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Physics Labs with Flavor

Mikhail M. Agrest, College of Charleston, Charleston, SC

T his paper describes my attempts to look deep-er into the so-called shoot for your gradelabs, started in the 90s, when I began apply-ing my teaching experience in Russia to introductory physics labs at the College of Charleston and otherhigher education institutions in South Carolina. Theterm shoot for your grade became popular amongteachers of a projectile motion lab where studentsare graded based on their ability to predict the rangeof the projectile. I describe here several additionallaboratory exercises in which students are required

to predict results of the experiment. I also discussan essential element of these exercises which I callrecurrent study.

A variety of the aspects of this topic havebeen presented at meetings of SACS-AAPTand NCS-AAPT, as well as at the SC Academy of Science and elsewhere. Other authors, 1

also looking for improvement in the teaching of physics labs, have developed similarapproaches.

In my opinion it is important to bring some fla-vor into studies, some dramatic experience to spiceup the meal for students brains. Often, in the courseof a traditionally run lab, students perform numerousobservations and measurements but leave the analy-sis of the results for the lab report, which may notbe completed until long after class. In that case, they may not experience the emotional satisfaction associ-ated with their accomplishments in the lab. Most lab

manuals provide students with a more or less detaileddescription of the experiment in order to increase theeffectiveness of the time spent in the laboratory. Thisleads to a one-dimensional flow of the experiment,and alternative approaches may not occur to students.On the other hand, when the recurrent method of studying phenomena, described below, is employed, Ibelieve the learning process is enhanced, and studentsbecome excited about their work and can better appre-ciate the results of their efforts. Such an approach canalso be employed in physics lectures.2-4

Recurrent MethodThe recurrent method that I propose for studying

a phenomenon consists of three phases. In the firstphase, forward study, students review the phenom-enon, perform experiments, analyze the data, and thenform conclusions about the results. Based on theirmeasurements and analysis, and, of course, a theoreti-cal model, they determine the value of an unknownconstant associated with the phenomenon. In the sec-ond phase, backward study, students imagine the ex-periment being carried out under different conditions.They use the results of the first phase, along with themodel and the calculated constant, to predict the valueof a parameter that can be measured in this follow-upexperiment. Finally, in the third phase, experimentalassessment, students actually perform the new experi-ment to test their prediction in the presence of the in-structor. Visual assessment of the students predictiongets them involved on an emotional level and makesthe learning process more effective. The accuracy of

The Physics Teacher Vol. 47, M 2009 DOI: 10.1119/1.3116842 297


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R3 R5

R4

R1

V

R

V 4

V 9R10

V

R 6 R 7

R 8

R 9

Fig. 1. Circuit for Kirchhoffs equations experiment.

the prediction is used in grading the performance of the lab group.

As a teacher I have spent many years finding waysof addressing two major purposes of educationac-

quiring knowledge for practical purposes and expe-riencing the joy of learning. It is well known that thelearning process is more effective when students areexcited about the results and/or the process of thestudy. Physics is not always the most popular sciencein the eyes of contemporary students. The recurrentapproach to the study of physics described here en-gages students and increases the effectiveness of theinstructional process as students become more open tolearning.

Recurrent study is not a new idea. Scientists often

check the results of a solved problem by using the solu-tion to determine a known parameter. This is a stan-dard procedure in teaching mathematics at all levels.

How can one design an experiment with the fea-tures just described? It is necessary to come up with anexercise in which there is a constant parameter that canbe set by the teacher and whose value is unknown tothe students. A simple example would be the muzzlespeed of a spring gun. Students can determine thisspeed from the measured range of a projectile firedby the gun at some known projection angle. Know-

ing this (assumed constant) speed, they can go on topredict the range of the projectile when it is fired at adifferent initial angle.

I have developed a number of lab exercises based onthe method of recurrent study. These deal with fric-tion, Newtons second law, uniform circular motion,energy, Bernoullis equation, specific heat, the speedof sound, electrostatics, dc circuits, Ohms law, Kirch-hoff s laws, lenses, reflection and refraction, interfer-ence of light, and the photoelectric effect, among oth-ers. Nearly any introductory physics lab experimentcan be designed as a recurrent study exercise.

