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C O L L E G E O F S T A T E N I S L A N D

C I T Y U N I V E R S I T Y O F N E W Y O R K

PHY 206 SLS 261

DR. ANATOLY KUKLOV ENGINEERING SCIENCE & PHYSICS DEPARTMENT

COLLEGE OF STATEN ISLAND

PHY 206/SLS 261

PHYSICS LAB MANUAL

ENGINEERING SCIENCE & PHYSICS DEPARTMENT

CITY UNIVERSITY OF NEW YORK

ENGINEERING SCIENCE & PHYSICS DEPARTMENT PHYSICS LABORATORY EXT 2978, 4N-214/4N-215

LABORATORY RULES 1. No eating or drinking in the laboratory premises. 2. The use of cell phones is not permitted.

3. Computers are for experiment use only. No web surfing, reading e-mail, instant

messaging or computer games allowed. 4. When finished using a computer log-off and put your keyboard and mouse away.

5. Arrive on time otherwise equipment on your station will be removed.

6. Bring a scientific calculator for each laboratory session.

7. Have a hard copy of your laboratory report ready to submit before you enter the

laboratory. 8. Some equipment will be required to be signed out and checked back in. The rest

of the equipment should be returned as directed by the technician. Remember, you are responsible for the equipment you use during an experiment.

9. After completing the experiment and, if needed, putting away equipment, check that your station is clean and clutter free.

10. Push in your chair. 11. Before leaving the laboratory premises, make sure that you have all your

belongings with you. The lab is not responsible for any lost items.

Your cooperation in abiding by these rules will be highly appreciated.

Thank You. The Physics Laboratory Staff

ENGINEERING SCIENCE & PHYSICS DEPARTMENT PHYSICS LABORATORY EXT 2978, 4N-214/4N-215

ENGINEERING SCIENCE & PHYSICS DEPARTMENT PHYSICS LABORATORY EXT 2978, 4N-214/4N-215

10 ESSENTIALS of writing laboratory reports ALL students must comply with

1. No report is accepted from a student who didn’t actually participate in the

experiment.

2. Despite that the actual lab is performed in a group, a report must be individually written. Photocopies or plagiaristic reports will not be accepted and zero grade will be issued to all parties.

3. The laboratory report should have a title page giving the name and number of the experiment, the student's name, the class, and the date of the experiment. The laboratory partner’s name must be included on the title page, and it should be clearly indicated who the author and who the partner is.

4. Each section of the report, that is, “objective”, “theory background”, etc.,

should be clearly labeled. The data sheet collected by the author of the report during the lab session with instructor’s signature must be included – no report without such a data sheet indicating that the author has actually performed the experiment is to be accepted.

5. Paper should be 8 ½” x 11”. Write on one side only using word-processing software. Ruler and compass should be used for diagrams. Computer graphing is also accepted.

6. Reports should be stapled together. 7. Be as neat as possible in order to facilitate reading your report. 8. Reports are due one week following the experiment. No reports will be

accepted after the "Due-date" without penalty as determined by the instructor. 9. No student can pass the course unless he or she has turned in a set of laboratory

reports required by the instructor.

10. The student is responsible for any further instruction given by the instructor.

PHY 206/SLS 261

CONTENTS:

1. INTRODUCTION 1

2. UNIFORM MOTION (1st Newton’s Law of Motion) 6

3. FREE FALL 9

4. FORCES AND ACCELERATION (2nd and 3rd Newton’s Laws) 12

5. MECHANICAL WORK AND ENERGY 15

6. HEAT AND INTERNAL ENERGY (CALORIMETRY) 18

7. ELECTRIC FIELD AND ELECTRIC CURRENT (Ohm’s Law) 21

8. WORK OF ELECTRIC FIELD (Joule Experiment) 23

9. REFLECTION OF LIGHT 26

10. REFRACTION OF LIGHT 30

11. SOUND WAVES 33

12. ATOMIC SPECTRA 36

13. RADIOACTIVE DECAY 39

DEMONSTRATIONS AND SUPPLEMENTARY EXPERIMENTS: 1. CONSERVATION OF LINEAR MOMENTUM 41

2. ELECTRIC FIELD AND ELECTRIC CHARGES 43

3. ELECTROMAGNETIC FIELD 44

4. COLOR AND WAVELENGTH OF LIGHT 46

5. FORMATION OF AN OPTICAL IMAGE BY A CONVERGING LENS 49

APPENDICES: 1. MATHEMATICAL REVIEW 51

2. ANALYSIS OF EXPERIMENTAL DATA 54

3. GRAPHICAL ANALYSYS 3.4 – FINDING THE BEST FIT 57

4. TECHNICAL NOTES ON VERNIER LABQUEST2 INTERFACE 61

5. TECHNICAL NOTES ON SENSORS AND PROBES 65

6. MULTIMETERS AND POWER SUPPLIES 71

1

THE COLLEGE OF STATEN ISLAND

Department of Engineering Sciences & Physics

THE NATURE OF PHYSICAL PROCESSES

Introduction: This one semester Physics course for future teachers has several objectives. One

of these is quite traditional -- giving an overview of the main physical facts and

explanations. This is the historical part of the course, and students may be tempted to rely

fully on just memorization of facts, laws and equations. However, the historical part is

not the main objective. A more important one is developing conceptual approach to

Nature as a whole in order to be able to recognize concepts which are relevant to a

particular problem. In other words, the most important goal is developing problem

solving skills.

Physics is not a collection of facts or equations. Physics looks for the most

general concepts which form the basis for the understanding of relationships between

various phenomena. In fact, only few general physical concepts can account for a huge

variety of natural phenomena. This is a direct manifestation of the unity of Nature.

Physics is the only intellectual achievement which, besides its cultural importance, is

endowed with an actual tremendous physical force. A few Physical concepts have

changed our world upon being implemented in industry and the military. No electronic

device could be manufactured without the understanding of the basics of electricity and

magnetism. No car engine would be possible without the knowledge of the laws of

mechanics. Even our social life is strongly affected by Physical concepts and their

implications. It is also good to realize that all medical imaging techniques such as X-rays,

ultrasound, MRI, isotopes etc. are all physics inventions. In addition, one of the most

critical cancer therapy – radiotherapy – is also the achievement of Physics.

At the same time, it is important to understand that not all Physical concepts are

equally general and are expected to be strictly valid. Some of them are only good

approximations to the actual behavior of physical objects. Such a difference will be

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emphasized during the course. It is expected that most of the learning efforts are

devoted to the fundamental laws and their applications.

A central part of the conceptual approach is the understanding of the relationship

between Theory and Experiment, that is, observing what actually happens under given

circumstances and relating the results to theoretical predictions. A theory is considered

trustworthy if it allows us to explain coherently various phenomena and make predictions

with good accuracy. The following story sheds some light on this relationship: Dogs do not like when anyone pulls their tail. Using this observation and the conceptual approach,

a theoretician John formulated a hypothesis saying: the number of times (B) a dog will bite you

is proportional to the number of times (N) you pull the dog’s tail. Mathematically this

relationship is expressed as B/N=const. A brave experimentalist Steve was checking the

hypothesis by pulling his dog’s tail N times and counting the number B of bites he received. Steve

was going to see that the experimentally measured value of B/N was indeed nearly constant, as

predicted by John’s theory. However, no conclusion can be drawn because Steve was eventually

eaten by his dog. John is looking for another brave experimentalist who would continue

experimenting and either will confirm or disprove John’s theory. This story is, of course, a joke. However, it contains the main elements of the relationship

between Theory and Experiment: Based on experimental observations, Theory formulates

a hypothesis which is supposed to be valid under certain circumstances. Experiment

realizes these circumstances in real life, and tries to compare the outcome with the

theoretical prediction. If the outcome is close to what is predicted, the theoretical

hypothesis can be considered reliable. Unfortunately, we are not always able to control

all the circumstances. Then more and more experiments are required in order to diminish

the role of these uncontrollable circumstances, and finally either to prove or to disprove

the hypothesis.

While working out a concept or preparing an experiment, it is crucial to simplify

the situation, so that unimportant factors are not interfering with the key factors. As you

will see, our laboratory experiments are composed in such a manner. However, not all the

unwanted factors can be completely eliminated. These introduce some uncertainty into

the measurements. Therefore, a very important issue which must be analyzed in each

experiment is the accuracy of the experimental result (see Appendix). So, estimating

errors of measured quantity is as important as finding the quantity itself.

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II. Organizing the Laboratory Report The laboratory report on the conducted experiment should contain the following:

1. Concise statement of objectives of a particular experiment;

2. A brief outline of the physical principles and assumptions used in the

experiment and a clear theoretical statement which is to be tested

experimentally;

Do not rewrite this manual ! Use your own words!

3. A short description of the experiment saying distinctly what (and how) is to be

measured and to be compared with the theoretical prediction;

4. Experimental data arranged in tabular form with labeled rows and columns, so

that the meaning of each number and its units in this table are evident;

5. Computations of the intermediate quantities and the final quantities which lead

to the main objective (the results of the computations are to be represented by

numbers and graphs);

6. Calculation of the percentage deviations (% difference) and errors (% error)

for each measured physical quantity;

7. Conclusion section which states clearly:

a) the value (-s) of the measured physical quantity (-ies);

b) the percent error (-s) and the percent difference (-s) for the

measured quantity (-ies) (see Appendix: Analysis of Data);

c) how reliably the experiment was done (refer to b));

d) what are the sources for the errors and the deviations which affect your

results;

e) based on b), your opinion on whether the experiment supports the

theory.

7. Answers to questions.

Technical Part

The laboratory report must be prepared personally by each student even though

the data was collected in group work. The report will not be accepted unless a student

4

personally took part in the measurements during the class work (or during a specially

arranged time). The report should be word processed, with the first page indicating the

name of the student and of the partners, the title of the experiment, the class, and the date

of the experiment. Graphs must be neatly drawn either by computer or by hand on graph

paper.

III. Report on Demonstrations During each demonstration some topic will be discussed and corresponding

experiments or simulations will be performed. After each demonstration, a short report on

its essence must be written. This report should include a short description and physical

explanation of the experiments (or simulations) done during the demonstration. Finding

parallels and common ground with other experiments as well as facts and phenomena are

very welcomed. Extended conceptual discussion of the topic will be highly appreciated.

Problems related to the topic of the experiments will sometime be suggested for

solving. The solutions should be included in the report.

IV. Laboratory Rules and Regulations (not to be taken lightly

The following rules and regulations are to be followed by anyone entering the

premises and using the laboratory facilities of the Nature of Physical Processes course

offered by the College of Staten Island.

)

1. Students are not to be in the laboratory unless the assigned instructor or

technician is present.

2. No drinking or eating are allowed in the laboratory at any time.

3. Order and decorum is to be maintained at all times.

4. The equipment should be left untouched until authorization for its use is given

by the instructor.

5. Tables and equipment are to be kept and left in a clean, neat and orderly

condition.

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6. Each procedure which is to be performed on a computer or other equipment

must be considered first in order to avoid any harm to people, to the computers,

and to the software and other equipment.

The above rules and regulations are required primarily for the safety of all students, and

will also help the student to swiftly and correctly complete the laboratory assignments.

