Leigh come inand 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, especiallythe pre-meds. There are lots of other experiments that can be done, such assqueezing the electrodes, having multiple people touch the electrodes in variouspositions, 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 totransformers. Constantly remind students not to leave the batteries connected tothe coil for too long. This quickly drains the batteries and other students may getconfused 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 nowhave an AC voltage. Some students don’t realize that batteries produce a constantvoltage and may ask, “Is this an AC or DC battery?” Stress the points thatbatteries produce constant voltages, and that transformers only work for ACvoltages.

LAB #4: Fun with Light and LasersThe fourth lab allows the students to see diffraction and interference effects first-hand using a He-Ne laser and a Cornell plate. The students also have theopportunity to flex their lab muscles a little more in this lab because they have tosetup their own experiments and be able to interpret their results.

PRECAUTIONS: This goes without saying, but make sure the students do not lookinto the laser beam or reflect it off a metallic object and shine it around theclassroom.

PART I: The students made predictions as part of their pre-lab as to how theintensity pattern changes if you change one aspect of the experiment. They haveto 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 nothave seen combined interference and diffraction effects in lecture. We want thestudents to realize the similarities between the pairs of slits that they have tocompare. They may need some more assistance from the TAs on what exactly tolook for in this part. Have the students trace out the intensity patterns on a sheetof paper so that they can visually see the similarities and differences. Also, notethat the Cornell plates are not perfect and the slit width and separation numbersquoted on the lab report are approximate. Thus, the intensity patterns will notmatch up exactly like one would expect.

PART III: Again, the students have to devise their own experiment to accomplishthis part. There are many ways this can be done, and most methods will yield agood answer. We don’t ask them to give their uncertainty in their measurementbecause 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 asmaller uncertainty.

LAB #5: Fun with OpticsThe fifth lab allows the students to see how converging lenses behave and howtheir focal lengths can be measured. At the end of the lab, the students get tomake and use their own telescope.

PRECAUTIONS: Everything is fairly safe in this lab. If their light source is batterypowered, remind them to shut it off when not in use. Sometimes the imagesprojected on the frosted screen will be difficult to see with the room lights on, soadvise 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 thefocal length. If you set up the light source, lens and screen so that you have aclear image, all you have to do is measure the i and o and plug them into the lensequation. The other method involves a collimated beam—if the light source is atthe lens’ focal point, you can produce a collimated beam and directly measure thefocal length. Do not tell your students the two methods right away; remind themof 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 thereal world and analyze a slide projector. The students have to figure out why allthe major components are oriented the way they are. In addition, they have tofigure out what type of lens is being used and why. The slide projectors are notstandard lab equipment for this lab, so be sure to ask Jerry Leigh for them andtrack down some slides that the students can use.

PART IV: The last part of the lab has the students build their own telescope andtest it out to measure the angular magnification. This part relies on the studentshaving read the appropriate section in their book on telescopes so they have anidea of where to begin. If students are initially stuck, tell them to consult their textbook first.

If time permits, the students can try to build a three-lens telescope. It is difficult toset up, so keep that in mind.

LAB #6: Fun with AtomsThe last lab allows the students to explore the various emission spectra fromdifferent atoms. They also get to use a prefabricated spectrometer to observe thedifferent wavelengths of light, in addition to making their own spectrometer to seehow the instrument actually works.

PRECAUTIONS: The discharge tubes and diffraction gratings are both fragile, somake 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 theprefabricated spectrometer. Make sure that they calibrate the spectrometer, asnoted in the lab. By observing the emission spectrum from the discharge tube, thestudents have to figure out what they are looking at. The tube is actually filled withHydrogen, but don’t tell them this right away.

PART II: In order to get a feel for how a simple spectrometer works, the studentshave to build their own from a meter stick and a diffraction grating. Some groupsmay find this rather difficult and will get stuck when trying to observe thespectrum. Make sure that you attempt to set up the spectrometer yourself beforehaving the students do the lab themselves.

The students also have to figure out how to calculate the wavelengths of the lightthey observe. Some students may find this challenging, but remind them of whatvariables they already know (or can easily measure). This portion of the lab usuallytakes the longest to do.

There are also a few questions about the uncertainty of their spectrometer, andwhich one is more accurate. We are looking for some qualitative reasoning andexplanations for these questions. Remember, most of them have no formalknowledge of error and uncertainty, but you can definitely get them thinking aboutthese aspects of the experiment.

PART III: The most important aspect in this part is the last question: why do thelight bulb and fluorescent light both appear white when we know they arecomposed of different wavelengths of light? Try to get them thinking deeply aboutthis question and about how our eyes interpret various colors.

PART IV: If there is enough time, have the students figure out the composition ofthe mystery substances. Talk to Jerry Leigh about this and make sure you knowwhat is in each discharge tube. Some students have gotten conflicting data fromthe giant wall chart in the lab, so make sure you have an up-to-date versionsomewhere for the students to look at.

If there is even more time remaining, you can give a better explanation as to howdischarge tubes work.

Physics 2010 Labs

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

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 someproperties 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 tohurt yourself or others in this lab. Still, pay attention at all times to what you and your lab matesare doing.

Your next priority is to treat the equipment safely and respectfully. DO NOT BREAK THEEQUIPMENT. They are cool instruments … and they are sensitive. Do not elevate the airtracks past approximately 10 degrees.

Have fun and learn some physics. There is a challenge at the end of this lab. So, if you wish tobe deemed MASTERS of the LABORATORY pay close attention (plus it may well help yourgrade).

Lastly, your PRE-LAB HOMEWORK is embedded in these lab instructions. YOU MUSTTURN THOSE IN ON A SEPARATE PIECE OF PAPER at the beginning of lab. You shouldalso have a copy in your lab notebook. (It is okay if you print out copies of your prelab and tapeone in your book).

