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Salisbury University Physics Department Physics 123 Laboratory Manual1

Laboratory Exercises of Electricity, Magnetism, Light, Waves, and Optics.

PHYSICS 123 Laboratory Manual

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INDEX 3

I. ANALYTICAL TOOLS 4

1. RECORDING DATA 4 CALCULATING PRECISION OF THE DATA 5

CONVERSION OF UNITS 6 DATA TABLES 7

2. GRAPHICAL ANALYSIS OF DATA 8 PLOTTING DATA 9 BEST FIT CURVE AND SLOPE 10

3. FURTHER ANALYSIS OF RESULTS 11

II. ORIENTATION 12

1. PHYSICS UNITS FOR THE 123 PHYSICS LAB 12 2. PRECISION AND ACCURACY OF MEASUREMENTS 13

PRECISION 13 ACCURACY 14

3. ERRORS IN THE EXPERIMENT 15 4. SIGNIFICANT FIGURES & ROUNDING 16

ROUNDING 17 5. LABORATORY REPORT 18

III. EXPERIMENTS Week of 20

CHARGES AND ELECTRIC FORCES (09/05) 20 ELECTRIC FIELD MAPPING (09/12) 25 CAPACITORS (09/19) 26 BATTERIES AND BULBS (09/26) 28 RESISTANCE, VOLTAGE, AND CURRENT IN CIRCUITS

(10/03) 30 MAGNETIC FIELD MAPPING (10/10) 32 MAGNETIC INDUCTION (10/17) 33

SIMPLE HARMONIC MOTION 35 SPRINGS AND SIMPLE HARMONIC MOTION (10/31) 38 STANDING WAVES ON A STRING (11/07) 40 SOUND WAVES (11/14) 41

MIRRORS (12/05) 43 LENSES (11/28) 46 OBSERVATION OF INTERFERENCE PATTERNS 48

IV. ADDITIONAL EXPERIMENTS 49

MAGNETS AND MOTORS (10/24) 49 MIRRORS AND LENSES 52 MEASUREMENT OF INTERFERENCE PATTERNS 55 DOUBLE SLIT INTERFERENCE 56 SINGLE AND MULTIPLE SLIT DIFRACTION 57

V. APPENDICES 58

SAMPLE PRE-LAB QUESTIONS 58 SAMPLE LABORATORY REPORT 59 NUMBERS AND SCIENTIFIC NOTATION 65 SYMBOLS 66 CONVERSION FACTORS 67


I. ANALYTICAL TOOLS 1. Recording Data

The ability to objectively evaluate the reliability of an observation and discipline in recording your observation are of great importance in the investigations you will be making in this course.

Data should always be recorded neatly in columns (or rows) with appropriate headings for each column. The units in which the measurements are made (centimeters, seconds, etc) should appear at the top of each column. Always record raw data and later make necessary computations. If you obtain a datum which you believe is greatly in error, do not erase it. Draw a line though it, but leave it legibly visible. Write a brief note on the reasons why you suspect that particular piece of information to be inaccurate.

Experimental data are always subject to “error.” This experimental uncertainty is imposed by the limitations of the instruments (including our hands and eyes) and the method used for making the measurement. (Ultimately, there is a quantum uncertainty associated with everything we can observe, although we shall not approach that limit in this class!) The experimental “error” can be reduced by increasing the precision of the instruments and using more sophisticated methods but it will always be present. For a particular measurement to be useful it is necessary to evaluate this experimental uncertainty (see section titled “significant figures” for more information).

Suppose several measurements are made of a particular quantity. Because of the limitations imposed by the method of measurement, inability to exactly reproduces experimental conditions, and the instruments used the values of these measurements will differ, i.e., there will be experimental uncertainty. However, if the average value of these measurements is taken a number will be obtained which best represents the measurement. We shall call this the “best value” of the quantity, and designate it M for the mean or average.

Suppose that we measure a large number, N, of data points xi (x sub “i”). Here i =1,2,3,4…N represents the individual data points (that is x1 is the first point, x2 is the second point, and so forth). The average or mean is then given by:

The “Average equals one over N times the sum of the “x” data points.” The symbol “Σ” is Sigma, the Greek letter “S” and stands for “sum.” This equation is the average you are familiar with – simply add all the data points of the same type and divide by the number of points.