The full sets of lab instructions and recommenda-tions both for students and teachers fall beyond thescope of this paper. Interested readers may contact theauthor for additional details and suggestions. Here arebrief descriptions of some examples.

Kirchhoffs Equations for ElectricalCircuits

A variable power source supplies unknown voltage

V to an electrical circuit containing several resistors(Fig. 1).

Forward study: Finding voltage of the

power sourceThe terminals of one of the resistors (lets say resistorR 4) in the circuit are accessible, so students can mea-sure the potential difference (V 4) across this resistor.From this measured voltage, students can calculate thevoltageV of the power source. To get a more accuratevalue, they repeat this experiment several times usingdifferent values of R 4 and average their results. Finally,they estimate the uncertainty in the average value.More details on employing Kirchhoffs rules in a cir-cuits lab are found in Refs. 5 and 6.

Backward study: Finding the potential dif-ference across the test resistor The test circuit can be the same as the original, withone or more of the resistors replaced, or it can be acompletely different one (see, for example, Fig. 2).The test circuit for the backward study contains thesame power source providing the same voltage as inthe forward study. The assignment is to calculate thevoltage drop across one of the resistors based on the

Fig. 2. Possible test circuit for backward study.

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experimental value of the voltage supplied.

Experimental assessment: Comparing theresults

After the predicted voltage is announced, the poten-tial difference should be measured with a voltmeterand the answer called out. Usually this event attractsstudents from all other groups in the lab as it is accom-panied by high fives, shouts of Hurrah, Yes! andother expressions of satisfaction. Of course there willgenerally be at least a small discrepancy between thetheoretical and measured values; the grade for this partof the lab can be based on the percent error.

Bernoullis Equation for a Waterfall

A laminar waterfall is running out of an openingin a can into a pan in which it stands (Fig. 3). A shorthorizontal tube (not shown) of the same diameter asthe opening prevents a vertical component of the ve-locity of the water as it leaves the can.

More details on the Bernoullis equation lab can befound in Ref. 7.

Forward study: Estimation of the semi-empirical coefficient for prediction of thewaterfall landing distance

The two-dimensional motion of a liquid particle inthe moving stream can be described with a high accu-racy by the following equations:

x V t

h gt x =

=

0

2

2. (1)

Eliminating the time t , one can determine the initialspeed

(2)V x t

x g h x

02

= = .

Performing this experiment several times, studentscan calculate the average launching speed with ashigh an accuracy as their measurements of the land-ing place and the height of the opening would allow.

To relate the landing distance to the heighth of theopening and the levelH of the water in the can, westart by applying Bernoullis equation,8

(3)P v gh P v gh1 12

1 2

2

2

22 2

+ + = + +

,

to two points at different heightsh1 (= H ) and h2 (= h)in the can. Here P 1 and P 2 are the corresponding pres-sures at the two points; the water flow speeds arev 1 and v 2, respectively.

Considering that P 1 < P 2 and v 1 < 0, we cansolve this equation explicitly forv 2 = V th :

V g H hth = 2 ( ). (4)

In practice, this theoretical value of the exit speedfound from the Bernoulli equation does not match

the initial velocity calculated using Eq. (3). This isnot unexpected since Bernoullis equation assumes anon-viscous fluid, which water is not.

We introduce the coefficient,

k V V

x g h g H h

x h H h

x = =

=

0

2

1

2 2th ( ) ( )

.

In the forward study, students determine an averagevalue of the coefficientk from measured values of H ,h, and x .

Backward study: Finding the landing distanceFor the backward study, the values of bothH and h arechanged. This can easily be achieved by placing a block under the can (see Fig. 4).

Students use Eq. (5) to find V th, and then, usingthe experimental value of the coefficientk found in theforward study, they determine the expected exit speed:

x

h H

V x0

Fig. 3. The waterfall experiment.

(5)

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V kV k g H h x 0 th= = 2 ( ). (6)

To predict the landing distance under changed condi-tions, they calculate

(7) x V t k g H hh

g k h H h x = = = 0 2

22( ) ( ).

Experimental assessment Students should mark the predicted landing spot onthe pan. The actual landing is then observed and thepercent error in landing distance calculated.

Interference of Light A laser emits light of unknown wavelength toward

either a double slit or a diffraction grating. A patternof bright and dark spots appears on the screen as theresult of interference. More details on the interferenceof light lab can be found in Ref. 9.