Activity I: Pre-amble to the lab: (15 minutes)a. Turn on the air tracks (get instructions from the TA)

b. Level your track -- With the air on, place a glider on the track, and adjust the track's feet untilthe 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 movesii. 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. Acard 10.0cm long, placed on top of the glider interrupts a light beam in thephotogate and triggers a timer. The photogate timer can be used to measureeither the time for the glider to travel between two gates (when the timer controlis set to PULSE mode) or the time for the card to pass through one gate (whenset to GATE mode). The timer can be set to read either milliseconds (msec) or0.1 msec. With 0.1 msec resolution, the timer will count up to a maximum of 2sec, before overflow.

photogates

air track glider

card

2010 Lab 1 Fall '03 ©PER@C (NF) UC Boulder 2

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 whenyou push it. Note the times in your lab books. In your groups discuss the following andanswer 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 themiddle-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 thedifferences 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 describeeach?)

Convince your lab partners of your answers to Prelab Ic (below). Collectively agree on goodexamples 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 itpossible that average velocity is ever larger the instantaneous velocity (at anygiven time during the trip)?

c. What are some real world conditions where you measure instantaneousvelocity, 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 onlyhaving 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. NEVERINCLINE THE TRACK MORE THAN 10 degrees.

i. Convince yourself (make measurements) that an object accelerates faster when the track issteeper. 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 3

glider!) that you drop straight down from the same height. (You need not measure the time offree-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 awayDo 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 bookii. 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 onemeasurement 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 youare confident in your measurement skills you can just use one length (fix x- xo) and

2010 Lab 1 Fall '03 ©PER@C (NF) UC Boulder 4

average the times for several trials. Use equation for acceleration from your Prelab IIabove 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:

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 theglider, by noting that only a faction of g is in the direction of the air track andhence, g is diluted or thinned out. If you precisely know the angle you canfigure 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 tomeasure distances along the air track (only L, not vertically or horizontally). Your team will beable to make one measurement of the glider running down an air track. Based on that singlemeasurement, 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 NASAtrying to land a spacecraft on Mars.

In the last 10 min of lab, each team will present their measurement of the angle with reasoningand 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.

L

θ

h

Lab II: Physicists Can Fix AnythingPhysics 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, makingthe clock tick forward once per swing. You are a group of artist-physicists anddecide to build a new housing for the clock, decorate the face, and build a newpendulum out of materials from your studio. However, when you assemble theclock with the new pendulum, which is lighter, and longer, you notice that theclock no longer keeps the correct time. Before you rebuild the pendulum, youdecide to figure out how the mass and length of the swing affect the time ittakes to complete a swing (the period.) Then you can be sure you can buildboth an interesting and accurate clock.

Prelab 1:a) To measure the period of a pendulum, do you want to measure 1 time, 10times, 100 times, 1000 times, 50,000,000 times? Explain why.

b) What exactly is the length of a simple pendulum? Make a diagram toillustrate your answer. (Hint: In the figure of a pendulum at the end of thislab writeup, where precisely is the lower tip of the pendulum associatedwith length L?)

c) What is the best way to measure Length, Mass and Period? (give a moredetailed 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) differentreasons why your expect your measurements to vary and, hence, why youranswers to the two lab questions may not be EXACTLY correct.

Note: "Experimental error" or "human error" are not acceptable answers here, orat any time in your lab writeups! These phrases alone contain no useful orthoughtful information. Here is an example of an acceptable kind of answer:"Difficulty in using a flat ruler to estimate the radius of a spherical pendulummass, 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 todefend 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 guidelinesfor lab:

I. Prelab Homework Discussion: 5 min Whole ClassCome into class ready to discuss your prelab … particularly Prelab 1c

II. Board Meeting: 15 min Groups of 4Plan your experiment. Things to include: what is your goal? methods? what data will youcollect? 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 PairsMake sure you will be ready at the beginning of the second hour to present yourexperimental method, your data, and your conclusions about whether changing themass or length affects the period. The goal of the presentation is to convince otherstudents that your conclusions are correct. So, please put some thought into yourpresentation; it’s the main point of this lab. For instance, how will you convince a groupwhose measurements turned out very different from yours to believe your data? How willyou 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 yourconclusions, so you’d better be ready for them!

IV. Class Discussion Whole Class 30 minEach group will present answers to at least one of these two questions. Be prepared to answerquestions 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 beactually 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 extendbeyond 5 degrees.

Uncertainty: In cases where the total number of measurements is small (4 or less), then theuncertainty δT is roughly half the spread in values of T. However, if the number ofmeasurements is large (10 or more), a more accurate estimate of the uncertainty is given by

€

δT = (half the spread)N

, where N is the number of measurements. Note that, with this equation,

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-walksand work on the international space station. However, they are particularly concerned aboutmaking the suits light enough to send to space and robust enough to withstand the effects ofcollisions due to docking, bouncing into other space walkers, and catching flying objects inspace. Thus, they have challenged you to sort our the parameters that seem to affect energy andmomentum.

The purpose of this lab is to study the conditions under which kinetic (or mechanical) energy isconserved, 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, conductingthem, and presenting / justifying the results to the rest of the class. Note: throughout this lab youshould 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 aboutmomentum 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, youcannot create momentum out of nothing, nor can you get rid of it - you can onlytransfer 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 movingoppositely 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 -- Itis important that you ATTEMPT this problem, but not necessary for you to complete it, if youhave 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 willbe 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 mightencounter. 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 aircushion 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. -- playaround with the GATE mode and the READ button. These will have some sort ofmathematical 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 throughphotogate 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 timeΔ Δ

Δ

t t

t2 1

1

−. Repeat this experiment a few times and display your data in a table. The

average value of Δ Δ

Δ

t t

t2 1

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 oneanother. 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 toanswering the lab question. Make sure you clearly list your research question and yourexperimental 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 canextend 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?

air track glider 1

card

gate 1

glider 2

wax cup pin

gate 2

What are the most compelling forms of data?What is reasonable measurement uncertainty? (aka when are two measurements considered thesame / 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 beactually 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..