6

UNIFORM MOTION (NEWTON’S FIRST LAW)

One purpose of this experiment is to analyze the concept of Uniform Motion and to learn how to perform measurements. A second purpose is to see the role of various factors in the process of measurement which contribute to deviations (errors). THEORETICAL BACKGROUND: An object executes Uniform Motion, that is, it moves straight with constant velocity (or remains at rest), unless other bodies exert a finite resultant force on the object. This statement is known as Ist Newton’s Law of motion. Thus, in order to realize Uniform Motion it is crucial to eliminate (or strongly diminish) the main sources of such forces. In this lab friction and gravity are of a particular concern.

Uniform motion can be described in terms of the distance S traveled during the time t by a simple formula

S=Vt, (1)

where V is the object velocity which stays constant during the motion. Units used for S are meters (m) or centimeters (cm=1/100 m). Time is measured in seconds (s). Correspondingly, the units for velocity are m/s or cm/s. The formula (1) can be viewed graphically, if the horizontal axis of the graph is used for t and

the vertical axis for the distance S. Then, this graph is a straight line whose slope gives the

velocity V.

Graph: Distance vs time

The concept of Uniform Motion implies that:

For any measured pair of S and t the ratio S/t=V is independent of S and t, whenever the object is not subjected to a net force.

7

Practically, all the objects around us experience external forces. This implies that in reality the ratio S/t=V always deviates from a constant. In other words, the experimental data for S and t represented on the graph by dots are in general not on the straight line.

If the external forces are reduced or compensated, an object’s motion becomes more and more close to Uniform Motion. This is exactly what has to be tested by the experiment.

EXPERIMENT: Leveling the air track compensates for the gravity, and the air blowing through the holes greatly reduces friction. Thus, after giving an initial push, the glider should move nearly uniformly along the track in accordance with Newton’s First Law. In order to check this, the glider coordinate as a function of time is to be measured by the synchronized timer with two photogates set up along the track so that the distance between them is S. The glider will be launched several times by the rubber band stretched to the same degree, so that the glider should repeatedly perform the same motion. Once the glider passes through the two gates the time reading on the timer screen gives the value of t.

PROCEDURE: Set the photogates the distance S apart (see the sketch). Make readings for several distances S and the corresponding time intervals t. The velocity of the glider is to be found in two ways: a) by the formula (1); b) as the slope of the graph -- distance vs time.

ANALYSIS OF DATA: Arrange a table with the following columns: 1) distance traveled by the glider; 2) time; 3) velocity; 4) deviations of the velocity from the mean velocity. Plot your data for S and t on a graph distance vs. time. Make the linear fit of the data by drawing a straight line through the data, and determine the velocity from the slope of this line. Also find the velocity as an average of the entries in column 3). Calculate the mean deviation of the velocity (see the Appendix: Analysis of Data). DISCUSSION: Compare the results for V you obtained with what is expected for Uniform Motion. Discuss reasons for the deviations of the velocity from the mean value. QUESTIONS: 1) With what accuracy in percent does (or does not) your experiment support the concept of the Uniform Motion? 2) The theory predicts that the velocity calculated by the slope and as the average of column 3) should be the same. However, in practice these two methods give slightly different results. Why is this so?

8

3) Will the coordinate vs time graph remain a straight line if the air track becomes inclined? Explain. 4) What is the average velocity you measured if expressed in mm/s, m/s and km/h? 5) For your one specific measurement of the velocity, make a prediction what the glider displacement would be, if the glider were moving with this velocity for 5 seconds.

9

FREE FALL

Uniformly accelerated motion will be analyzed and applied to an object falling freely due to gravity. THEORETICAL BACKGROUND: In the Uniform Motion experiment we learned that if there is no external force, the distance covered by an object is proportional to the time it moves. This statement is no longer true, if a constant force is applied to the object. Earth’s gravity pulls all objects to the Earth’s surface. If gravity is the only force acting on the object, the object’s motion is called Free Fall. In this case velocity varies in time. Therefore, the distance S the object covers is not proportional to time t anymore. Instead,

the velocity change is proportional to time as

V-Vo = g t, (1) where Vo is the object’s initial velocity at the time moment t=0. In this relation, the constant g shows how fast the velocity of the freely falling object changes in time. It is called the acceleration of free fall. The value of g is expected to be independent of the nature of the object. Close to Earth surface g = 9 80 2. /m s =980 cm s/ 2 . This value will be considered as a known (or given ) value to be tested experimentally. The Free Fall Motion is an example of Uniformly Accelerated Motion. The theoretical graph V vs. t is a straight line.

V(cm/s)

Vo

t (s)

Graph: V vs. t

The distance covered by the object in the free fall is now related to g and t as well as to Vo. Specifically,

S V t gto= +12

2 . (2)

While the graph of V vs. t is a straight line with the slope given by g, the graph of S vs. t is not a straight line. The theoretical graph S vs. t is a parabola:

10

Graph: S vs t

Measurements are aimed at finding the value of g and comparing it with the given value and also at how accurately the concept of Uniformly Accelerated Motion can be applied to a freely falling object.

EXPERIMENT: The measurements will be done with the help of Behr Free-Fall apparatus. The distance S(n) of the falling object traveled during n intervals of time is tracked by the spark timer every ∆t =1/60 second on the waxed paper tape:

S

t

11

The displacement ∆S(n) during the nth time interval can be measured as the distance between two successive spark traces:

∆S(n)=S(n+1) - S(n). (3) The velocity at the nth interval is

V(n)= ∆S(n)/∆t. (4)

The acceleration can be obtained as a slope of the linear fit of the graph V vs. t=n∆t.

ANALYSIS OF DATA: Make a table containing four columns: 1) the time t=n∆t; 2) the distance S(n) (assigning S=0 to the initial point n=0); 3) the velocity V(n) for each t.

Plot your experimental data for V on a V vs. t graph and make the linear fit of these data. Find the acceleration g as the slope of the best linear fit line. Plot also a graph of your experimental distances S vs. t. DISCUSSION: Compare the value of g you found with the known one. Discuss the reasons for the deviations of the V vs. t data from the corresponding points on the V vs. t straight line graph. Evaluate the error of measuring g and compare it with the percent difference. Discuss the shape of the S vs. t data graph and compare it with that obtained in the experiment UNIFORM MOTION. QUESTIONS: 1) What is the percent difference of the found g with the known? 2) What is the percent error of the measured g ? 3) How does the air resistance affect the measurement of g ? 4) If the same experiment were performed on the top of a mountain, would you expect g to be larger or smaller than what you have obtained ? 5) Does this experiment prove that the value of g is independent of the mass of the falling object? 6) Can a freely falling object be close to Earth and yet never hit the Earth?

12

FORCE AND ACCELERATION (NEWTON’S 2nd and 3rd LAWS) The behavior of a physical object subjected to a constant external force is to be studied. THEORETICAL BACKGROUND: The interaction between various objects is responsible for a whole variety of phenomena in our Physical World. If no interaction existed, our world would be a bunch of objects performing Uniform Motion in accordance with Newton’s 1st law. We would not even exist because no forces would bind the constituents of our organisms together. What a boring world! So Force is one of the central physical concepts. It is not possible for us to trace out all the possible means by which various forces act, and what are all the implications. However, we will consider a specific situation which can be studied completely. This is based on the observation that a force applied to a single object produces acceleration of this object. Furthermore, a constant force produces a constant acceleration. In accordance with Newton’s second law of dynamics, the acceleration is proportional to the force.

This law can be formulated as (Newton’s 2nd Law):

F=MA, (1)

where A is the acceleration and F is the force. While F is essentially due to other objects, the coefficient M is a property of the accelerating object. This property is called mass. Applying this equation, we immediately deduce that due to gravity any object of the mass m feels the force m g⋅ close to Earth’s surface. This force will be applied to an object of mass M in order to verify the equation (1) experimentally. Unit of force is a Newton (N) and mass is measured in kilograms (kg). Accordingly, kg m / s21 1N = ⋅ . The 3rd Newton’s Law tells something very important about the action-reaction forces between interacting objects: if the action force F is produced by some other object of mass, say, m, then exactly the same reaction force in the opposite direction is produced by the object M on the object m. EXPERIMENT: A glider of mass M is placed on the air track with a string and hanging weight of mass m attached. Gravity pulls the hanging mass m down with the force W=mg. The action force on the glider is transferred from the hanging weight through the string as the string tension F. The force F should produce the acceleration A in accordance with the formula (1).

13

In order to measure A, two photogates are placed at a distance S apart so that the time tthe glider moves through this distance can be measured. If the glider starts moving from rest with some constant acceleration A, this acceleration can be computed by the following formula

ASt= 2 2 . (2)

Finally, if indeed the formula (1) is valid, the mass M can be found as either the slope of the linear fit of the graph F vs A or from the ratio

FMA

=

(3)

In order to find F, we use 2nd and 3rd Newton’s Laws as: mg-F=mA and F=MA. From these equations:

( )F m g A= − (4)

Summarizing, the purpose of these measurements is to obtain data on F (from Eq.(4)) and A (from Eq.(2)), and check that these are related to each other through the theoretical dependence given by equation (1). The glider mass M is to be found and compared with the value obtained from the scale

.

PROCEDURE: Set S at an appropriate distance (approximately 80-90 cm). For several hanging weights mg measure time t . Do at least three measurements of t for each weight. Compute the acceleration A in accordance with the formula (2). Do not forget to

14

measure the glider mass M on the scale in order to compare it with the value obtained from equation (3). ANALYSIS OF DATA: Arrange your data in columns: 1) hanging mass m ; 2) Force F=m(g-A) ; 3) time t; 4) acceleration A (as given by equation (2)); 5) glider’s mass M=F/A; 6) deviations of the mass M. Plot a graph of the tension force F vs. A, and find the slope of the best linear fit of this graph. Compare the mass M obtained from the slope with that obtained from the scale. Also, calculate the mass as the mean of the entries in column 5). Find the mean deviation of M. DISCUSSION: Give a conclusion as to whether this experiment supports Newton’s 2nd and 3rd Laws of dynamics. Discuss the precision of your measurements for the glider mass, and possible reasons for the errors. QUESTIONS: 1) How close is the value of the glider mass obtained from the slope to that obtained from the scale? What is the percent difference? 2) How could you check that the glider acceleration is constant during the motion, and does not depend on the distance S ?

3) Use elementary algebra and express A in terms of m,M and g from Newton’s equations mg-F=mA and F=MA.

4) For your one specific measurement of the acceleration, make a prediction what the glider velocity and the displacement would be, if the glider were moving with this acceleration for 4 seconds.

15

MECHANICAL WORK AND ENERGY

Conservation of mechanical energy will be studied as a fundamental law of Nature in a simplest mechanical setup. THEORETICAL BACKGROUND: The concept of Work and Energy is crucial for understanding Nature. Its importance is not limited to the mechanics of a single object. This concept can equally be applied to complex systems -- atoms, molecules, substances, and even organisms. All acts of motion, transformation, and creation in our world are due to Work and Energy. We will begin study of this concept for a simple mechanical system -- the glider on the airtrack. In future experiments we will also analyze how the Work and Energy concept can be applied to substances, electricity, and even our organisms. A very special significance is endowed to the Law of Conservation of Energy which states that

total amount of Energy in the world is constant. That is, Energy can neither be created or destroyed. It can be only transformed from one form to another and redistributed between objects. The process of Energy transformation and redistribution is called Work.