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1. Recording Data (continuation) Calculating Precision of the Data

For a variable that is measured N times, the precision of the data can be determined by calculating the standard deviation or the dispersion of the data as recommended by statistical methods. However, this course is limited in mathematical tools and an approximated way to calculate the dispersion or how spread the data are it is seen in the section of Orientation.

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Salisbury University Physics Department Physics 123 Laboratory Manual

1. Recording Data (continuation) Conversion of Units

Conversion of units is something that can give a lot of trouble, but which is easy once you learn a few simple rules: 1.The word “per” means “divided by,” so that:dollars per liter means , kilometers per hour means

2.The units should cancel just like numbers in an equation, as in the following example:

3.When you are given a conversion factor, you can use it to make any number equal to one, any number may be multiplied by one, and so to convert:a). 100 centimeters equals 1 meter.

Therefore

So to convert meters to centimeters: 3 m = 3 m × 1 = 3 m × 300 centimeters = 3×102 cm

4.A more complicated example: 1 mile is 1.609 kilometers, therefore:

where we have assumed that 1.609 is a constant and 67 miles is the measured value. The correct result should written as 110 km/h, having only two significant figures 110 km/h as does 67 mi/h. We noticed that miles had to cancel out.

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1. Recording Data (continuation) Data Tables

Before drawing a graph or using the data for calculations using the physics involved, however, we must obtain the data and construct a data table. Below are standard ways in which data may be presented in table form:

Table I: Table II: Table III: Weight force versus Stretch Area vs. Radius Period of a Pendulum vs. Amplitude

The variables listed in each column (or row) in the tables are clearly defined along with the associated units. In a laboratory notebook, the experimental conditions would be clearly described as well. If there is more than one possible independent variable those that are held constant are clearly noted (as in Table III).

In the experiment that generated Table III one could vary mass or length while holding the amplitude constant, and continuing using the same table to record our data. The data that are directly observed by our experimental instruments (which may include our eyes and ears!) should always be directly recorded. If any data appear to be erroneous because of a mistake or error, it should be crossed out with a single line and an explanation given for tossing out the data.

Later there will be time to calculate additional quantities from the “raw” data. Additional column or rows, clearly distinguished from the original data, can be used to list the calculated values along with the methods or formulae used in the calculation or references pointing to them (see Table II).

At no time should the reader be confused about what is measured and what is calculated from the measurement. Because the “raw” data is directly recorded, if the calculation turns out to be in error you can always go back and recalculate by a different method.

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Amplitude (degrees)

Mass (kilograms)

Length (m) Period (sec)

5.0 10.0 20.0 30.0 40.0

(constant)0.1500

(constant)0.2050

2.68 2.80 2.78 2.82 2.73

R a d i u s (cm), R 2.5 5.0 10.0

Area (cm2) “measured area”

19.6 78.3 314.0

πR2 (cm2) “calculated area”

19.7 78.5 314.2

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Mass (kg) Weight (N) (Kg x 9.80m/s2)

Δ length (meters)

0.200 1.96 0.140

0.400 3.92 0.203

0.500 4.90 0.234

0.600 5.88 0.262

0.700 6.86 0.300

0.800 7.84 0.334

0.900 8.82 0.365

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2. Graphical Analysis of Data Scientific data are usually collected by observing some natural activity or obtained in planned experiment. One can then look for

overall patterns explained by scientific theories or “laws.” To aid in interpretation, data are usually organized in some way to enhance the possibility that a pattern or relationship that may exist will be evident to the scientist. Patterns, relationships, and generalizations permit deductive reasoning and allow us to make predictions, develop theories, and then design further experiments or observations to test those theories. There is no one best way to organize data to ensure that patterns will emerge, but a visual representation can be one of the best ways to “see” that overall picture. In other words, a graph can be worth 103 tables of numbers.

A graph is simply a visual way of representing our numbers or data. Graphs might be one dimensional, as for example a thermometer, a speedometer, or a fuel gauge, the “bar graphs” on the graphic equalizer of your stereo. A medical thermometer gives a visual representation of temperature with the rise and fall of mercury. The change in volume of the fluid is proportional to the change in temperature and so the height of the mercury column changes linearly with temperature. A speedometer has a needle whose angle changes in proportion to the speed of the car and so gives a visual representation of the speed. In both cases, it is often easier to immediately grasp changes in temperature or speed than it would be if we had to first read, then comprehend a series of numbers, then think about their relative magnitudes.