Rubber band bumper

Flat metal contact

Glider 1

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 diskon 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 / setupThe 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 morework required to get it moving in a straight line. Alloy rim wheels on bicycles have a lowermoment of inertia I than steel rim wheels and so are easier to get spinning, making fastbicycle 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. Themoment of inertia of a body about a particular axis is defined as:

I m ri ii

= Â 2

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 thebody consists of discrete point masses. But if the body is a continuous object of somearbitrary shape, then performing the sum requires the techniques of integral calculus. In thiscourse, we simply tell you the answer for various shapes. For a disk with an axis through thecenter of symmetry, the moment of inertia is

I M Rdisk =1

22 . (1)

4.2

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

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

= +

R

radius r m

mdisk

axle

†

Itot = Idisk + Iaxle =12

mdiskR2 +

12

maxler2 (2)

In this experiment, you will determine I in two ways. First, you will measure themasses and radii of disk and axle and then compute I from the formula above. Then you willcompute I by timing the wheel as it rolls down inclined rails and using the principle of theconservation of energy.

Consider the wheel, consisting of disk and axle, rolling down an inclined set of railsafter starting from rest at the top, like so:

ho

v

w

h

axlerails supporting axle

(figure 3)

R

mass M

axis of rotation

4.3

The total energy at any time is the sum of the translational kinetic energy, the rotationalkinetic energy, and the gravitational potential energy.

†

Energy = KEtrans + KErotational + PE =12

Mv 2 +12

Iw 2 + Mgh . (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 itsinitial kinetic energy (both translational and rotational) is zero and its total energy is allpotential.

†

Energyinitial = PE = ________ (4)

When the wheel reaches the bottom of the rails, h=0, and the energy is all kinetic:

†

Energy final = KEtrans + KErotational =12

Mv f2 +

12

Iw f2 (5)

where vf is final translational speed and wf is the final angular speed.

Because the rolling friction is very small, we can assume that the total energy isconstant 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 translationalspeed v are related by

†

w =vr

(7)

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 youwould 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 Earthor 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 heightho, 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 havesections on goals, experimental setup, and data collection tables already drawncoming into lab.

Part 0. Arriving in lab:Check off with your TA and with your lab partners the answers to pre-labs 1,2,310 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 metersand kilograms for all your measurements. This is because the moment of inertia of our disksturns out to be a very small number in MKS units (roughly 10-3 kg-m2) and it is a littleawkward to work with small numbers. If you use cgs (centimeter-gram-second) units, youmust 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 youdo not need to know r very precisely, but you will in part 2, so measure the diameter of theaxle very carefully three or four times with the calipers. Use the average of yourmeasurements and estimate the uncertainty in r. (If you don't know how to use the calipers,ask your instructor.)

Using Eqn (1), find Idisk and Iaxle separately and then compute I I Idisk axle= + . (Is

Iaxle significant, compared to Idisk, or can it be ignored?) In using Eqn (1) to compute Idisk, weare 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 issignificant.

Part 2. Measurement of I using energy conservation.

One end of the rails can be raised and lowered to one of three positions. Place therails in the lowest position, at which they are approximately level, and then using theadjustable screws in the base, make the rails exactly level. Use the bubble level to get arough level and then place the wheel on the rails to get a precise level. (If the rails are exactlylevel, 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 thetwo 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 startedresting against both blocks and will roll straight down the track when released. Using themeter stick attached to one rail, record the positions of the sharp tip of the axle in the startingand stopping positions and compute the distance d through which the wheel rolls. Leave thestarting blocks fixed from now on, so that the value of d is the same for all timings.

starting block

stop

adjustable feet

base

H

H

2

1

To determine the heights h1 and h2 through which the wheel descends, begin bymeasuring the height changes H1 and H2 of the end of the rail when it is raised from the levelposition to the two upper positions. H1 and H2 can be measured quite accurately bymeasuring 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 wheeldescends, since it does not roll the whole length of the rail. Instead, the situation is as shownbelow, 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

top.) The two triangles shown are similar triangles, therefore

†

hH

=dD

. Use this relation to

calculate h1 and h2 from measured values of d, D, H1, and H2.

4.6

D

d

hH

Now use the stopwatch to measure the time t1 for the wheel to roll down the rail whenit is in position 1 (height H1). This is best done with the same person operating the stopwatchand releasing the wheel. Make a few trial runs to determine the best procedure. Have eachmember of your team measure t1 a few times and record all values. From yourmeasurements, determine an average value of t1 and estimate its uncertainty. Repeat thiswhole 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 twopositions. Be careful! The quantity d/t is the average speed of the wheel. In the case ofconstant acceleration, the average speed is related to the final speed by

†

v final = 2vaverage

Prelab 5:Justify the above equation. [Hint consider the definition of average (using v- final andv(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 twopositions of the rail. Be careful to display the correct number of significant figures in yourfinal answers.

Part 3:Display your three final values for I: your value from part 1 and your two values from part2. If there is a large discrepancy among the values, comment on possible sources ofexperimental error.

Part 4 (time permitting):As a class, using the notions of energy and conservation of energy, discuss, predict andexperiment 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 findyourself attempting to avoid the clutches of the evil Dr. Evil (no relation to any of yourprofessors). You want to transport as much $$ value as possible. However Dr. Evil's stealthyagents are wary of your plans and looking for high density materials using fancy physicsdetectors. Thus, you wish to optimize your $$ / density ratio (by minimizing density andmaximizing $).

You can transport, quarters, dimes, nickels, or pennies. Which do you chose in order tomaximize 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 accuratelyb) know your uncertaintyc) write out your experimental methodd) 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 section1. 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 eachmeasurement you make and how they propagate through the equations you use in (2). E.g. ifyou 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).

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”University of Colorado at Boulder, 2000

Physics 2010 Organ Recital Experiment 6

Congratulations! You've just won yourself an auditionat 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 ofthe organ pipes is broken and needs replacing. Fortunately,you recall some of your favorite days as a physics studentin Boulder… You remember that the pitch (or frequency) ofa standing wave in a tube is somehow related to tube itself.Being an experimentalist by nature (in addition to a worldclass organist) you decide to answer the following question:

What are the conditions for resonance of a standingwave inside a closed tube?

Being a perfectionist, and having an audition in a short twohours, you want to document your experiments,demonstrate your methodology, record measurementscalculations, uncertainty and conclusions.