Here we will talk only about Mechanical Energy and Work. Any moving object possesses

Kinetic Energy KEMV

=2

2 . The larger the object mass M or the velocity V, the greater

is KE. If two moving bodies are considered, then their total kinetic energy is

KEM V M V

= +1 12

2 22

2 2 , (1)

where the indices refer to the first and the second object, respectively. Forces produce Work upon objects, and thereby change their KE. Another form of mechanical energy is Potential Energy (PE). The PE depends on the particular kind of force, acting on the object, as well as on the object’s position. It does not depend on the velocity of the object. For example, in the gravitational field close to Earth’s surface, an object of the mass M2 has the PE

PE= M2gh, (2) where h is the height of the object’s position above some reference line. So the PE

changes with height. The unit of energy is the Joule (J) where 1 kg ms J⋅ =

22 1 .

If the mechanical system is isolated from the environment, the total Mechanical Energy is

E=KE+PE=constant. (3)

16

In other words, the total mechanical energy is conserved, in accordance with the general statement given above. Mechanical energy can be lost or acquired, if it is transformed to or from other forms of energy. For example, friction decreases the KE and heats the environment. If, however, no friction is present, the equation (3) says that any increase of the KE occurs at the expense of the PE, or conversely any increase of the PE occurs at the expense of the KE. Reformulated in terms of the KE change ∆KE and the change ∆PE, this statement becomes

∆KE = - ∆PE (4) In this experiment, we will test the statement (4). EXPERIMENT: The setup is similar to that we used in the earlier experiment we did on “Newton’s 2nd Law”.

The first object with mass M1 is the glider on the level air track. The second object with the mass M2 is the hanging weight. The total energy of this system -- the glider and the hanging weight -- must remain the same during the joint motion of these two objects. Thus, the graph ∆KE vs |∆PE| should be a straight line with slope one. Note that, while the mass M2 changes its height by h, the mass M1 advances along the airtrack by the same distance, that is, by h. PROCEDURE: Make sure that the weight does not hit the floor before the glider passes through the gate

M2

. Starting from rest (V=0), the velocity will increase uniformly due to the object . For given M1 and M2, the velocity V will be measured by the timer in the photogate in the regime gate. To calculate V use the formula:

V=d/t, (5) Where d=0.1 m which is the length of the flag on the glider and t is the time it takes for the glider to cross through the photogate.

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From equations (1), and (2), calculate the values of ∆KE and |∆PE|. Repeat this procedure for several heights and masses M1 and M2. ANALYSIS OF DATA: Arrange the following data columns: 1) M1 (kg) 2) M2 (kg); 3) h (m); 4) time t (s); 5) V(m/s)=d/t (m/s); 6) ∆KE = ( ) /M M V1 2

2 2+ (J); 7) |∆PE| = M2 g h (J). Plot the graph ∆KE vs |∆PE|. Find the slope of the best linear fit line for this graph and compare it with the expected value 1. Compute the percent difference from the expected value. Evaluate the percent error of the slope. DISCUSSION: Conclude on whether your data supports the Law of Conservation of Mechanical Energy and with what accuracy. Discuss possible physical reasons for the deviations of the experimentally determined slope from the expected value. QUESTIONS: 1) If the kinetic energy of an object has increased by 16 times, by how many times has its speed increased? 2) If the slope of the graph ∆KE vs |∆PE| is greater than 1, does this mean that the total energy has increased or decreased ? 3) Do frictional forces increase or decrease the total mechanical energy of an object during its motion? 4) How would the slope (if compared to 1) of the best linear fit graph change in the presence of friction? 5) Discuss possible deviations of the slope in cases when the air track was not level.

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HEAT AND INTERNAL ENERGY

The concept of Energy is applied to complex objects -- solids and liquids consisting of huge amounts of atoms and molecules. Temperature is introduced as a parameter characterizing the internal energy of substances. The Law of Conservation of Energy is to be analyzed for the case of the internal energy of substances. THEORETICAL BACKGROUND: In the work “Mechanical Work and Energy” the energy of macroscopic objects -- glider connected to a weight -- has been discussed. The Law of Conservation of Mechanical Energy was analyzed for a simple physical system. It is not obvious that the same concept can be applied to atoms and molecules -- extremely tiny objects. However, the notion of Energy turns out to be very general and applicable for the whole Universe from galaxies to subatomic particles. Temperature characterizes the kinetic energy of chaotic motion of atoms and molecules. The hotter a piece of steel, the faster the motion of its atoms and electrons. This means that the internal kinetic energy increases with the temperature. Nevertheless, Temperature should not be identified with Heat

Q Mc t tf i= −( )

. There is a simple relation between the change of the internal energy Q of an object (or heat supplied to it) and the change of temperature t of the object:

(1)

where the subscripts “i” and “f” refer to the initial and final states, respectively; M is the object’s mass, and c denotes the Specific Heat for the material the object is made of. This quantity indicates by how many Joules the heat energy of each kg of the body increases, if the temperature is raised by one degree Celsius. Temperature also controls the heat transfer from one object to another. Heat normally flows from a hotter object to a colder one until temperatures of both objects become equal. If no mechanical work is being done on the system, the total internal energy of this system will not change.

th

This is a consequence of the Law of Energy Conservation. In order to analyze the law, three objects are used -- calorimeter, water and a piece of metal. If the metal is heated until some temperature and then immersed into cold water, the metal will change will give up some heat

Q c M t tm m m f h= −( ) , (2) where the subscript “m” refers to the metal in equation (1) and t f is the final temperature of the mixture -- metal, calorimeter and water in it. Accordingly, the water and the calorimeter, which were initially at the temperature ti , will change their energy so that their mutual change becomes

Q c M t t c M t tcw c c f i w w f i= − + −( ) ( ) (3) where the subscript “c” and “w” refer to the calorimeter and the water, respectively.

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Expressing this as a formula, one has

The total internal energy of the closed system which performs no mechanical work does not change in time. In other words, the internal energy change must be

zero.

0 =+ cwm QQ . (4) From this equation it is possible to find the temperature th the piece of metal had before it was immersed into the water. If this temperature coincides with the actually known temperature, then this will confirm the law of the energy conservation in this experiment. The expression for th which is obtained from equations (1)-(4) is

t tM c M c t t

M ch fc c w w f i

m m= +

+ −( )( ) (5)

EXPERIMENT: A sample of metal is placed in boiling water so that its temperature th becomes 100o C . This sample is then immersed into a calorimeter containing water at room temperature, and the final temperature t f is measured. Finally, the initial temperature of the sample th can be calculated in accordance with the prediction (5) made from the conservation law and then compared with the known value of 100oC .

PROCEDURE: Measure the quantities M M Mm w c, , , and ti prior to immersing the sample. Note that the mass of the inner cup plus the stirrer only should be measured for Mc . Measure the final temperature t f after the sample was heated up in the boiling water and then immersed into the calorimeter. Stir the water in the calorimeter a little, so that the final temperature becomes the same for all three objects -- the sample, the water, and the calorimeter. The three required values for the specific heats are

cJ

g C cJ

g C cJ

g Cc o m o w o=⋅

=⋅

=⋅

0 90 0 45 419. , . , .

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ANALYSIS OF DATA: Arrange columns for ti , th and deviations of th. Repeat the procedure several times, so that you will have several results for th. Calculate the mean of th and the mean deviation of th (see Appendix). Compare the mean of th with the known value 100o C . DISCUSSION: Discuss what you have tried to prove in this experiment. Make a statement on the accuracy. Discuss possible physical reasons for the deviations. QUESTIONS: 1) How close in percent is th to the known value and what is the error of

th ? 2) If the calculated value of th is always below 100o C , what can you say about the total internal energy of the system, -- was it lost or gained? 3) If the calculated value of th is steadily well above 100o C , what can you say about the total energy of the system, -- was it lost or gained? 4) A 10 g bullet is stopped by 12 kg of water in a calorimeter. As a result of this collision, the temperature of the water has increased by 0.05oC. Assuming that all the kinetic energy of the bullet was transferred to the water, calculate the velocity the bullet had before the impact.

21

ELECTRIC FIELD AND ELECTRIC CURRENT (OHM’S LAW)

Based on the demonstration “Electric Field and Electric Charges”, the concept of electric current is introduced. A property of the conductor -- resistance and Ohm’s law are is discussed. The difference between strict laws of Nature like the Law of Energy Conservation and empirical rules is discussed. THEORETICAL BACKGROUND: Materials containing electric charges which can move freely are called conductors. Applying an electric field to such a material results in the mechanical motion of the charges in one particular direction. This unidirectional motion of electric charges is called electric current. The applied electric field is characterized by the difference of the electric potential V along the conductor. It is measured in Volts (V). The electric current I is characterized by the amount of charge transferred through the conductor each second. It is measured in Amperes (A). For most conductors, the relation between V and I follows Ohm’s law

V=RI , (1) where R is the resistance of the conductor, which does not depend on either V or I. Resistance depends on various factors -- the material the wire is made of, the length of the wire, its cross sectional area. Resistance also depends on the temperature of the wire. The unit of R is the Ohm (Ω). If graphed on axes V vs I, the equation (1) yields a straight line with the slope R. However, not all conductors obey Ohm’s law. This means that, if plotted, the data V vs I may be far from the straight line. Such conductors are called non-ohmic. EXPERIMENT: To test the relation (1), a resistor which obeys Ohm’s law is used. It is to be connected in series with the power supply and ammeter - the device measuring the current I. The voltmeter is used to measure the voltage V across the resistor. Use this chart for making the connections.

Subsequently, use the lamp as a non-ohmic resistor R, and repeat the measurements. PROCEDURE: The current I should be measured for various V for the ohmic resistor and the lamp. For each case, the graph V vs. I is to be plotted.

22

ANALYSIS OF DATA: For the ohmic resistor, arrange columns for V , I. Plot the data V vs I and make the best linear fit. From the best linear fit line find the resistance R of the ohmic resistor and compare it with the known value. For the lamp, set up three columns V, I,R. Plot the graph V vs I for the lamp. DISCUSSION: For the ohmic resistor, discuss how accurately your data supports (if any) Ohm’s law. Discuss the percent error and percent difference. For the lamp, conclude whether the direct proportionality indicated in equation (1) does or does not hold. Give your opinion on the meaning of Ohm’s law within the context of general laws of Nature. QUESTIONS: 1) For the ohmic resistor, how close in percent is R to the known value and

what is the error of R? 2) What is your physical explanation for the fact that the lamp data does not follow Ohm’s law? 3) From your lamp data, find the lamp resistance at 15 V. 4) From your lamp data, find by how many times the resistance of the lamp changes while the voltage changes from small to high values. 5) A 120Ω resistor is connected in series with another one, so that the resulting resistance is 200Ω. What is the resistance of the second resistor?