“Y” versus “X” (Vertical axis versus Horizontal axis)

More commonly, we think of a graph as a two-dimensional picture showing the relationship between two sets of numbers. Usually a horizontal axis (which we often think of as the “x” axis) shows an independent variable, while the vertical axis (often thought of as the “y” axis) shows a dependent variable. The independent variable is a set of data points which we vary experimentally, while the dependent variable is the quantity that we measure as a function of the independent variable: we say “y” is a function of “x” or “y=f(x).” Thus the graph shows “y” versus “x” or “f(x) vs. x.” The variables “y” and “x” might be position as a function of time, speed as a function of position, gallons of fuel used as a function of miles driven, etc. In our experiments, we will be able to control one or more variables and will measure other data as a function of those variables. In order to perform a systematic experiment, we will only vary one thing at a time (“x”) while we observe the results (“y,” “z,” etc). A graphical representation of “y(x) versus x” or “z(x) versus x” is often the best way to look for a pattern in the data which will tell us about the science behind our experiment.

x-‐axis

y-‐axis

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MAIN MENU2.Graphical Analysis of Data (continuation) Plotting Data

Once the data has been carefully recorded in the data tables, graphs are constructed to try to determine patterns which may exist in the data. Here is a suggested procedure: 1.Determine the data range: Most of the data you will see this semester will consist of data very similar to the data in the sample tables shown above (although many of your tables will be much larger!). By a data range, we mean the range from the smallest to the largest values you are going to plot. This will ensure that you can fit all of your data within the limits of your graph. For example, in Table II the range for the area might be from 0 to 315 cm2. The range of the radii would be from 0 to 10 cm.

2.Determine the scales: Make sure that the scales you use are linear – that is the “tick” marks are equally spaced with the same range of values between each. Note also that the size of the scales do not have to be the same for both axes if the ranges are very different. Your scales should be even divisions of the range you decided upon to fit your data.

3.Draw and label the axes: It is very important to clearly label the axes of your graphs (including units!) so that you will know what you have plotted when you review your notes. The graph is labeled “Vertical Variable versus Horizontal Variable.” Thus when you are told to plot Variable A vs. Variable B this means that A goes on the “y axis” while B goes on the “x axis.”

4.Plot the actual data: Mark the positions of your data carefully with dots or crosses, then outline these smaller points with larger symbols such as circles, squares, etc.

Once the data has been carefully plotted, your graph should look like the one shown in the sample of the lab report. As seen from this example, the graph should occupy all the page with the axes labeled and the correct intervals. If you are going to determine the slope, then follow the following steps: (turn the page.)

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2. Graphical Analysis of Data (continuation) Best Fit Curve and Slope

5.Draw the “best fit” curves: One of the most useful aspects of a graph is that it can be used to average random experimental errors made in obtaining the data. Because of these uncertainties, even if theory predicts that it should, your data will rarely fall on a straight line and it looks even worse if you connect the points. Do not connect the data points on the graph. However, you can draw a “best fit” straight line representing the data - if the data has a linear relationship. Sometimes straight lines do not describe the data. In many cases the data should be fit to a curved line such as a parabola, and a smooth curved line can be drawn through the data points on the graph. For example:

6.Determine the slope: If the data represents a straight line. In the case of the last two graphs, only the left graph represents a straight line. Then, the slope is the tilt or steepness of a straight line defined as change in the vertical units (or “Δy,” where the symbol “Δ” delta is used to mean a change in some value) divided by the change in the horizontal units (“Δx”). We can determine the slope of a straight line by taking any two points on it (not data points, but rather points on the line we have drawn). If the coordinates of any two points on the straight line are (x1,y1) and (x2,y2). If the points are from the left graph then the slope is:

Some times in the exercise, the calculation of a certain parameter is done by using the slope instead of plugging the data into the formula. As in the case of the straight line in the left graph, the meaning of the slope is the acceleration. A way to know what the the slope means is to obtain the units of it. In the case shown here, the units of the rise are m/s, the units of the run are s. Then, the units of the slope are m/s2.