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 smallvariation in the pressure of the air near our ear

In this experiment, we will be studying standing waves, which should not beconfused 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 showsa right-going traveling wave at two different times. The solid line is the wave at an

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

l A

v

You

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”University of Colorado at Boulder, 2000

A standing wave occurs when two travelling waves of the same wavelength l, thesame frequency f, and the same amplitude A, but moving in opposite directions, passthrough each other. The two traveling waves interfere, producing a standing wave whichoscillates between large amplitude (when the two waves are in phase) and zero amplitude(when the waves are out of phase).

+

=

in phase out of phase

+

=

Time 1 Time 2

One way to produce two travelling waves of identical l, f, and A, but moving inopposite directions, is to generate a travelling wave that reflects from a surface. Thereflection, 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 endattached 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 snapshotsof the standing wave at two different times; the solid curve is the wave at an instant whenit has maximum amplitude; the dashed curve is the wave at an instant one half-periodlater. The standing wave oscillates between these two extremes. Points along thestanding wave where the amplitude of motion is zero are called nodes; between the nodesare antinodes where the amplitude of the motion is a maximum

nodes

antinodes l l/2

reflecting wall

A sound wave in air can produce a standing wave in a tube. In this experiment, asinusoidal sound wave of variable frequency is generated by a speaker at one end of a

6.3

”University of Colorado at Boulder, 2000

tube. The sound wave bounces from the other, closed, end of the tube. As you willobserve in this lab there are conditions when the tube is said to resonate, and a largeamplitude standing wave forms in the tube. A movable microphone inside the tubeallows us to measure the sound intensity in the tube and see where the nodes andantinodes are occurring.

The figure above showing standing waves on a taut string is a plot of thedisplacement (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 thepressure of the air. So the oscilloscope will show you where pressure nodes and anti-nodes 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.

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

The microphone is hooked to an oscilloscope, which is a device that displays agraph of voltage vs. time, with voltage on the vertical axis and time on the horizontalaxis. Your TA will introduce you to the use of the oscilloscope. If the voltage is DC, thatis, constant in time, then the oscilloscope displays is a horizontal line. If the voltage isAC, that is, sinusoidal, then the oscilloscope will display a sinusoidal wave. Theoscilloscope 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

movable piston end speaker

movable microphone

Resonance occurs when L = N (l/2), N=1, 2, 3,..

tube length L

Function Generator

COARSE

AMPLITUDE

FREQUENCY

FINE OUTPUT

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”University of Colorado at Boulder, 2000

and horizontal position of the display. There is small knob in the center of both thevolts/div and time/div knobs, called the CAL or calibration knob. This should always bein 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). Thisshould always be in the DC position.

AC GND DC

CAL

POSITION

CH.1 VOLTS/DIV

AC GND DC

CAL

POSITION

CH.2 VOLTS/DIV

CAL

POSITION

SEC/DIV

Oscilloscope Front Panel

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 tubeare covered with the sliding clips.

Note that the way you will be able to tell that sound is resonant with thetube is that the microphone detects a maximal signal --- think about wherethe microphone should be placed.

Play with the knobs and see what happens. Turn on the oscilloscope, the frequency generator, and themicrophone. 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 maximumin the signal (resonance) when you move the piston end in or out or when you vary the frequency. If youlisten 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 amaximum signal, move the microphone around in the tube and look for nodes and antinodes. (What canyou 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 thenmeasure the positions of the nodes. At resonance, the signal on the oscilloscope screenwill be a maximum. Adjust the piston so that the length L is large, and then fix the pistonposition with the clamp. With the microphone against the piston, set the frequency at aresonance 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

6.5

”University of Colorado at Boulder, 2000

end to the speaker end of the tube, while looking for nodes (signal minima) andantinodes(maxima) on the oscilloscope screen. Using the meter scale in the tube, recordthe microphone position x of every node. Compute the distance Dx between each adjacentpair 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.

l/2=D/N

D = N l/2

Part II. FOR THE SAME FREQUENCY, determine the effects ofvarying the tube length.

Here we will fix f and vary L to find the resonant positions. Set the frequency as itwas in part I. Start with the piston pulled all the way out (maximum L) and themicrophone positioned against the piston. Slowly push the piston in, decreasing L, whilekeeping the mike against the piston. Record the positions x of the piston at whichresonance occurs. Compute the distance Dx between each adjacent pair of resonantpositions.

Where are the resonances occurring?

Part III: Repeat Parts I and II for two other frequencies (in the range1500-2500 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) andyour Dx (the spacing between your nodes or spacing between your anti-nodes)?

What happens to the node and anti-node spacing when you increase thefrequency?

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 thebattery dies).

6.6

”University of Colorado at Boulder, 2000

Appendix Pressure waves vs. Displacement waves

When a sinusoidal sound wave passes through air, the air molecules are displacedfrom their original positions. The displacements of the air molecules at an instant intime are shown by the arrows in the figure below and by the dashed line in the bottomgraph. Note that displacement to the right corresponds to a positive displacement on thegraph, and displacement to the left is negative on the graph. Because of the sinusoidaldisplacement, 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 densityN/V, according to the ideal gas law.] The solid curve on the graph is a plot of the pressurevs. position. Note that the pressure peaks where the displacement is zero. Displacementnodes corresponds to pressure antinodes, and vice-versa.

Air with soundwave present.

Undisturbedair.

displacement

Solid line = pressure Dashed line = displacement

6.7

”University of Colorado at Boulder, 2000

Prelab Questions

1. What is the relation between frequency and the sound you hear? How doeswavelength 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 goalsfor the lab and any questions you have for the TA.

Physics 2020 Labs

LAB #1: Fun with ElectrostaticsPhysics 2020, Spring 2004

One of the downsides to living in Boulder is that annoying and painful electric shockyou get when you touch a doorknob. If you’re not from around here, you mayknow that this doesn’t happen as often in other parts of the world. Why is this, andwhat physical process is going on when you get shocked? These are some of thequestions you’ll discover and resolve in this lab on electrostatics. It’s alwaysrewarding to have a solid understanding of these things we encounter everyday inour lives, and by the end of the lab, we should all have a better idea of what’sgoing on.