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WORK OF ELECTRIC FIELD The work done by the electric field driving the electric current is analyzed. The Law of Conservation of total Energy is tested for the case of electric energy conversion into internal energy. THEORETICAL BACKGROUND: In the two preceding experiments “Mechanical Work and Energy” and “Heat and Internal Energy”, the concept of energy was discussed and developed. All physical objects and processes can be described in terms of the Energy content and the Work done. The electric field possesses energy and can therefore perform work. If a current I is driven by a voltage V across a resistor, some work is continuously being done. The amount of this work during the time t is

W IVt= (1) This work heats the environment. The Law of Conservation of total Energy requires that the heat Q acquired by the environment is exactly equal to the work W done by the current

Q=W. (2) The relation (2) is of crucial importance. It says that the work done by the electric field is not being lost. It is being converted into heat energy. The purpose of the following analysis is to develop an experiment for testing the Law of Energy Conservation represented by equation (2).

If the heat Q is delivered to a known amount Mw of water contained in a calorimeter of mass Mc , the temperature increase of the water and the calorimeter can be found from the formula

Q c M t t c M t tcw c c f i w w f i= − + −( ) ( ) (3)

(see the experiment “Thermal Energy”; c Jg Cw o= ⋅419. is the specific heat of water,

c Jg Cc o= ⋅0 90. is the specific heat of the calorimeter).

EXPERIMENT: A heat producing resistor is immersed into the water in the internal can of the calorimeter. Voltage is applied to the resistor. The temperature of the water is monitored by a thermometer. Time of current flow is also monitored.

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PROCEDURE: 1) Weigh internal can of the calorimeter together with the stirrer. Fill the can about 3/4 full of water, and weigh it again, and obtain the mass of the water. 2) Connect the voltmeter, ammeter, and the heating coil (resistor) according to the diagram.

3) Once the circuit has been checked, place the heating coil in the water and then turn on the power supply by closing the switch. Record both the voltage V and the current I. Open the switch once this is done. Stir the water gently and record the initial temperature

Do not turn on the power supply until it has been checked by the instructor.

ti 4) Close the switch to reconnect the power supply, start the timer, and constantly and gently stir the water. Observe the temperature rising. Take the readings of temperature, current and voltage every 100 seconds for about 1000 s. Continue gently stirring during the experiment. Avoid spilling the water from the internal can to the external can! ANALYSIS OF DATA: Organize your data as the following columns: 1) time; 2) voltage ; 3) current; 4) temperature; 5) work of electric field; 6) heat acquired by the calorimeter. Do not forget to measure and record the other quantities entering equation (3), i.e. the mass of the water and the mass of the calorimeter together with the stirrer. Plot a graph of the experimentally determined values of the heat acquired by the calorimeter vs the work of the electric field. If the experiment were absolutely precise, the slope of the best linear fit line of this graph would be exactly 1. Find the actual slope and compare it with 1. DISCUSSION: Discuss what you have tried to prove in this experiment. Analyze possible physical reasons for deviations of the measured slope from the predicted one.

25

QUESTIONS: 1) What is the percent difference of your measurement of the slope, and

what is the error of the experimental slope? 2) If the measured value of the slope of the Q vs W line is below the theoretical prediction, is the work done by the electrical field greater than or less than the heat transferred to the water in the calorimeter? 3) Given your data, calculate the time required to boil the water.

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REFLECTION OF LIGHT The law of light reflection is investigated and used for constructing images by mirrors. THEORETICAL BACKGROUND: Light is reflected by a mirror. The law of reflection states that the angle of reflection (let us call it θr ) is equal to the angle of incidence θi, and the three lines -- the incident ray, the reflected ray and the perpendicular (normal) to the mirror -- are all in the same plane. θr = θi (1)

The image S’ of an object S giving off light is formed either by the intersection point of the reflected rays (solid lines) or their geometrical continuations (dashed lines). In Fig.1 the point S’ is the image of the point S.

S S’ θi θr

Fig.1. Plane mirror (vertical solid line) This image is the intersection point S’ of the rays sent by the object S. Here only two rays are shown. It is important to note that any third ray sent by S will be reflected by the mirror in such a way that its continuation will also pass through the image point S’. Such an image is called a virtual image. We will use this method for constructing images in more complex situations. Concave mirrors can produce real images. An important characteristic of the concave mirror is its focal point. This is the point F where the beams of light parallel to the axis of the mirror converge, that is, they create an image of a very distant object (say, a star). Convex mirrors produce virtual images. Accordingly, its focal point F lies behind the mirror surface. The distance from the focal point to the mirror vertex is the focal distance f. For the concave mirror it is positive and for the convex – negative. This distance is given by half of the mirror curvature radius.

27

Fig.2. In order to construct an image of any object placed in front of a mirror, two incident rays can be used – one going parallel to the main axis (and then reflected through the focal point) and the other going through the focal point (and then reflect parallel to the main axis). This procedure is shown on Figs.3,4:

Fig.3: Real image S’ formation by the concave mirror

Fig.3: Virtual image S’ formed by the convex mirror: the incident ray 2 continued (dot-dashed line) through the focal point F so that the reflected one goes parallel to the main axis; the incident ray 1 is parallel to the main axis and the reflected one continued backward through the focal point.

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The distances do , di of the object S and the image S’ are related to the focal length f through the equation

0

1 1 1

id d f+ = (2)

The image can be larger or smaller than the object. The ratio M of the image height hi

to the object height ho is called magnification. The value hi is taken positive if the image is upright and negative if inverted. Using simple geometry it is possible to show that

i

o

dMd

= − (3)

Where di is positive for real images and negative for virtual. EXPERIMENT: Using the ray box, the property of reflection of light will be studied for the three types of mirrors – plane, concave and convex . Procedure I: Place the plane mirror on a sheet of paper and adjust the light source so as to produce a single ray. Aim the ray toward the center of the mirror so that the ray is reflected on itself. Trace the ray on the paper. This line which is perpendicular to the plane mirror is the mirror axis. Now aim the ray at an angle to the mirror so that it strikes the mirror at the point where the axis crosses the mirror. Draw both the incident and reflected rays and measure the angle of incidence θi and the angle of reflection θr.

Repeat the procedure for two more angles of incidence. Compare the angles θi and θr and conclude whether they obey the condition (1). Procedure II: Locate the principle axis of the concave mirror as in the procedure I and trace it. Adjust the ray box to produce a bundle of parallel rays. Aim the rays at the mirror, parallel to its principle axis, so that the reflected rays cross each other at a point on the principle axis. This point is the focal point. Trace these rays on the paper. Repeat this procedure for the convex mirror. Take into account that in this case the reflected rays must be continued backward until their intersection. Record the value of f. Procedure III: Using the results of the procedure II, trace the rays through an object S placed some distance do from the mirror (concave and, then, convex). Notice the

reflected beams and trace them on paper. Locate image S’. Record di. Repeat the

procedure for two more distances do. Use di and do in equation (2) and determine the

29

focal length f . Compare the focal length values obtained in the procedures II and III. Record also the sizes of the object and image. ANALYSIS OF DATA: For the procedure I arrange the data in 3 columns: 1. Angle of incidence; 2. Angle of reflection; 3. Percent difference between the two. For the procedure III put your data into 7 columns: 1. Object distance; 2. Image distance; 3. Focal length determined from the equation (2); 4. Deviations of the focal length from the mean value; 5. The magnification determined by direct measurements of the object and its image; 6. The magnification determined by the equation (3); 7. The difference between the columns 5 and 6. DISCUSSION: Discuss with what accuracy in % your data support the laws of geometric optics. . QUESTIONS: 1) How close to each other (in %) are the values of the angles θi

and θr ? 2) How close (in %) is the mean focal length determined in the procedure III to that found in the procedure II? 3) What is the error of the focal length found in the procedure III? 4) What is the mean percent difference between the magnification determined directly and through equation (3)? 5) If di is twice of do, what are these in terms of the focal length f (hint: use the equation (2))?

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REFRACTION OF LIGHT THEORETICAL BACKGROUND: Refraction (bending) of light occurs at the boundary between two transparent media, e.g., air and glass. This is because the speed of light in the glass is smaller by a factor n=n2/n1 , called the index of refraction, than the speed of light in the air.

Snell’s Law gives a relation between the angle of incidence θ1 , the angle of refraction θ2 and n in two media:

1 1 2 2sin sinn nθ θ= (2)

Both angles are measured with respect to the normal (NN’ line in Fig.3):

Fig.3. Refraction through a prism Refraction by convex or concave surfaces is used to create images of objects quite similarly to mirrors. Even the equations relating the object and image distances and the magnification are the same as for mirrors (see (2),(3) in the lab “Reflection of Light”). Converging lens focuses a beam of light parallel to the main optical axis of the lens to the focal point F behind the lens. A diverging lens, made of concave surfaces, diverges the parallel beam of light so that their continuations converge at the focal point F in front of the lens. The difference with mirror is that lens has two focal points – symmetrically at its both sides:

31

Fig.4. Focal points of lenses. EXPERIMENT: Using the ray box, the properties of refraction of light will be studied for the three optical elements: the prism and converging and diverging lenses. Procedure I:

Draw a straight line (NN’) and place the trapezoidal prism (the frosted side down) in such a way that the line is perpendicular to the base. Trace the outline of the prism. Set up the light source to produce a single incident ray at some angle through the point where the normal NN’ crosses the base so that the refracted beam goes through the second base. Trace the incident and refracted beams. Measure the angles defined as in Fig.1. Repeat the procedure for 3 more angles of incidence.

Procedure II: Using the ray box, trace a single ray on the paper. Place the converging lens in the way of this ray so that the ray remains unrefracted. Trace the position of the lens. These two traces on the paper give the position of the lens and its principle axis. Now, aim a parallel bundle of rays at the lens so that the refracted rays intersect each other at a point on the principle axis. Trace the rays. Their point of intersection is the focal point. Find the second focal point by shining light from the opposite side. Repeat this procedure with the diverging lens, keeping in mind that the refracted rays must be continued backward in order to find the focal point F and its distance f from the center of the lens. ANALYSIS OF DATA: For the procedure I put your data into 4 columns: 1. Angle of incidence; 2. Angle of refraction; 3. Index of refraction n2 determined from the equation

(1) (use n1 =1) ; 4. Deviations of n2 from the mean value. For the procedure II, determine the focal lengths f and compare them with the known values. DISCUSSION: Discuss how good your data support the law of refraction. QUESTIONS: 1) With what accuracy (percent error) have you found the trapezoidal

32

prism index of refraction? 2) What is the percent error of your measurements for n2? 3) Use the focal lengths obtained in the procedure II and determine the image positions for an object ho = 2 cm tall placed do= 8 cm from a lens. What are the sizes of the corresponding images (use equations (2),(3) from the lab “Relection of Light”) ?