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◉ ◉

◉

◉

◉◉

◉

Time (sec)

Velocity (m

/s)

20 3010 40 50 600

42

86

◉◉

◉

◉

◉

◉

◉

Time (sec)

Length (m

)

2 31 4 5 60

0.40.2

0.80.6

10 10

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3. Further Analysis of Results

Once you have calculated a variable from the physics of the experiment. You need to compare that result with a result obtained with a different experimental method carried during the same experiment or other experiments. Usually, one of the experimental methods is more accurate than the other one. A comparison of both results can be obtained using

Where value1 could be less than value 2. Since this is calculation is an absolute value, the percent difference must be positive always. The average2 is again defined as

This measurement can not tell much about the accuracy of the experiment finding the value of the physical parameter, but this measurement can tell about the precision of both methods with respect to each other. If it is known that one of the methods is more accurate than the other one, the percentage difference reflects the existence of errors during the experiment. Theoretically, an expected value of 0% of the percent difference will indicate that both experiments carried the same result. However, performing an experiment can carry different sources of error. If the value for the percent difference is higher than 15 or 20%, there is a high probability that the experiment was performed poorly or the math and physics were applied wrong by the experimenter, or an external agent was introduced in the experiment without notice. If this value is below or equal to 20 - 15%, the difference can be explained due to the systematic errors. A better way to compare the experimental results is to use the theoretical value. In this case we use the following formula:

If the result of the last calculation is again lower than 20 - 15%, then it is possible to argue that the experimental result is accurate. If this last percent is higher than 15% or 20% means that the experimental value is not accurate.

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II. ORIENTATION 1. Physics units for the 123 laboratory exercises

Units of measurement: All measurements must be in SI units (the metric system) What are the standard units for: Length? Meters (m) Mass? Kilograms (kg) Time? Seconds (s) All your measurements must be converted to the last system of units. An abbreviation for the meter, kilogram and second is MKS. These are the units used on this entire course.

Precision of the instruments: The precision of your instruments is reflected in the amount of significant figures for your measurements. The precision of the instrument is how small the instrument can measure the required parameter. As an example, let us use a ruler. A ruler has 30 cm = 0.3 m = 300 mm. When you measure in centimeters you will have one significant figure after the decimal point, for example 23.4 cm. After converting into meters this reading is 0.234 m, this is three significant figures after the decimal point. Thus, the precision of the ruler is 0.001 m. While in the lab, find the precision for the following instruments:

the meter stick? _____________________ the rulers? 0.001 m the balance? _____________________ the stopwatch?___________________

ALWAYS make your measurement as precisely as possible and BE SURE to record that measurement with the correct number of significant digits. Additionally, always convert units to MKS. Sometimes the instruments are not correctly calibrated. Be sure to have a zero value in your instrument every time you measure a variable.

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2. Precision and Accuracy of Measurements

Precision Imagine that you collected the 15 measurements of the size of a box. These are the measurements:

Table IV. Measurements of the size of a box.

There are two things that are easily noticed from the last table. The first one, is that all the measurements are close to each other. Then, a question that rises after this observation is how close these measurements are? A way to answer this question is to use the standard deviation or dispersion of the data, but these statistical tools are out of the scope of this course. So, instead of calculating the last two values we can calculate the %Difference of the highest and lowest value of the sample, this is

Where average2 is:

The percent difference can be taken as an estimation of the precision of the sample. The lowest the percentage, the higher the precision of the sample, this is, the closer the values to each other. Then, the higher the percentage, the lower precision, the further apart of the values from each other. In the example, the percent is less than 15%, which means that this percent can be explained by the systematic errors that occur during the experiment. If the percentage is greater than 15%, the dispersion can be explained by extreme lack of care when experiments were performed or the bad use of the math or/and physics. A second question that arises about the measurements of the box is if the average value, or each of the values recorded in the table match the real value of the box.

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Size of the

box in meters

1.563 1.565 1.587 1.499 1.601 1.614 1.495 1.567 1.512 1.547 1.497 1.521 1.593 1.555

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2. Precision and Accuracy of Measurements (continuation)

Accuracy Imagine that the real value of the size of the box is 1.567 m and the average value from the table is 1.446 m. The last two values are called the theoretical and experimental value, respectively. Then a measurement of the accuracy of the data can be obtained by calculating the %Error:

This calculation can be obtained for each value in the table, or just for the average value as we did. Using the same argument as in the case for the calculation of precision, if the percent is less than 15%, the experimental value is accurate and the percent can be explained by the systematic errors. Finally, one more observation can be made about Table IV. The values are different. Then, the question that follows after the last reasoning is why the values are different?