In order to answer these questions, we will be using a variety of plastic rods thatwe can charge with a cloth (as seen in lecture). You will then figure out how to usea device called an electroscope, which will allow you to determine some of theproperties 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, orcarpet? In the summer or winter? In the morning or at night? Does it onlyhappen when touching doorknobs?)

2) Can you think of ways that you’ve purposely tried to shock someone to annoythem? 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/electricity-simulations.htm Try the simulation called “John Travoltage.” (Move his armand leg around and see what happens.) After playing with it, describe in yourown words what you think is going on.

PRECAUTIONS & NOTES:The electroscope is a sensitive device and can be easily damaged. The small pieceof gold colored foil inside is real gold! Be sure to follow these precautions duringthe 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 foiland rip it off.

3) In order to ground the electroscope (that is, remove all the net charge from it soit’s neutral), touch the metal grounding plate to the metal ball on top of theelectroscope. Touching your hand to the top of the electroscope can sometimeswork, if you do not have any charge on your hands.

4) Before charging and testing the plastic rods, make sure that they are neutralfirst. 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 withthe electroscope to make sure it is neutral first.

5) If you rub two objects together to test the charge on each, make sure you holdthe side that was rubbed near the metal ball on the electroscope.

PART I: USING AN ELECTROSCOPEThe questions to answer for part I of your lab are these: How does an electroscopework, and what is it good for?

Imagine that at the end of this lab you have to describe how this thing works to afriend who has never seen an electroscope. Answer this question and be preparedto defend your explanation and reasoning. Here are some things to get youstarted:

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 theelectroscope. Observe what happens and explain in your own words what youthink is going on.

B. Now take a charged rod and touch it to the metal ball on the electroscope, thentake the rod away. Again, observe what happens and record your results.

C. After touching the metal ball with the charged rod, what happens when youbring another charged object towards the electroscope? Try to figure out whyyou would want to do this, and what information it can give you. Record yourthoughts and observations.

D. Try anything you like now and get a feel of how the electroscope is used. Figureout what this thing is useful for; that is, what can it measure, and what can itnot measure? Can you measure the sign and magnitude of the charge? Do youthink 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 shapesand colors of the rods all differ, but the important thing to know is that they are allcomposed of different materials. Therefore, they should behave differently whenyou try to charge up each rod. We already know that when rubbed with wool, theplastic become negatively charged (the plastic wants to hold these negativecharges, so it takes them from the wool). However, what happens when you rubtwo neutral plastic rods together? Which one becomes negative and positive? Theanswer 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 mostnegative 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 rodsagainst each other to see which one in the pair can hold the most negative

charge. If there are 6 plastic pieces in all, how many different pairs can youform?

B. First charge the electroscope with some charge, either negative or positive—it’syour decision.

C. Take a pair of plastic rods and make sure they are neutral first. Rub the tworods together to charge up each one, and test each with the electroscope. Canyou 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 knowexactly 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 electroscopeinstead of a neutral one for these tests? Why can’t we charge up each rod andcompare all of them at once with the electroscope?

PART III: ALUMINUM CAN RACEAnd now for the fun part. Once you have determined which plastic rod can hold themost negative charge, challenge another group to a race. Here’s how the racegoes: if you lay a soda can on its side, you can get the can to roll towards yourcharged rod. Try it! Line up 2 soda cans and see which one of you can get the canacross the table the fastest without touching the can with the rod. You are allowedto use any tricks and insights that you learned from the lab to make your can gofaster, including “preparing” the can before the race. However, once the racestarts, 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 CircuitsPhysics 2020, Spring 2004

The field of electronics has revolutionized the way we live and what we do. We canfind circuits everywhere—from our cell phones, digital watches, calculators,televisions, computers, etc. Understanding how these things work is interesting intheir 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 notelectrocute ourselves.

In this lab, we will first look at a few simple DC circuits that will give us an idea ofhow these things work in the first place. We will learn how to use a DC powersupply 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 identicaland ideal. Note also that bulb brightness reflects the power dissipated in thebulb and that the bulb is just like a resistor.

4) In 50 words or more describe why the bulbs are ranked as they are. Presentyour reasoning in every day language so that a friend who has never takenphysics would understand your reasoning for why you ranked the bulbs as youdid (you can use words like voltage difference, current, energy, etc, but noexplicit formulas).

5) Look at the picture on the following page. Select the schematic diagram for theresistors and power supply shown in the picture.

(A)

(B) (C)

(E)(D)

resistor -->

voltage source -->

wire -->

PRECAUTIONS & NOTES:

The two instruments you will use in this lab are aDC power supply and a digital multimeter. The DCpower supply produces a constant voltage, whichcan be adjusted anywhere from zero to 30 voltswith the voltage knobs (coarse and fine) on thefront panel. The power supply has three outputterminals: plus (red), minus (black) and ground(green). The ground terminal is always at zerovolts. In this experiment, the ground and minusterminals are tied together by a metal connectorso the minus terminal is also at zero volts. Boththe current and voltage produced by the powersupply 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 maximumoutput current, to prevent damage to sensitivecircuits. In this lab, the current knob has been set

and clamped in place so the power supply cannot produce more than about 0.6amps.

The hand-held digital multimeter (DMM) is a wonderful little device which can beused to measure the voltage difference between any two points in a circuit, thecurrent, 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 theCOM (common) terminal. To measure either the voltage difference or theresistance, the second wire is attached to the “VΩ” input. In this lab, all ourmeasurements will be DC, so the DC/AC switch (upper right) should always be inthe DC position. The DMM has an alarm; it rings if you have wires plugged intopositions which conflict with the central knob’s position.

The 2 wires attachedto the DMM are called"needle probes". Youcan quickly measurethe change in voltagebetween any twopoints in a circuit bytouching the pointswith the needleprobes.

When measuring aresistance with aDMM, you mustdisconnect the source

+-current

voltage

fine

coarse

DC Power Supply

current

voltage

metal connector

com VΩ

DC AC

V

Ω

DMM

needle probes

Measuring a resistancewith the DMM.

DCV

of the resistance from any other devices, such as power supplies. Never try tomeasure the resistance of a resistor while it is still in a circuit.

PART I: MEASURING RESISTANCEYour goal of this part of the lab is the following: Figure out how to measure theresistance of various things using the DMM.