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SOUND WAVES Properties of sound as a wave phenomenon are studied. The speed of sound in air is measured by employing the effect of Wave Interference. THEORETICAL BACKGROUND: A sound wave is a process of propagation of oscillations of the density of a substance. The wave transfers the energy of these oscillations over long distances with the speed VS referred to as the speed of sound. The speed of sound is a property of the particular substance. In the air at room temperature, sound propagates with the speed

VS =330 m/s . (1) Other characteristics of the wave are its frequency f and its wavelength λ. The frequency is number of oscillations of the density per second. This unit is Hz=1/s. A duration of one oscillation is called the period T. There is a simple relation T=1/f. The wavelength is the distance a single oscillation propagates during one period T. Thus the relationship between wavelength λ and period T is

λ= VS T. (2)

A property very specific for wave phenomena is wave interference. A simple way to realize wave interference is to make two identical waves moving in opposite directions meet each other. Then a standing wave is formed. It is characterized by specific points called nodes where the two waves exactly cancel each other. The distance between two adjacent nodes is λ/2. At the midpoint between two adjacent nodes, there is always an antinode -- a place where the amplitudes of the two waves enhance each other (add constructively). The distance between two adjacent antinodes is also λ/2. Standing waves are always being formed in the strings or the pipes of musical instruments. A typical resonant sound coming from the open end of the pipe is due to the antinode formed exactly at the end. One can use this property to measure the speed of sound. If the other end of the pipe is closed (as will be the case in this experiment), then at this end a node is formed. Thus, if a strong (resonant) sound is heard from the pipe, it must contain some whole number n of the halves of λ plus one quarter of λ. That is, its length is

L=n λ/2+λ/4. (3) This situation is depicted on the sketch where the filled circles indicate the nodes and the open ones – the antinodes. Here the pipe contains two antinodes (n=2) inside the pipe and one antinode at the open end. It also has three nodes.

34

λ/4 λ/2 λ/2 closed open end end

Fig. 1 Then, using equation (2) in (3), we find L=(n+1/2) VS /2f. For a given frequency f, the length L for a particular n can be measured and the speed of sound can be found from the expression

VS =2fL / (n+1/2). (4) EXPERIMENT: For the given frequency f of the tuning fork, the shortest length L of the acrylic tube not filled with water (see the picture) should be found so that the first resonant sound is clearly heard. This is an indication that the condition n=0 for equations (3) and (4) is achieved. Increasing L will result in the occurrence of the second resonant sound. Correspondingly, this implies n=1 in equations (3) and (4). Similarly, one can find corresponding length L for higher n.

ANALYSIS OF DATA: Make a table with the following columns: 1) the number of the antinodes n inside the pipe; 2) the length L of the corresponding empty part of the tube; 3) the speed of sound VS ; 4) deviations of VS. Find the speed of sound as the average of the entries in column 3). Calculate the mean deviation as the average of the entries in column 4), and find the percent error of your measurements of VS. Compare the speed you obtained with the standard value of 330 m/s. DISCUSSION: Discuss how close is the measured value of the speed of sound to the standard value. Explicitly discuss whether the mean deviation of the measured speed is larger or smaller than the difference between the measured VS and the standard value. If these are close, what does this prove? QUESTIONS: 1) Suggest another way to find VS which does not require measurements

35

of the wavelength. 2) During a thunderstorm the lightning is seen first and then the thunder is heard. What can you say about the ratio of the speed of light to the speed of sound? 3) If the time delay between the lightning and the thunder is 5 seconds, how far from you is the place where the lightning and the thunder occurred? 4) For the design of an organ pipe to play the musical note at 420 Hz, of what length should the pipe be?

36

ATOMIC SPECTRA

The effect of light interference is used to measure the wavelengths of light emitted by various atoms. This lab is based on the demonstration “Colors and Wavelength of Light”. THEORETICAL BACKGROUND: Every chemical element or compound, after being excited by delivering energy to it, emits a unique pattern of wavelengths of light (or colors). In fact, such a pattern makes it possible to recognize unambiguously the element presence even in a very tiny amount. As discussed in the work “Color and Wavelength of Light”, each color corresponds to a particular wavelength of the light wave. Therefore, to analyze the pattern precisely, the wavelengths of light should be measured. This direct measurement would be difficult to perform because of the very small values of the wavelengths of visible light (400 - 700 nm). However, the wave properties -- interference and diffraction -- turn out to be very helpful. The interference effect has already been used to measure the wavelength of a sound wave (see the work “Sound Waves”). In fact, standing waves can also be formed by light similarly to what happened with sound in the resonating pipe. In this experiment, another device -- the diffraction grating -- will be used to explore the interference of light. A key element of the grating are the very tiny parallel lines set on the transparent slide. The distance d between these lines is a very important parameter. Normally, each grating is labeled as to how many lines per mm it has, from which the distance d can be determined. Light striking the grating splits into many rays interfering with each other. As a result, the interference antinodes (bright lines) are formed on the screen. The position of the each antinode depends on the wavelength λ and the parameter d. This dependence is given by the following equation

d sina=nλ (1)

where a is the angle of diffraction (see the sketch below ) and n=0,1,2,3 stands for the order of the antinode. grating screen incident light a x S Fig.1. Diffraction and interference of light due to the diffraction grating

37

Measuring S -- the distance from the grating to the screen and x -- the distance from the zero order antinode to the n-th order antinode, the sin(a) can be found as

22sin

Sxxa+

= .

(2) The wavelength can then be determined as λ=d sin(a)/n from equations (1). A substitution of the sin a from equation (2) gives

λ =+

d xn x S2 2 . (3)

Such a method for measuring λ was used already to find the wavelength of light emitted by a Laser in the work “Color and Wavelength of Light”. EXPERIMENT: Each chemical element is excited by the High Voltage Electric Discharge which is dangerous if handled improperly. Never touch the spectrum tube or its holders ( SHOCK HAZARD !) The human eye will play the role of the screen in this experiment. The grating and a short ruler are to be placed on the meter stick. The ruler has a slit in its center. This slit is to be aimed at the spectrum tube containing the glowing element.

.

Fig.2. Schematic of the meter stick optical bench with the spectrum tube . First make sure you can find the spectrum of colors by looking through the grating at the light emitted by the element. You will see the colored lines at the sides of the light source. These lines form a group which repeats itself as one looks farther from the center line. Each group corresponds to a different n in equations (1) and (3). The first group of lines for which n=1 is to be analyzed. Record the distance x along the short ruler for each distinct colored line, keeping the distance S along the meter

38

stick fixed. A normal sequence of the colors is violet- blue-green-yellow-red counting from the slit. Note the names of the elements whose spectra you have analyzed. For each element, identify its spectrum from the chart given in class and compare the corresponding wavelengths with those of the lines you have measured. ANALYSIS OF DATA: For each chemical element whose spectrum you have analyzed, make a table with the following columns: 1) color of the line 2) position x (cm) of the line 3) the wavelength calculated from formula (3). For each color identify the corresponding line from the chart and enter its wavelength in column 4). Do not forget to record the distance S in cm. For this work a grating having 600 lines per mm will be used. Find the corresponding value of d which is to be used in the equation (3). Represent your answer in nanometers (nm). Refer to the Appendix “Mathematical Review” in order to convert correctly the value of d measured in mm into nanometers. DISCUSSION: Discuss how precisely you have identified the wavelengths of the spectral lines for each element you have studied.

39

RADIOACTIVE DECAY Natural radioactivity is discussed and the process of radioactive decay is simulated. The method of scientific simulation as a mean for analyzing a real situation is introduced. THEORETICAL BACKGROUND: Each atom has a nucleus. Some of the nuclei are unstable,-- these can break apart or transform into other nuclei. These processes are called Radioactive Decay. As a result of the decay, various kinds of radiation are emitted. The radioactive decay can be described by the following general model. There is some probability p that an unstable atom decays during the time interval T (specific for each element). For some elements this time can be very long (years and even thousands of years), while for others it could be days or even seconds. If initially N atoms existed, after the time interval T has elapsed the remaining number of atoms is (1-p) N . After 2 intervals of T have elapsed, the remaining number is (1-p)(1-p) N. After 3 intervals of T have elapsed, the remaining number is (1-p)(1-p)(1-p) N, and so on. Finally, we can arrive at the general expression for the number of atoms N(t) remaining after n time intervals have passed:

N t p Nn( ) ( )= − ⋅1 . (1) Radiation can be harmful if handled without caution. Therefore we will not use any radioactive substance in the class. Instead, a simple simulation with dice will be done. A single die imitates a radioactive atom. Internal processes leading to the decay are simulated by random throws of each die in the common large basin containing, e.g. 100 dice. We consider the “atom” having decayed, if the number 6 appears on the upper side of the die. Then this “atom” should be removed from the basin. We can predict that because of the random nature of the tossing, the probability for each die to display 6 is p=1/6. Therefore, there is a high likelihood that 1/6 of all the atoms decays after a first tossing, so that the remaining atoms are (1-p)=5/6 of 100. If the number of throws is n=0,1,2,3.., we can make a table for the remaining number of atoms 100, 100×5/6, (100×5/6)×5/6, etc. (of course, the numbers are rounded off to make N(t) an integer): n 0 1 2 3 4 5 6 7 8 9 10 11 N(t) 100 83 69 58 48 40 33 28 23 19 16 13 Algebraically, this dependence is given by the formula

N tn

( ) = ⋅

56 100 (2)

in accordance with the general expression (1).

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EXPERIMENT - SIMULATION: Throw the 100 dice once and remove all the decayed “atoms” (the “6” `s). Count the number N left and record it. Repeat the process for the remaining atoms similarly until less than 10 atoms left. Repeat this procedure for 10-12 trials. ANALYSIS OF DATA: Arrange the following columns: 1) throw number n; 2) N for the first trial; 3) N for the second trial; 3) N for the third trial; 4) N for the fourth trial, etc. Reserve a column for the average of N over all trials (not throws !

). Finally, reserve a column for the analytical dependence given by the formula (2). On a single graph plot a) your data -- average of N vs. n and b) the dependence obtained from formula (2).

DISCUSSION: Discuss what you have tried to prove in this experiment. Make a statement on the accuracy by estimating the deviations in your data as well as by comparing the graph for the average of N vs n with the graph obtained from formula (2). QUESTIONS: 1) Looking on your data, find the “time interval” (number of throws) corresponding to the reduction by a factor of 1/2 of the number of “atoms”. 2) Does this “interval” depend on the initial number of “atoms”? Give the answer both by relying on your experimental data and by analysis of formula (2).

41

CONSERVATION OF LINEAR MOMENTUM

Conservation of linear momentum will be studied as a fundamental law of Nature in a simplest mechanical setup. THEORETICAL BACKGROUND: Conservation of linear momentum is another fundamental law of Nature – as important as the law of energy conservation. It says that, if there is no net external force on a system of objects, the total momentum of such system is conserved, that is, it does not change with time

.

If there are two objects with masses M1 and M2 moving at the corresponding velocities V1 and V2 the total momentum of the system P= M1 V1 + M2V2 is a constant, provided all external forces are zero (or compensated). This law is a consequence of the 3rd Newton’s Law of motion. In contrast with kinetic energy, momentum is a vector. This means that in the simplest setup Fig.1 it can be positive or negative depending on the direction of the velocities. Choosing positive direction to the right, velocity and momentum will be positive if an object is moving to the right and -- negative otherwise. EXPERIMENT: The setup consists of two gliders on leveled air track where two major sources of the external net force – gravity and friction – have been greatly reduced. These gliders will be allowed to collide with each other and the total momentum will be measured before, Pb , and after the collision, Pa. According to the law: Pb =Pa, or

1 1 2 2 1 1 2 2 b a b b a aP P M V M V M V M V= → + = + (1)

Where the indexes “a,b” refer to the velocities after and before the collision, respectively. This condition will be tested in the experiment by measuring momenta of each object and, then, finding the totals.