Forward study Using the given slit separation for the double slit, stu-dents find the wavelength of the laser light.

Addressing the forward study assignment;Students direct a laser beam of unknown wavelengthat a double slit with given slit separationd . The dif-fracted light falls on a screen a distanceL away (see Fig.

5). The value of y m for one of the interference maximais measured and the wavelengthl is calculated usingthe equation10

(8)dy L

mm = l ,

where m is the order number for the chosenintensity maximum. The calculation is repeated forother diffraction orders. The values of l are averagedand the uncertainty in the result is estimated.

Backward study The same laser beam is directed at a diffraction gratingthat has a known number n of lines per mm. Usingthe value of the wavelength determined in the forwardstudy, students predict how far from the center of thegrating interference pattern the first-order bright spots

will appear.

Addressing the backward study assignment:To find the location of the first interference maximum(m = 1) for the light emerging from the grating, the

equation

l = d sin q (9)

is used. Here

grooves/mmd

n( )=

1

and

sin qy

L y 2 2+

.

h r H r

x r

Fig. 4. Backward study setup.

y

L

Laser

Double slit

Fig. 5. Forward study: double-slit diffraction.

y

L

Laser

Diffractiongrating

Fig. 6. Backward study: diffraction grating.

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Solving for y ,

(10) y L

d =

l

l2 2.

Experimental assessment The predicted positions of the bright spots should bemarked on the screen before turning on the laser. Usu-ally the bright spots appear on the screen very close tothe expected places. This generates excitement and afeeling of satisfaction about the experiment. Studentsare graded in part on how the percent errors in theirpredicted values compare with the experimental un-certainty.

I find that the dramatic experience of making a suc-

cessful prediction results in a learning experience thatis both enjoyable and memorable.

AcknowledgmentsMy deep gratitude goes to my students who inspiredme in my search for new forms of teaching, to my col-leagues in the Physics and Astronomy Departmentof the College of Charleston for the support in thissearch, to fellow members of SACS-AAPT, NCS-

AAPT, and National AAPT for support of the ideas,and especially to John Hubisz for his help and encour-

agement.

References1. A.J. Greer and J.D. Bierman, Challenge laboratories,

Phys. Teach. 43, 527 (Nov. 2005).2. M. Agrest,Lectures on General Physics I (Calculus-Based

Course) with illustrations (Brooks/Cole, ThomsonLearning, 2005).

3. M. Agrest,Lectures on Introductory Physics I,Revised(Algebra-Based Course) with illustrations (Brooks/Cole,Thomson Learning, 2006).

4. M. Agrest,Lectures on Introductory Physics I , Revised, with illustrations, (Brooks/Cole, Thomson Learning,2007).

5. David H. Loyd, Physics Laboratory Manual,3rd ed.(Brooks/Cole), Laboratory # 34, Kirchhoff s Rules,pp. 339-347.

6. David R. Sokoloff, Priscilla W. Laws, and Ronald K.Thornton, RealTime Physics Module 3 Electric Circuits (Wiley, Hoboken, NJ, 2004).

7. General Physics Laboratory Manual , edited by Laney Mills (Physics and Astronomy Department, College of

Charleston, Charleston, SC, 1998), Fluids the Ber-noulli equation, pp. 117119.

8. James S. Walker,Physics,4th ed. (Addison-Wesley,2010), p. 520.

9. Cicero H. Bernard and Chirold D. Epp, Laboratory Experiments in College Physics (Wiley, Hoboken, NJ),Experiment # 44, The Wavelength of Light, pp. 315320.

10. Jerry D. Wilson, Anthony J. Buffa, and Bo Lou,College Physics , 6th ed. (Pearson Prentice Hall), p. 763.

PACS codes: 01.50.Pa, 01.50.Qb, 47.00.00

Mikhail M. Agrest has an MS in fluid mechanics from Leningrad State University and a PhD in physics and mathematics from the Academy of Sciences of the USSR.After 20 years of research in membrane science and tech- nology there, he has been on the College of Charleston

faculty since 1993. He was also SACS-AAPT president in 2007.Physics and Astronomy Department, College ofCharleston, 66 George St., Charleston, SC 29424;[email protected]

The Physics Teacher Vol. 47, M 2009 301

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