At your table, you should have 5 resistors: one 15Ω, one 40Ω, one 1500Ω, and two3000Ω resistors. These values are given by the manufacturer and are approximate.Each resistor is mounted in a double-banana plug connector. Carefully measure theresistance 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 theresistance of each light bulb filament, and record your results.

What is the resistance of other things around you? The tabletop, your hands, yourlab partner, your lab book, etc. Explore. Are these consistent with how well thesematerials 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 seriescombinations 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 resistanceof the combo and see if your prediction matches—does it?

PART II: CIRCUIT BEHAVIORNow that you understand how to use the DMM, you will now build a circuit andinvestigate its behavior.

Construct the circuit shown below, consisting of two light bulbs in series with thepower supply. (The resistor R will be added later). Slowly increase the voltageuntil the bulbs are glowing, but not too bright. Predict what will happen to thebrightness of the bulbs when you place a R = 40Ω resistor in parallel with bulb #2as shown in the schematic. Go ahead and add in the resistor, and describe in yourown words what happened and why. Measure the voltage across the light bulbsand resistor and verify that they match your prediction (i.e., if you know the powersupply voltage and all the resistances, do the other voltages make sense?).

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

V

R

1 2

PART III: MEASURING RESISTANCE IN MULTIPLE WAYSIn Part I of this lab, you learned how to measure the resistance using the resistancefeature on your DMM. Go back to one of the circuits that you built in Part II andmeasure the resistance of the resistor in parallel with bulb #2 without using theresistance setting on your DMM. Your group will have to figure out a clever way todo this using the power supply and the other features of your DMM. Describe indetail how you were able to accomplish this.

Note: Besides not being able to use the resistance feature on your DMM, makesure that the light bulbs are still glowing when you take any measurements.

LAB #3: Fun with AC CircuitsPhysics 2020, Spring 2004

In the previous lab, we studied some simple DC circuits, where all the voltages andcurrents did not change with time. What happens when the voltages and currentsdo change with time? It turns out that we live in a world where most circuits are infact AC instead of DC. In this lab, we will explore two different applications of ACcircuits—electrical impulses from our own hearts and transformers. Feel free to askyour TA why we have AC circuits rather than DC.

PRELAB QUESTIONS: (there are morepre-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 theperiod, frequency and amplitude of this voltagesignal? Assume that the volts/div setting is 50V/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 besure to indicate the horizontal and verticalscales (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 willdrain 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 thesurface of the skin. An EKG (electrocardiograph) is an instrument that can measurethese signals and produce a visual image (and sometimes an audible sound, as inthe "beep . . . beep . . . beep . . .” you hear in movies) of the signal your heartproduces. Your goal for this lab is to obtain an accurate recording of this voltagesignal 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 isused more often for historical reasons.

Our makeshift electrocardiograph is made from an oscilloscope, which is a veryuseful tool for measuring voltages that are changing in time. Think of theoscilloscope just like the DMM we used in the last lab—it measures voltage, but nowit 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 thescreen is used to measure the voltage and time of your signal—think of it like graphpaper. Each little box on the grid is called a division, and you can adjust the scaleof 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 thegrid 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-varyingvoltages as it beats. These heart voltages produce small voltage differencesbetween points on your skin that can be measured and used to diagnose thecondition of your heart. Usually, nine electrodes, positioned at various points of thepatient's body, are used when recording a full electrocardiogram. However, in thislab, we will only use two electrodes to measure the voltage between your right andleft hands.

A typical plot of voltage difference between two points on the human body vs. timeis shown above. The P deflection corresponds to the contraction of the atria at thestart of the heart beat. The QRS group corresponds to the contraction of theventricles. The T deflection corresponds to a recovery (or re-polarization) of theheart 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 astorage 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 measuredis the potential difference between the two electrodes. However, the voltagedifference between your hands is inconveniently small to measure directly. Tocompensate for this, the signal from the electrodes is given a boost by theamplifier.

Enough talk for know...let's get to business:

A. You should have a battery at your lab station. Play around with the battery andmake sure you understand how to measure its voltage correctly using theoscilloscope.

B. The voltage displayed on the oscilloscope differs from the input voltage of yourhands by an amplification factor. To find this factor, switch the amplifier mode

switch to "calibrate" and then press the red button—this produces an inputvoltage whose peak (positive) value is 1 mV = 10-3 volts. Measure the voltageon 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 withhis or her hands wrapped gently around the electrodes, palms down. Adjust thesettings 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 theEKG in your lab notebook and record any specific details of the signal that youcan measure. Using the amplification factor, what is the actual voltageproduced by your lab mate’s heart?

D. Now grab and squeeze the electrodes with your hands. What happens to thevoltage signal, and what could explain this?

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 ofyour lab partner from this data.

F. After everyone in your lab group feels they have a solid understanding of whatyou are measuring and how you exactly do it, predict what would happen if twopeople holding hands were to touch the electrodes (that is, on person grabs itwith their right hand and the other person grabs the other electrode with theirleft 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’regoing to play around with a bunch of wire, right? Well, it turns out thatelectromagnets are extremely interesting and are found all over the place—electricmotors, speakers, your car, etc. Your goal in this part of the lab is to figure outwhat makes electromagnets stronger and weaker, and to figure out howelectromagnets and transformers are related.

A. First, build an electromagnet. Take a 3 ft. long piece of wire and wrap it aroundone of the rods you have (wood, iron or aluminum) and secure the ends withelectrical tape (see figure below). Count and take note of the number of turnsof wire that are wrapped around the rod. Draw a picture of it in your labnotebook.

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 adifferent rod this time. Is the electromagnet stronger or weaker? Use all 3materials and rank them on how strong they make your electromagnet.

D. Reduce the number of turns by one-half. Did this strengthen or weaken yourelectromagnet?

E. Reflect on these observations—given what you know about magnetism, do yourobservations make any sense at all?

F. Now you will build a transformer (as shown in the figure below). For theprimary coil, it is best to combine two of the 3 foot wires into one long wire andwrap them on the iron coil. Now take one of your longer 12 foot wires and windit over the top of the primary coil as shown in the figure below. Count thenumber of turns as you wind. This will serve as your secondary coil. Secureboth ends with electrical tape. Is this a step-up or step-down transformer, andwhat 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 itsbehavior.