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MAIN MENU3. Errors in the Experiment

It is well known that errors occur during an experiment. Independently of what these are called, it is more important for the experiment to know what are those errors. Thus, errors that originated at the time to obtain data can be produced by faulty equipment, an uncalibrated system (incorrectly set the zero level of the recording device), and the limitations by the observer. The limitations of the observer are the optical resolution of the eye; the precision of the hands to locate objects and the reaction time to execute a task (such as pressing a button ); and the reaction time of the ear and the range of sound frequencies that the ear can detect, for example. The last type of errors are called systematic errors. However, the focus of understanding this type of errors is not the name of them but the sources of them. There is another type of error that depends on the physical conditions for example, variations of temperature, pressure that may affect the measurements of variables. A way to overcome these errors is to obtain a large amount of measurements of the same variable. The last type of errors are called, random errors. After the data is taken, several mistakes occur in the process of finding the final results. Some of this mistakes are the use of incorrect units. Forgetting to convert to the correct units can cause that all results be wrong. Another example of this kind of errors is if a wrong physics formula is used to calculate a variable -gravitational waves-. Calculating wrong one of the parameters will affect the other calculations that depend on the first calculation. As a consequence, the final result is wrong. This kind of mistakes are wrongly called calculation errors. However, these are not errors per se since this kind of errors can be controlled by the person doing the experiment. That is why, the last ones are not sources of errors. Finally, another misconception about errors appear when during calculations the parameters are rounded. Rounding variables depend on the significant figures. Rounding variables properly is not a source of error. Because this operation is very well determined by the rounding and significant figures rules, that is why the last one is not a source of error. As a final remark about errors, imagine that a spaceship is sent to Mars. The systematic errors will cause to miss the landing target a few meters from the predicted value, the calculation error will cause the spaceship get lost into space. There is not such a thing as calculation errors.

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4. Significant Figures and Rounding As remainder you have learned in your lecture there are some rules to obtain the correct amount of significant figures when you

are not measuring the variable. As a summary, let us give an example of this procedure. With your calculator you will often get numbers to your calculations that give you many digits plus an exponent if you are using scientific notation. For example:

The significant digits of a number are those that tell you meaningful information. Particularly in experimental science, the number of digits is used to help indicate the uncertainty of the problem. In the example above, both 5.6 and 3.8 have two significant digits – this is basically telling us that we don’t know those numbers to any greater accuracy than that. That is we don’t know if the number 5.6 might really be 5.61 or 5.59 – we are uncertain to that extent. When we do the arithmetic with uncertain numbers than the results must be uncertain to the same degree. Therefore we should report that:

Notice that we have rounded off 1.4737 to 1.5 – the closest two-digit number. If the next digit is above 5 we round up to the higher number, if it is below 5 we round down to the next lower number. If it is exactly 5 (any following digits are also zero) then we round off so that we are left with an even numbered digit – that way we will round up half the time and round down half the time. Thus if we are rounding to three significant digits:

1.4587 → 1.46 3.67298 → 3.67 7.54500 → 7.54 7.53500 → 7.54 1.3009 → 1.30

The Role of ZerosZeros can be either significant digits or they can merely be placeholders. If the zeros are after the numbers they are

counted as significant digits. When we say 1.50000 we mean that we know the number is really 1.50000 and not 1.499 or 1.501, although it could be 1.500001. Zeros that appear before the first non-zero digit are placeholders that tell us what power of ten we have and disappear when we use scientific notation. Thus 0.000150 has three significant digits and in scientific notation would be 1.50x10-4 (Note that we move the decimal point over by four). Numbers larger than 10 can be ambiguous unless scientific notation is used. By 6,000,000 do we mean one significant digit or seven? The lack of a decimal point can indicate that not all seven digits are significant, but it is still confusing. 6.0x106 tell us that in fact we mean only two significant digits.

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2104737.1108.3

106.5 ×=×

×−

31

2105.1108.3

106.5 ×≅×

×−

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MAIN MENU4. Rounding Rounding Calculated Parameters

When doing calculations the significant digits of the answer should agree with the significant digits of the least measured variable you have, that is the one with the least number of significant digits. It does not matter if you know all of the other numbers more accurately; your accuracy is limited by the precision of your instruments.

In order to round correctly, after each operation, the number of significant figures must be obtained, before you start a following calculation. Then, you will use the variable just found with the correct precision (correct number of significant figures) combined with a new measured or calculated variable with the correct amount of significant figures.