Fig.1

42

PROCEDURE: For given M1 and M2 , the velocities before and after the collision will be measured by the timers in the regime GATE, provided the collision occurs between the photogates. The teacher will explain how to find the velocities before and after the collision. ANALYSIS OF DATA: Arrange the following data columns: 1) V1b ; 2) V2b ; 3) V1a;

4) V2a (kg); 5) Pb = M1 V1b + M2 V2b; 6) Pa = M1 V1a + M2 V2a. Record the velocities according to their direction (positive if moving to the right and negative – if to the left). Perform at least 10-15 measurements with different initial velocities, starting from the case when one glider is stationary between the photogates. Use elastic and inelastic collisions. Change gliders masses by adding weights to them. Make sure Pb varies within sufficient margins so that the graph Pa versus Pb can be constructed. Construct the graph Pa versus Pb. In the ideal situation this graph should be a straight line going through the origin at the slope =1. Perform the linear fit and find the actual slope. Compute the percent difference from the expected value of the slope. DISCUSSION: Conclude on whether your data supports the Law of Conservation of Linear Momentum. QUESTIONS: 1) Can two objects moving at some finite velocities have the total

momentum zero? Explain and give an example. 2) Can two objects moving at some finite velocities have the total kinetic

energy being zero? 3) Two pieces of clay, with M1= 2kg and M2=3kg , move toward each other at the speed of 12 m/s. Then, they collide and stick together. Find their mutual velocity after the collision. What is its direction – continuing in the direction of M1 or M2 before the collision?

43

ELECTRIC FIELD AND ELECTRIC CHARGES

Besides the contact interaction explored previously, we have heretofore

considered only gravity as a force which acts through empty space. We now consider

another very important force which acts through empty space – Electrostatic interactions.

Simple experiments on static electricity are to be performed. The following

instrumentation is used: ebony and glass rods, silk, fur, plastics (comb) etc. The effect of

the deflection of running water by an electrically charged rod (comb) is also to be

demonstrated. It is also to be observed that no static electricity effects can be produced

with massive objects made of metal.

The nature of electric charge and electric field is to be discussed, and the basics of

Coulomb’s law are to be outlined. Two effects should be clearly distinguished:

1) attraction or repulsion between objects carrying net charges;

2) the attraction of a substance carrying no net charge (running water, paper, hairs etc.)

by an electrically charged object due to the polarization effect of a neutral substance.

The structure of atoms is to be presented, and the electric charge of the electron is

to be introduced as the smallest unit of electric charge.

Different types of materials with respect to their ability to conduct electricity are

mentioned. Then, the concept of electric current is to be introduced as the background for

the experiments “ELECTRIC FIELD AND ELECTRIC CURRENT” and

“WORK OF ELECTRIC FIELD”.

44

ELECTROMAGNETIC FIELD These demonstrations introduce students to electromagnetism as a basis for studying

wave properties of light and atomic spectra.

Magnetism is considered as a third example of an interaction through empty space in

addition to that of gravity and the electric field. Basic experiments with permanent

magnets are to be performed.

Special attention is to be paid to the fact that electric and magnetic effects are well

distinguished from each other. Crucial differences are to be emphasized:

1. The magnet does not affect paper, hairs and running water, while the rubbed comb

does;

2. Rubbing of the iron rod does not result in its activation for the attraction of polarizable

materials (paper, water, hairs); even without rubbing it attracts magnets.

It is to be stressed that despite the apparent differences, there is a common source

for electric and magnetic fields -- electric charges. It is to be pointed out that the electric

current -- a unidirectional motion of charges -- serves as a source for a magnetic field. A

demonstration of compass needle deflected by electric current is to be performed. The

reversal of the compass needle direction when the current is reversed should be pointed

out. Even stronger evidence for this effect will be demonstrated by a heavy iron rod being

pulled into the coil interior, when the current flows through the coil.

The concept of the electromagnetic field is to be introduced through the

demonstration of Faraday’s electromagnetic induction. It should be emphasized that if

the magnet and the coil were stationary, no induction current would have been created.

Only temporal changes of the relative position of the coil and the magnet result in

producing electric current.

Two coils are now to be placed in front of each other, so that turning on or

off the current in one of them induces a current in the other. Finally, the crucial link in the

Maxwell theory of the electromagnetic field is to be discussed -- the direct creation of a

magnetic field by a changing electric field. This effect, together with the Faraday’s

induction, leads to electromagnetic waves. Characteristics of electromagnetic waves - -

45

speed, frequency, period, wavelength, polarization -- are to be introduced and compared

with previously studied sound waves. It is pointed out on the electromagnetic wave

nature of light.

46

COLOR AND WAVELENGTH OF LIGHT

This demonstration serves as a basis for the lab “ATOMIC SPECTRA”

Light is a wave phenomena. In contrast to sound, it can propagate in empty space -- vacuum. Light is a bundle of electromagnetic waves, each characterized by the same

speed C ≈ ×30 108. /m s in vacuum. Each wave is characterized by a wavelength λ and a frequency f. The relation between all three parameters is exactly the same as for sound

λ=c/f.

Electromagnetic waves are perceived by our eyes, analogously to sound which we can hear. However, the range of the wavelengths is very different. Visible light has wavelengths in the range 450-650 nm which are too small to be seen directly – like waves on the surface of water. In this range, light is percieved as various colors. White light is a mixture of electromagnetic waves with wavelengths covering the entire visible range. These colors are those which we see in a rainbow --- from short (violet) to long (red) waves. How can a single visible wave be produced? In analogy with sound, we might look for some sort of “tuning fork” which is capable of giving off a single electromagnetic wave. However, the frequency of such a wave is huge (about 1015 Hz); thus no simple mechanical “tuning fork” is actually available. The LASER (Light Amplification through Stimulated Emission of Radiation) is a device which allows us to produce nearly perfect visible electromagnetic waves of a required wavelength. The physics of this device is based on the quantum nature of light. This behavior is subtle, but the outcome is pretty obvious -- the production of a visible wave characterized by a single wavelength. In this demonstration, three lasers, each producing different colors, are to be used. A diffraction grating -- a device employing the effect of light interference -- will analyze these colors so as to give the corresponding wavelengths. A key element of the grating are very tiny parallel lines set on the transparent slide. The distance d between these lines is a very important parameter. Normally, each grating is labeled as to how many lines per mm it has, from which the distance d can be determined. Light striking the grating splits into many rays which then interfere with each other. As a result, the interference antinodes (bright lines) are formed on the screen. The position of each antinode depends on the wavelength λ and the parameter d. This dependence is given by the following equation

d sin(a)=nλ (1)

where a is the angle of diffraction (see the sketch below ) and n=0,1,2,3 stands for the order of the antinode.

47

grating screen incident light a x S Fig.1. Diffraction and interference of light on the diffraction grating Measuring S -- the distance from the grating to the screen and x -- the distance from the zero order antinode to the n-th order antinode, the sin(a) can be found as

sin( )ax

x S=

+2 2 .

(2) The wavelength can then be determined as λ=d sin(a)/n from equations (1). Substituting the sin( a) from equation (2), we find

λ =+

d xn x S2 2 .

(3) Using the equation (3), the wavelengths of all three lasers -- red, yellow and green,-- will be found. Here is the actual setup

48

49

FORMATION OF AN OPTICAL IMAGE BY A CONVERGING LENS

Image formation by a converging lens is to be studied. THEORETICAL BACKGROUND: The effect of the refraction of light can be used to create optical images. A converging lens focuses a beam of light which is parallel to the main optical axis of the lens to one of the two lens focal points (see the work “Refraction of Light”). The distance between each of the focal points and the lens is called focal length f . The focal length is a specific property of the lens, which is determined by the lens shape and the index of refraction of the lens material. If an object is placed on one side of the lens (farther than the focal distance from the lens), a real and inverted image of this object can be formed on the other side of the lens. To find the position of the image, the ray tracing diagram can be used

ho f di

do f hi

The image distance di obeys the lens formula

1 1 10d d fi+ = . (1)

The image could be larger or smaller than the object. The ratio Mhh

i

o= of the image

size to the object size is called the magnification. Referring to the above diagram, one finds that the magnification can also be expressed as

0ddM i−=

. (2)

Where the sign convention is used: the image height hi is taken negative if the image is

upside down; di is positive for real image (and negative for virtual).

50

EXPERIMENT: A converging lens of known focal length together with an object and a

screen are placed on the optical bench. Measure the object size ho (it remains the same throughout the experiment). The distance between the lens and the screen should be

adjusted until a sharp image of the object is formed on the screen. Then, the distances d0 ,

di as well as the image size hi can be measured. From d0 and di, the focal length can be found from equation (1), and then compared with the known value. Dividing the image size hi by the object size ho , the magnification M can be determined, and then compared with the prediction (2). Repeat this procedure for several

d0 .

ANALYSIS OF DATA: Arrange your data in six columns: 1) the object distance d0 ; 2)

the image distance di ; 3) the magnification Mhh

i

o= ; 4) the magnification as predicted

by formula (2); 5) the sum 1/ do + 1/ di ;(it determines 1/f according to the

equation (1)); 6) deviations of the experimentally measured 1/f.

Plot the magnification |hi | / ho vs. the ratio di / dio . The slope of this graph should be 1, as given by formula (2). Find the percent difference for this slope. Determine the reciprocal of the focal length as the mean of the column #5. DISCUSSION: discuss how well your data supports the lens equations (1) and (2). Include in your statement the main values you have found. Evaluate the percent differences for the slope and for the focal length. Estimate the error with which you have found f , and compare the error with the percent difference. QUESTIONS: 1) How close to each other is the value of the focal length you measured to

the known value? 2) If di is twice d0, what are these in terms of a) f ; b) in cm for your particular lens? 3) If di is three times d0 , what is the magnification?

4) If the object is placed between the lens and its focal point, what kind of image is the lens producing? Can it be captured on the screen?

51

Appendix: Mathematical Review (selected topics)

Scientific Notations

Instead of writing long numbers, it is convenient to use scientific notation. In this

notation

10 = 10 , n zeros) = 101 n100 10 1000 10 1000000 10 12 3 6= = =, , , ...( . (1)

Very small numbers have negative powers:

01 10 0 01 10 0 001 10 0 000001 101 2 3 6. , . , . , . , .= = = =− − − − etc (2)

For example, we wish to round off the number 1574394908437269 so that only the first

three digits are displayed. We can do this by writing 1570000000000000 (the 13 digits

after the first three were replaced by zeros). This number is very inconvenient to handle.

Using scientific notation, 157...(13 zeros)=157 ×1..(13 zeros)= 157 10 157 1013 15× = ×. .

In the last part the identity 157 157 102= ×. and the rule 10 10 102 13 15× = have been

used.

Now suppose that a very small number 0.000000023157 is to be rounded off so

that only the first three digits are to be displayed:

0 000000023157 0 0000000232 2 32 10 8. . .≈ = × − . (3)

Note that the decimal point has been moved to the right by 8 places, and the power “-8”

of 10 was introduced in accordance with the rule (2).

The following describes how one multiplies and divides numbers in scientific

notation. The general rules are

10 10 10 10 10 10a b a b a b a b× = =+ −, / (4)

52

For example, let us find the ratio of the very large number 1574394908437269 to the very

small number 0.000000023157. Normally, the first three digits are sufficient. So these

numbers should be rounded off, as we did above, and represented in scientific notation:

1574394908437269

0.000000023157 =

=

=

157 102 32 10

1572 32

1010

0 677 10 0 677 10

15

8

15

8

15 8 23

.