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.) Describeand explain what goes on in your lab report.

LAB #4: Fun with Light and LasersPhysics 2020, Spring 2004

For quite some time, scientists believed that light was composed of tiny particlesthat carried energy. It wasn’t until the early 19th century that people started toview light as a wave instead of a constant stream of mysterious particles. In thislab, we’ll explore some of these early experiments that convinced scientists of thewave-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 anddescribe how the pattern changes):

A. The width of each slit is decreased (while keeping the distance betweenthe slits constant)

B. The distance between the slits is increased (while keeping the width of theslits constant)

C. The screen is moved closer to the double slitsD. The wavelength of the incoming light is decreased

PRECAUTIONS & NOTES:1) Do not look into the laser beam.2) Do not move the laser.3) Do not put your head near the laser beam.4) Last but not least, do not look into the laser beam.

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

Now go back to your predictions youmade in pre-lab question #1. Makesure all your lab mates agree on whatshould happen and why. With theavailable equipment you have,determine which predictions you cantest, and which ones you cannot. Forthe changes that you can make, set upan experiment to test these changes.Record in your lab notebook a picture ofthe setup, what you did, how you did itand what the results were. If any ofyour predictions are incorrect, you’llhave to determine if your experiment oryour original prediction itself is wrong.

The diagram on the left is a picture ofthe mask containing all the slits thatyou 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, sinceapertures of this kind where first used at Cornell University. Next to each set ofslits, you will see 3 numbers. The top number indicates the number of slits, themiddle number is the width of the slit(s) and the bottom number is the distancebetween the slits (in millimeters).

PART II: Interference and Diffraction CombinedSo far, you have learned what an interference pattern looks like and what adiffraction pattern looks like. The diffraction pattern arises because of the behaviorof light as it passes through a single narrow slit. For the interference pattern, wealso have light passing through narrow slits. So, shouldn’t we get some sort ofdiffraction 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 thingsto get you started:

A. Use the single (D=0.107 mm) slit to create a pattern on the screen. Take noteof 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 twodifferent patterns? Do the two have anything in common? Again, trace out afew diagrams of the patterns so that you can compare them. (Notice that boththe 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=0.345mm) to the double slit (D=0.10 mm, d=0.35 mm) pattern. Again, what are thesimilarities and differences between the two patterns?

1 15 1

1 30 2

1 75 3

1 37 4

1 20 10

1.43

0.755

0.345

0.195

0.108

0.05

0.05

0.01

0.027

0.044

0.05

0.05

0.05

0.05

0.05

_ 0.176

0.088

0.034

0.066

0.088

_

0.132

0.132

0.132

0.132

1

2

2

2

2

0.107

0.10

0.10

0.10

0.10

0.175

0.35

0.70

1.40

_

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

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

LAB #5: Fun with OpticsPhysics 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 themselvescontain lenses. There is an array of other fields, from photography tocommunications, that all take advantage of optics. In this lab we will studyconverging 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 lightand 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 havelearned so far. When a bundle of parallel light rays enters a converging lens, therays are focused at a point in space a distance f (the focal length) from the lens. Aconverging 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 theedges).

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

1 1 1

f d do i

= + . (1)

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

f

Converging lens, convexf

Diverging lens, concave

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 o

i

h

hm= . From the diagram above,

one can show that m can also be written as o

i

d

dm= .

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 areplaced, with a ruler on the side for measuring distances. The other equipmentincludes a bright light source, which acts nearly like a point source, and twoconverging lenses labeled A and B. There is a frosted glass screen, labeled "I", onwhich you can view images. Finally, there is a metal plate with a hole in the shapeof an arrow. The hole is covered with scotch tape. When this aperture is placed infront of the light source, it forms a convenient object for image-formingexperiments.

Play around with the equipment for awhile to get a feel of how things work and howthe different lenses affect the image. Now test your prediction from pre-labquestion #2 by covering half of the lens. What happens to the image? If yourprediction 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 yourprocedure and results in your lab note book. (NOTE: there is more than one wayto measure the focal length)

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

do

di

image

object F

Fho

hioptic axis

their ability to produce a large image of a slide. Your TA has a couple of slideprojectors 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 majorcomponents (lens, slide, screen and light source). Explain in your own wordswhy they are set up in this orientation (i.e., why is the slide always on oneparticular side of the lens, and not the other?)

B. What is going on when you focus the image of the slide? Why does thischange the focus?

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

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

Be sure to describe in detail where everything is located in your slide projector andwhy 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? Getgoing! Try to make a telescope (using both lenses) with the largest angularmagnification 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 agraduated scale. You should already have calculated the angular magnification ofyour telescope, but now try to use the picture on the wall to estimate and measurethe angular magnification.

A. Do the two different measurements agree?

B. With just the two lenses you have, is it possible to make a different telescopewith a different angular magnification?

C. Determine the critical factors in designing a telescope. What matters? Lensdiameter? Focal length? etc.

D. If your TA has access to a third lens, get one, measure its focal length anddetermine whether or not you can improve your telescope with this new lens.

Note: the more you prepare in your lab notebook in advance, the morethorough and easier your lab write-up will be in section.

LAB #6: Fun with AtomsPhysics 2020, Spring 2004

If we were to give you a solid block of material, you could probably find out what itwas made of. You could measure its density, see if it conducted electricity, whetherit could hold charges, etc. and compare that info to existing data. However, what ifwe gave you a tube filled with gas? How would you determine what type of gas isinside? It seems a little harder to analyze this. However, there are otherproperties of atoms that we can look at—the way atoms emit and absorb light isvery unique, which gives rise to a unique spectral signature or "fingerprint." In thislab, we will use a spectrum analyzer to see what colors of light atoms emit, andfrom 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 tofree itself from the proton. This is what is meant by “ionizing” the atom. Howis this problem similar to calculating the escape velocity of a mass from thegravitational effects of a larger mass (for example, a rocket being launchedfrom Earth into space)?