As an example, you can follow the calculations section in the sample of the lab report. In the table for Part A, the weight force has three significant figures because the mass is given with three significant figures. As a consequence, the slope of the graph has also three significant figures (400 N/m), because the force and the distance reported with three significant figures.

Finally, the value for the slope, represent the spring constant k. This value is used, to calculate the potential energy of the spring. Because the spring constant and the distance have three significant figures, the value for the potential energy also has three significant figures (0.157 J.).

The rest of the calculations in the sample of the lab report are done in the same way until the mechanical energy is obtained.

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5. Laboratory Report: Here is a general format for lab write-ups that you should follow. Some parts may be modified depending on the exercise done, but the components of the laboratory report must be kept.

Name (s)

Full names of each person in the team.

Title of lab and date

Introduction

Describe the goal (s) of the experiment. This is, what you are trying to probe. Mention all the required physics to accomplish the experiment.

Experiment Description

Materials used (including the measuring instruments used)

Description. Describe the adventure of doing the experiment. Make a sketch of the setup and draw the physics parameters involved in the experiment such as forces (FBD), measurements and initial and final positions of the objects involved in the experiment and how they do move. Include the physics formulae used in the calculations. Along with the last description, the following questions may help you to do a good description of the experiment.

What did you measure?

What did you observe?

What did you calculate?

Data. In this section you should record all of your measurements as they come from the instruments. The significant figures of the measurements should be consistent with the precision of the instruments.

Making a data table Refer to the section in the tools section about how to build a table. Include a header with the units and name of variables. Make a consistent table with the correct number of significant figures for all the measurements. Include the trials.

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5. Laboratory Report (continuation):

Results

May be a calculated result or an observed result. Include in this section all your findings using the physics described in the introduction and the experiment description and your calculations. Write your calculations in the following way:

If there are repeated calculations, show one sample for each repeated calculation. If there are not repeated calculations show all of them. (Show the equation, then show the equation with numbers in place including units.) Show the answer with correct units. Your first calculations should be converting measurements to the correct units (MKS). Calculate the precision for repeated measurements. If required calculate the slope of the best fit line. If required calculate here the percentage error or percentage difference. If the experiment is observational. You should record here your observations. Graphs - from time to time you will make graphs. Make a graph using the recommendations given in the tools section. Make your graph using the whole page do not try to save the paper making a tiny graph. Use the sample of the lab report at the end of the manual to help yourself how to do it.

Conclusions

Answer here all the other questions in the procedures for which you do not have to do calculations. Here is the section where you think about the physics. Mention if you accomplished the goal(s) of the experiment.

Talk about the accuracy of your results. This question can be answered based on the precision of your measurements.

Tell how you obtained the amount of significant figures for your results.

Mention why the results are not perfect compared with the theoretical results. Describe the systematic errors.

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III. EXPERIMENTS Charges & Electric Forces

Concepts: • Charged and Neutral Objects • Charging by Direct Transfer and by Induction

Pre-lab question: 1. Explain where electric charge comes from. 2. Print the tables to complete the exercise (pp. 23-24) Procedures: **Note: Write your observations on the tables that you brought for the exercise.

A. Charged Tapes To make the tape charged, first tear off a piece of tape that is about 20 cm (8 in) long and stick it on the lab bench. This will be

your base (B) tape that you will use to make all of the other tapes. Now tear off another piece of tape about 20 cm long and fold one end over to make a non-sticky handle. Stick this tape on top of the B tape and smooth it down. Pull it off rapidly, and you have a top (T) tape. Hang the T tape from a thread on the string above the lab table.

1. Bring your hand near the T tape. What do you observe?

[You should observe that the T tape interacts to your hand. If it does not, remake the tape following the procedures above (the B tape does not need to be redone).] **Note: You may have to remake the tape occasionally throughout the lab—whenever it is no longer interacting to your hand, it needs to be recharged.

2. Now try some other objects like your pencil. What happens?

Interactions between two T tapes: 3. Make a second T tape. Bring it close to the first T tape. What do you observe? You should observe that the T tapes move when

they are brought close together, providing evidence that they exert forces on each other. Recall that force is a vector, so it has both magnitude (the strength of the force) and direction.

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Charges & Electric Forces (Continuation) 4. When you bring the T tape close to the other one, observe in what direction the first tape moves. You must be careful –

sometimes the tape will move due to air currents. Also, if the tapes are curved or twisted they can fool you. Look for the direction the tape first begins to move.