...

. .( )

××

= × =

× = ×

− −

− −

(5)

Metric Units:

Length -- meter (m) is the basic unit.

1 centimeter (cm) = 1/100 m= 10 2− m; 1 millimeter (mm) =1/1000 m= 10 3− m

1 nanometer (nm) = 10 9− m, 10 19 nm m= , 1 103km m= .

Mass -- kilogram (kg) is the basic unit.

1gram (g) = 1/1000 kg = 10 3− kg

Conversion of Units:

The following examples illustrate the procedure.

23 m = 23 × 1m=23 × 100 cm=2300 cm; 530

× = × × = × × =− − −10 530 10 1 530 10 10 5309 9 9 9m m nm nm.

The following examples illustrate the conversion of complex units.To express a volume

of 25 m3 in cubic centimeters, the relation between the meter and the centimeter is used:

25 25 1 25 100 25 10 25 103 3 3 2 3 3 6 3m m cm cm cm= × = × = × = ×( ) ( ) ( )

Here the general rule

( )10 10a b a b= × (6)

has been used.

As another example, let us express the density of oil 800 kg/m3 in grams per cubic

centimeter. We proceed

53

800 80010

10800 10

800 10 08 10 10 08 10 08

33

6 33 6 3

3 3 3 3 3 0 3 3

kg mg

cmg cm

g cm g cm g cm g cm

/ /

/ . / . / . /

= × = × =

= × = × × = × =

−

− −

54

Appendix: Analysis of Data

Every measurement is subject to error. This results in deviations of the measured

quantity. For example, the length of the same pencil measured several times would come

out differently because of the manner in which the ruler was applied. Personal blunders

due to carelessness are also a source of error. Each particular instrument never gives the

result precisely. Many external factors which cannot be completely controlled change the

conditions of measurement and thereby affect the results. Thus, errors of measurement

and the associated deviations of the measured quantity are an inherent part of the

measurement process. Patience and experience are required in order to reduce the errors

and the deviations. What is especially important, is that the

deviations can be significantly diminished by the repetition of observations

This means that the same quantity should be measured as many times as possible within a

reasonable duration of the experiment.

.

As an example, result of the measurement of a length of some object is given in

the table below N 1 2 3 4 5 6 7 8 9

L (cm) 15.2 15.3 14.9 15.4 15.2 15.1 15.0 14.8 15.2

DL =|L- L |(cm) 0.1 0.2 0.2 0.3 0.1 0.0 0.1 0.3 0.1

The upper row marked by N gives the number of the measurement. The second row

shows the object’s length obtained during each measurement (for example, the result of

the 4th measurement is 15.4 cm). The bottom row gives the deviations (or errors)

DL L L= −| | (1)

of each measurement from the average value (mean value) of the length

L avg L= ( )=(15.2 + 15.3 + 14.9 +15.4 + 15.2 + 15.1 + 15.0 + 14.8 + 15.2 )/ 9 =

=15.1 cm

55

calculated from the 9 measurements. In calculating the average, the result must be

rounded off so that the number of significant digits is not more than that for each

measurement. The average deviation (mean deviation)

DL avg DL= ( ) (2)

indicates how the measured value varied due to all of the factors mentioned above. For

our example, DL = 0 2. cm. The final result for the object length is expressed as

L L DL= ± . (3)

For our example, L cm= ±( . . )151 0 2 . This means that in the measurement of the length

the result obtained was between 14.9 cm and 15.3 cm with high certainty.

Can we say that these measurements are reliable? In order to arrive at a

conclusion, we have to calculate the percent deviation (or the percent error). This is

DLL ⋅100% . (4)

The percent deviation indicates how small in percent the mean deviation DL is with

respect to the mean value L . For our example, the percent deviation is

0 2151 100% 1%

.. ⋅ ≈ . For our laboratory, measurements are considered accurate if the

percent deviation is less than 10%-15%. As long as 1% is less than 10%, we consider

the result of the measurement of the length L accurate. This sort of analysis should be

applied to measurements of other physical quantities.

Sometimes a purpose of the laboratory experiment is to measure some quantity

whose standard (given) value is well known. For example, we have measured the length

L of the object, and the given value of the length of this object is Lst . In this case it is

very important to compare these two quantities L and Lst in order to make a

conclusion on whether your experiment confirmed the value Lst and thereby supported a

56

theoretical concept underlying this value. An important quantity is the percent difference

between the measured (mean) value and the standard value

| |L L

Lst

st

−×100% . (5)

In fact, if you are asked to compare the measured value with the standard (known) value,

you should calculate the percent difference (5) and make a statement on whether the

percent difference is less or bigger than 10%-15%.

Lst

If it is less than 10%-15%, the

measured value is considered to be close to the standard one. For example, let us assume

that the standard value for the length L is 15.0 cm. Then, the percent difference

between the measured value 15.1 cm and the standard value 15.0 cm is approximately

1%. Correspondingly, one can conclude that the measured value is close to the standard

value.

We can say that

Returning to our example, we see that the percent deviation and the percent defference

are both about 1%. Accordingly, we conclude that the result of measurement of L has

confirmed the standard value within 1% of the percent error. Had the percent difference

been bigger than the percent deviation, we would have concluded that the standard value

has not been confirmed.

the experiment does confirm the concept within the

experimental percent deviation (or percent error), if the percent difference given by

equation (5) is not bigger than the percent deviation given by equation (4).

The deviations should be always estimated for the experimental data.

Furthermore, any experimental result for which no mean deviation is calculated is

considered as unreliable. Therefore, the report on the laboratory work must contain at

least two main results. The first one is the set of physical quantities determined

during this laboratory work. The second is the set of deviations for each quantity

.

57

GRAPHICAL ANALYSIS 3.41

PLOTTING YOUR DATA POINTS AND FINDING THE BEST FIT

1. Click on the GA 3.4 icon

2. The Graphical Analysis screen will be displayed:

3. On the Data Set Table with X and Y columns

click on either column to start entering your

data. Use either the arrow keys or the mouse to

move to the next cell.

4. As you enter data you will notice a graph will

develop as the data is plotted. Just continue

entering your data till you are finished.

5. To delete the line that is connecting the points

either double click on the graph window. Select

the Graph Options tab.

1 Adapted from Vernier Software & Technology – Graphical Analysis User’s Manual

58

Click on Connect Lines to delete

the original line on your graph.

To add a title, click on the Title

window.

This window also gives the

option to add a legend to your

graph or change the grid style.

6. Finding the Best Linear Fit for

your graph:

On the graph window click and

drag the mouse across the

segment of interest. The shaded

area marks the beginning and end

of the range. You may also

select the segment of interest on your data columns and then clicking on the graph

window to activate it.

7. With the graph window activated, select the Regression option either by clicking the

Linear Fit icon, on the toolbar or by selecting it from the Analyze Menu. To remove

the regression line click the box in the upper corner of the helper object.

The Linear Fit function fits the line y = m*x + b to the selected region of a graph and

reports the slope (m) and y-intercept (b) coefficients. If more than one column or data

set is plotted, a selection dialog will open for you to which set you want to fit. You may

select more than one column for regression; in this case, a separate fit line will be applied

to each graphed column.

As aforementioned, you can fit a line either to the whole graph or to a region of interest.

Drag the mouse across the desired part of the graph to select it. Black brackets mark the

beginning and end of the range.

8. If you wish to graph a fit other than y=mx+b, such as proportional, quadratic, cubic,

exponential, etc, click on the Curve Fit icon from the toolbar. A Curve Fit

dialog window will pop-up:

59

Select the function you wish to use. Click Try Fit. Then click OK.

9. To change the labels of your X and Y axes and include their respective units click on the

column you wish to change and the dialog window below will pop-up:

On this dialog window, you will be allowed to give your column a name other than the

default name. You may also include units such as m/s, cm/s2, etc. The drop down arrows

allows you to enter a symbol, subscript or superscript.

10. To change the scaling of your graph, right click on the desired graph and select autoscale

or autoscale from zero. To modify manually, click on the highest or lowest number of

the axis you wish to change and enter the new number, press Enter.

60

11. Select the orientation of your page. This is done by using Page Setup under the File

menu.

12. To print the entire screen select Print from the File menu or click the icon on

the toolbar. A dialog window will pop-up allowing you to enter your name or

any comments you wish to add.

13. If you wish to print just the graph select it first and then go to the File menu and select

Print Graph… You may also print data table alone by selecting Print Data Table.

1For more information go to: http://www2.vernier.com/manuals/ga3manual.pdf

Note: These basic graphing instructions can also be applied to LoggerPro.

61

TECHNICAL NOTES ON VERNIER LABQUEST2 INTERFACE1

Once the LabQuest interface is connected to AC power or the battery has been charged, press the

power button located on the top of the unit, near the left edge. LabQuest will complete its

booting procedure and automatically launch the LabQuest App by default, as shown above. If the

screen momentarily shows a charge battery icon or does not light after a moment when used on

battery power, connect the power adapter to LabQuest and to an AC power source, then try the

power button again.

Power Button

Power on – If the screen is off for any reason (LabQuest is off, asleep, or the screen has

turned off to conserve battery power), press and release the power button to turn LabQuest

back on. If LabQuest was off, LabQuest will also complete its booting procedure that takes

about a minute and then display LabQuest App.

Sleep/wake – When LabQuest is on, press and release the power button once to put

LabQuest into a sleep mode. Note that the sleep mode does not start until you release the

power button. In this mode, LabQuest uses less power but the battery can still drain. This

mode is useful if you are going to return to data collection again soon, in which case waking

LabQuest from sleep is quicker than restarting after shutdown. To wake LabQuest from

sleep, press and release the power button. A LabQuest that is left asleep for one week will

automatically shutdown.

Shut down – To shut down LabQuest, hold the power button down for about five seconds.

LabQuest displays a message indicating it is shutting down. Release the power button, and

allow LabQuest to shut down. To cancel the shutdown procedure at this point, tap Cancel.

You can also shut down LabQuest from the Home screen. To do this, tap System and then

tap Shut Down.

Emergency shutdown – If you hold the power button down for about eight seconds, while it

is running. This is not recommended unless LabQuest is frozen, as you may lose your data

and potentially cause file system corruption.

1 Adapted from Vernier Software & Technology LabQuest2 User’s Manual.

Fig. 1 - LabQuest2 Interface

62

Touch Screen

LabQuest has an LED backlit resistive touch screen that quickly responds to pressure exerted on

the screen. LabQuest is controlled primarily by touching the screen. The software is designed to

be finger-friendly. In some situations, you may desire more control for precise navigation. In

such cases, we recommend using the included stylus.

If you are having trouble viewing the color screen or are using LabQuest outside in bright

sunlight, we recommend changing to the High Contrast mode. Tap Preferences on the Home

screen, then tap Light & Power. Select the check box for High Contrast to enable this mode.

Hardware Keys

In addition to using the touch screen, the three hardware keys can also be used to control your

LabQuest.