2) The colors of the four lines of the hydrogen spectrum are: red, blue-green, andtwo shades of violet. Which initial states ni = 3, 4, 5, or 6 correspond to thesecolors?

3) The grating equation (d sin θ = mλ) tells you at what angles different colors oflight will appear. Make a sketch based on the figure below to show a beam ofwhite light shining onto a grating with line separation, d = 1500 nm. Show theangles for red and blue light for m = 0, +1 and –1. You can find theapproximate wavelengths for red and blue light in your book.

Show on your figure each of the places where you could place your eye if youwanted to view red light. (Draw an eyeball in the appropriate place and label therays). 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 GRATINGSA diffraction grating is simply a piece of glass or plastic which has a series of veryfine scratches or grooves cut in its surface. The grooves are perfectly straight andparallel and are equally spaced so that there are a fixed number of grooves permillimeter, typically around 500 grooves/mm.

A grating behaves essentially like a screen with a bunch of equally spaced slits. Ifthe number of slits per length is n (grooves per mm), then the separation betweenadjacent slits is d = 1/n (mm per line or simply, mm). Consider what happenswhen a beam of monochromatic (single wavelength) light strikes a grating atnormal incidence, as shown below. Each slit scatters the light in all forwarddirections. However, in only certain directions will the light scattered from differentgrooves interfere constructively, producing a bright beam. This is just like thesingle & double slit diffraction you have done.

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

(1) d msinθ λ=

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

dincident beam

scattered light

grating

dθ

d sin θ

wavelength λ

to observer

interfere constructively, producing a bright beam in that direction. The integer m iscalled the order of the diffraction.

An incident light beam made of several different wavelengths will be split by thegrating into separate wavelengths, with each separate wavelength heading indifferent directions, determined by equation (1) above. In this way, the variouswavelengths can be determined by measuring the angles.

BOHR MODEL OF THE ATOMIn the 19th century, it was known that hydrogen gas, when made to glow in anelectrical discharge tube, emitted light at four particular visible wavelengths. In1885, a Swiss high school teacher named Balmer discovered that the fourwavelengths (here labeled λ i where i = 1, 2, 3 & 4) precisely obeyed themathematical relation:

(2)

−=

2

1

4

11

ii nR

λ

where R is a constant, and ni = 3, 4, 5 & 6. The four wavelengths (or "lines") werehenceforth called the Balmer lines. Why hydrogen emitted only those visiblewavelengths and why the wavelengths obeyed the Balmer formula was a completemystery.

The mystery was solved in 1913 by the Danish physicist Niels Bohr. According tothe Bohr model, the electron orbiting the proton in a hydrogen atom can only existin certain orbital states labeled with a quantum number, n (n=1, 2, 3, 4...). Whenthe electron is in orbit “n”, the total energy of the hydrogen atom is given by theformula:

(3) 22

6.13

n

eV

n

hcREn −=−= ,

where c is the speed of light, h is Plank’s constant and R is a number predicted bythe Bohr model called the Rydberg constant. The different energies En correspondto different orbital states of the electron. Smaller-radius orbits correspond tolower values of n and lower, more negative, energies. The n=1 state is the lowestpossible energy state and is called the ground state.

When an electron makes a transition from an initial state of higher energy Ei to afinal state of lower energy Ef , the atom emits a photon of energy

(4)E hf h

cE Ei fγ λ

= = = −

Here we have used the expression for the energy of a single photon: E = hf, whereh 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 finalquantum numbers like so:

(5)

hcE E R hc

n nRn ni f

i f f iλ λ= − = − −

= −

1 1 1 1 12 2 2 2,

.

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

PART I: Using a SpectrometerFor this lab, you will be using a simple spectrometer that separates light into itsindividual components. Point the spectrometer at the fluorescent lights on theceiling and look through the diffraction grating. You should see a scale that is usedto represent the wavelength (in nanometers) and a series of colored lines on thescale. We can now see that the white light is actually composed of a couple ofdifferent, yet distinct, wavelengths of light. These are the wavelengths of lightemitted by the atoms in the fluorescent tube. Let all the group members playaround 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 (blackstrip of plastic) either back or forth so that the green line observed from thefluorescent lights is at the known value of 546 nm. What are the otherwavelengths you see? What colors are they? Does this make sense? Why doesyour 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 oflight you observe as accurately as possible. Around the corner from the lab (askyou TA), there is a large poster of pictures of known spectrums of varioussubstances. Compare what you observed with what is given on the poster, andtry to determine what type of gas is inside the discharge tube. Are you sure thisis the correct gas? Why or why not?

PART II: Making Your Own SpectrometerNow you will make your own (and more precise) spectrometer using a diffractiongrating and a meter stick. This should give you some insight as to how aspectrometer works.

Observe the hydrogen source through the grating provided. In the first orderspectrum (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 isdark.)

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

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 itis perpendicular to the line from the lamp (that is, have the grating squarely facethe lamp). Place your eye very close to the grating and look through it toward thehydrogen lamp. On both sides of the lamp (above and below), you should clearlysee the images of the first-order Balmer lines. (Be careful to keep the gratingfacing the lamp. Move your eye position, not the grating, to see the lines to theside of the lamp.)

With a meter stick as close as possible to the lamp, as shown, measure the x-positions (on both sides of the central position) of each of the three lines asaccurately as possible. With your measured L and x's, compute the angle θ of eachof the first-order Balmer lines. (Hint: use tanθ = x/L) Make a table of your resultsin 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 ofeach of the (three or four) Balmer lines that you observe. Include a rough estimateof the uncertainty of your wavelengths (i.e., what part of your experiment may beinaccurate?).Record your method and results in your lab notebook.

Which spectrometer is more accurate? Why?

PART III: Everyday SubstancesUsing the same procedure as above, observe the light from the fluorescent lights onthe ceiling. Make a careful drawing of the spectrum lines and their measuredwavelengths 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?

grating

θ

L

x

eye H-lamp

position of a Balmer line

meter stick

images of Balmer lines

PART IV: Mystery Substances (time permitting)At the front of the lab, there should be a variety of mystery sources (in dischargetubes). 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 whatelements you are looking at. You may consult the poster or your textbook to figurethis one out