Collect – Start and stop data collection within LabQuest App

Home – Launch the Home screen to access other applications

Escape – Close most applications, menus, and exit dialog boxes without taking action (i.e.,

cancel dialog boxes)

Sensor Ports

LabQuest has three analog sensor ports (CH 1, CH 2, and CH 3) for analog sensors such as our

pH Sensor, Temperature Probe, and Force Sensor. Also included is a full-size USB port for USB

sensors, USB flash drives, and USB printers. In addition to the power button, the top edge of

LabQuest has two digital sensor ports (DIG 1 and DIG 2) for Motion Detectors, Drop Counters,

and other digital sensors.

Fig. 2 - LabQuest2 Control Buttons

Fig. 3- LabQuest2 Sensor Ports

63

Audio ports are also located adjacent to the digital ports, as well as a microSD card slot for

expanding disk storage. On the side opposite of the analog ports, there is a stylus storage slot, an

AC power port for recharging the battery, and a mini USB port for connecting LabQuest to a

computer. In between these ports, there is a serial connection for charging the unit in a LabQuest

Charging Station.

For more information on the LabQuest2 interface please go to:

http://www2.vernier.com/manuals/labquest2_user_manual.pdf

Fig. 4 - LabQuest2 Additional Ports

64

65

TECHNICAL NOTES ON SENSORS AND PROBES UTILIZED IN SELECTED EXPERIMENTS FROM THIS MANUAL1,2

1. PHOTOGATES Photogates allow for extremely accurate timing of events within physics experiments, for studying air track collisions, pendulum periods, among other things. The PASCO ME-9215B Photogate Timer (Fig. 1) is an accurate and versatile digital timer for the student laboratory. The ME-9215B memory function makes it easy to time events that happen in rapid succession, such as an air track glider passing twice through the photogate, once before and then again after a collision.

The Photogate Timer uses PASCO’s narrow-beam infrared photogate (Fig. 2) to provide the timing signals. An LED in one arm of the photogate emits a narrow infrared beam. As long as the beam strikes the detector in the opposite arm of the photogate, the signal to the timer indicates that the beam is unblocked. When an object blocks the beam so it doesn’t strike the detector, the signal to the timer changes.

Timing Modes: • Gate Mode: In Gate mode, timing begins when the

beam is first blocked and continues until the beam is unblocked. Use this mode to measure the velocity of an object as it passes through the photogate. If an object of length L blocks the photogate for a time t, the average velocity of the object as it passed through the photogate was L/t.

• Pulse Mode: In Pulse mode, the timer measures the

time between successive interruptions of the photogate.

Timing begins when the beam is first blocked and continues until the beam is unblocked and then blocked

1 Technical notes adapted from Vernier Software & Technology User’s Manual and Pasco Scientific User’s Manual 2 Some equipment may be for demo purposes only and might not be part of experiments in this manual.

Fig. 3 - Photogate timer with memory

Fig. 1 - Photogate timer with memory

Fig. 2 - Photogate head

66

again. With an Accessory Photogate plugged into the Photogate Timer, the timer will measure the time it takes for an object to move between the two photogates.

• Pendulum Mode: In Pendulum mode, the timer measures the period of one complete

oscillation. Timing begins as the pendulum first cuts through the beam. The timer ignores the next interruption, which corresponds to the pendulum swinging back in the opposite direction. Timing stops at the beginning of the third interruption, as the pendulum completes one full oscillation.

• Manual Stopwatch: Use the START/STOP button in either Gate or Pulse mode. In Gate

mode the timer starts when the START/STOP button is pressed and it stops when the button is released. In Pulse mode, the timer acts as a normal stopwatch. It starts timing when the START/STOP button is first pressed and continues until the button is pressed a second time.

• Memory Feature: When two measurements must be made in rapid succession, such as

measuring the pre- and post-collision velocities of an airtrack glider, use the memory function. It can be used in either the Gate or the Pulse mode. To use the memory: 1. Turn the MEMORY switch to ON. 2. Press RESET. 3. Run the experiment.

When the first time (t1 ) is measured, it will be immediately displayed. The second time (t2 ) will be automatically measured by the timer, but it will not be shown on the display.

4. Record t1 , then push the MEMORY switch to READ. The display will now show the TOTAL time, t1 + t2 . Subtract t1 from the displayed time to determine t2

2. SMART-PULLEY SYSTEM: A Smart-Pulley system is made up of a Vernier Ultra Pulley and a photogate to monitor motion as a string passes over a pulley. Note that the pulley has low friction and low inertia. When properly positioned, the spokes of the pulley will block the photogate’s infrared beam each time they pass by. In the Smart-Pulley systems one arm of the photogate emits a thin beam of infrared light which is detected by the other arm. The LabQuest2 interface discerns whether the beam strikes the detector (Fig. 4a) or is blocked by a spoke (Fig. 4b) in the pulley sheaf. The small LED light illuminates when the beam is blocked. By accurately timing the signals that arrive from the photogate, the computer is able to track the motion of any object linked to the pulley.

As the Smart-Pulley system performs motion timing it provides a Position vs Time graph; based on the data a Velocity vs Time graph can be developed as well as an Acceleration vs Time graph. For our experiment we will only be using the Velocity vs Time graph to obtain the required accelerations.

Fig. 4 – Smart-Pulley System

(a) (b)

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3. MOTION DETECTOR The Motion Detector is used to collect position, velocity and acceleration data of moving objects. Students can study a variety of motions with the Motion Detector, including: • Walking toward and away from the Motion Detector. • Dynamics carts moving on track. • Objects in simple harmonic motion, such as a mass hanging on a

spring. • Pendulum motions. • Objects dropped or tossed upward. • A bouncing object.

How the Motion Detector Works This Motion Detector emits short bursts of ultrasonic sound waves from the gold foil of the transducer. These waves fill a cone-shaped area about 15 to 20° off the axis of the centerline of the beam. The Motion Detector then “listens” for the echo of these ultrasonic waves returning to it. The equipment measures how long it takes for the ultrasonic waves to make the trip from the Motion Detector to an object and back. Using this time and the speed of sound in air, the distance to the nearest object is determined.

Fig. 5 - Vernier Motion Detector

Fig. 6 - Sample motion data of a bouncing ball

Fig. 7 - Cone of action

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Note that the Motion Detector will report the distance to the closest object that produces a sufficiently strong echo. The Motion Detector can pick up objects such as chairs and tables in the cone of ultrasound. The sensitivity of the echo detection circuitry automatically increases, in steps, every few milliseconds as the ultrasound travels out and back. This is to allow for echoes being weaker from distant objects. Features of the Motion Detector • The Motion Detector is capable of measuring objects as close as 0.15 m and as far away as 6

m. The short minimum target distance (new to this version of the Motion Detector) allows objects to get close to the detector, which reduces stray reflections.

• The Motion Detector has a pivoting head, which helps you aim the sensor accurately. For example, if you wanted to measure the motion of a small toy car on an inclined plane, you can lay the Motion Detector on its back and pivot the Motion Detector head so that it is perpendicular to the plane.

• The Motion Detector has a Sensitivity Switch (Fig. 8), which is

located under the pivoting Motion Detector head. To access it, simply rotate the detector head away from the detector body. Slide the Sensitivity Switch to the right to set the switch to the Ball/Walk setting. This setting is best used for experiments such as studying the motion of a person walking back and forth in front of the Motion Detector, a ball being tossed in the air, pendulum motion, and any other motion involving relatively large distances or with objects that are poor reflectors (e.g., coffee filters). The Track sensitivity setting works well when studying motion of carts on tracks like the Dynamics Cart and Track System, or motions in which you want to eliminate stray reflections from objects near to the sensor beam.

4. TEMPERATURE PROBE

The Stainless Steel Temperature Probe can be used as a thermometer for experiments in chemistry, physics, biology, Earth science, environmental science, and more. Note: Vernier products are designed for educational use. Our products are not designed nor recommended for any industrial, medical, or commercial process such as life support, patient diagnosis, control of a manufacturing process, or industrial testing of any kind.

Specifications: • Temperature range: –40 to 135°C (–40 to 275°F) • Maximum temperature that the sensor can tolerate without damage: 150°C

Fig. 8 - Sensitivity Switch

Fig. 9- Vernier Temperature Probe

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• Typical Resolution: o .17°C (–40 to 0°C) o .03°C (0 to 40°C) o .1°C (40 to 100°C) o .25°C (100 to 135°C)

• Temperature sensor: 20 kΩ NTC Thermistor • Accuracy: ±0.2°C at 0°C, ±0.5°C at 100°C • Response time (time for 90% change in reading):

o 10 seconds (in water, with stirring) o 400 seconds (in still air) o seconds (in moving air)

• Probe dimensions: o Probe length (handle plus body): 15.5 cm o Stainless steel body: length 10.5 cm, diameter 4.0 mm o Probe handle: length 5.0 cm, diameter 1.25 cm

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MULTIMETERS AND POWER SUPPLIES DIGITAL MULTIMETER A digital multimeter (DMM) is a test tool used to measure two or more electrical values—principally voltage (volts), current (amps) and resistance (ohms). It is a standard diagnostic tool for technicians in the electrical/electronic industries1

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Fig. 1 – Fluke Multimeter Dial Settings To perform measurements required in experiments in this manual set the dial to the desire mode • To measure DC ( ) Voltage set the dial to the proper setting (Fig. 1). The probes or wires

must be connected as shown on Fig. 2a. • To measure Resistance (Ω) set dial to the proper setting and connect probes as on Fig. 2a. • To measure small DC ( ) Current (mA) (0-400mA) set the dial to the proper setting. Press

the shift key to obtain DC readings. This setting will be used for Ohm’s Law experiment. The probes or connecting wires must be connected as shown on Fig. 2b.

• To measure large DC ( ) Current (A) with current ranges 0-10 A set the dial to the proper setting as shown on Fig. 1 and press the shift key to obtain DC readings. This setting will be used for Joule experiment. The probes or connecting wires must be connected as shown on Fig. 2b.

• To measure temperature turn dial to Millivolt/Temperature setting. Press the yellow key to read temperature. By default the temperature will be set to degrees Celcius. If Fahrenheit is preferred, press the Range key. A thermocouple will be inserted in the V and COM inputs instead of probes.

1 Definition from Fluke Multimeter User’s Manual.

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Fig. 2 – Probe Connections Note

: Exercise caution when using the multimeters to avoid burning a fuse or causing irreparable damage to the devices. To check if a fuse is burnt connect the red probe into the V Ω input, set the dial to resistance (Ω) and place the tip of the probe into the either the 400 mA or 10 A input. For the 400 mA the resistance should read less than 12 Ω while the 10 A input should read a less than 0.5 Ω. If the reading is OL then the fuse must be replaced.

POWER SUPPLIES 0-30 DC V Power Supply: This power supply will supply DC Voltage/Current to various experiments in this manual such as Ohm’s Law and Joule experiments. Pay close attention to voltage and current settings as designated by each experiment.

Fig. 3 – Extech 0-30 DC Volts Power Supply The voltage knob will display voltage and current readings in 0.1 V steps (0.8 V). Press the voltage knob once when whole number steps are desired such as 1.0 V, 2.0 V and so forth.

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0-12 DC V Power Supply This power supply has various small DC Voltages settings such as 3 V, 4.5 V, 6 V, 7.5 V, 9 V and 12 V.

Fig. 4 – 0 to 12 V Power Supply

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