5. Draw a view-from-above picture to illustrate the direction of the force between the two tapes. 6. Try bringing the tape in from different directions and come up with a general statement about the direction of the force that the

second T tape exerts on the first T tape.

This gives us an idea about the direction of the force. Now let’s look at the strength of the force, which could depend on a number of quantities. The one we will look at is the distance between the tapes. In order to tell if the force is changing, look at the deflection of the tape attached to the thread.

7. Determine a general statement about how the strength of the force depends on the distance between the two tapes. (You will not be able to come up with an exact mathematical relationship, but you can observe if the force is independent of distance, or if it increases or decreases as the distance decreases.)

Making another type of tape: Take one of the pieces of the tape and stick it to the B tape. This will be the middle (M) tape. Put another tape (T) on top of this

tape. (It might be helpful to label the tapes at this point.) Pull both pieces of tape off together. Hold both ends of the tapes and run your fingers down the smooth side of the top tape. The M-T tape should now be neutralized. Pull the M and T tapes apart rapidly and hang them on separate threads from the string. Make a second set of M and T tapes. Make sure that each tape is charged.

Interactions between the M and T tapes: 8. Bring the M tape near your hand, a pencil and any other two objects. What happens? 9. Is this the same or different from what happens with your hand and the T tape? 10.Bring the M tape near the hanging M tape. What happens? 11.Bring the M tape near the hanging T tape. What happens? 12.What happens if you bring the T tape near the hanging M tape? 13.Do the observations you made earlier regarding the direction still seem to be true? (Is it still along the line connecting them?

Is it still repulsive?) Do the observations you made earlier regarding the dependence of the strength of the force on distance still seem to be true? (Does it decrease with distance?) Provide evidence for either agreement or disagreement.

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Charges & Electric Forces (Continuation) **Be sure that the tapes interact with the objects. If not, recharge the tapes**

Interactions between charged rods and the M and T tapes: 14.Make sure that you have a good M and a good T tape hanging from the string (not too close together). Charge the plastic,

glass, and rubber rods by rubbing them vigorously on the cloths (wool or silk) or the fur. Try various combinations of rod and rubbing material, and see how they interact with the T and M tapes.

15.Is there a difference between the way the M and T tapes interact with your hand and the way they interact with the charged rods? Provide evidence to support your answer.

B. The electroscopes 1. Charge the electroscope by rubbing a charged rod on the top of it. Specify the type of rod and material that you use for this

test charge. What do you observe? Leave the electroscope charged for all of the following observations. 2. What is happening to the electroscope to make it behave as it does? 3. Now bring the same rod (charge it by rubbing it on the same material first) near the top of the electroscope (but not touching

it). What happens? 4. Try all of the other rod and material combinations and list them, along with your observations of the behavior of the

electroscope when you bring the charged rod near (but not touching) the top of the electroscope. Make a table similar to the one above. You should be able to find at least one combination that makes the “leaves” of the electroscope move farther apart when you bring the rod towards the top of the electroscope, and at least one combination that makes the leaves move closer together.

5. What conclusions can you draw about the charges generated by rubbing different rods with various materials?

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Your Hand Pencil/Pen Object 1 Object 2 T2 Tape

T1 Tape

Your Hand Pencil/Pen Object 1 Object 2 M2 Tape

M1 Tape

T TAPE INTERACTIONS

DRAW THE INTERACTIONS BETWEEN THE TWO T TAPES

M TAPE INTERACTIONS

INTERACTIONS BETWEEN TAPES

M1 Tape T1 Tape

M2 Tape

T2 Tape


Fur Silk Flanel

Plastic Glass Rubber Plastic Glass Rubber Plastic Glass Rubber

T1 Tape

M1 Tape

Fur Silk Flanel

Plastic Glass Rubber Plastic Glass Rubber Plastic Glass Rubber

Electroscope

INTERACTIONS BETWEEN RODES AND MATERIALS

TELL THE RODE AND MATERIAL USED TO CHARGE THE ELECTROSCOPE

INTERACTIONS BETWEEN RODES AND ELECTROSCOPE


Electric Field Mapping Concepts:

• Equipotential Lines • Electric Field Lines

Pre-Lab Questions: 1. What is an electric field? What other physical field are we familiar with? 2. What are the characteristics of electric field lines and how are equipotential lines related to electric field lines?

Procedures: 1. Set up the field mapping apparatus with the “point and plate” electrode configuration. Using a voltmeter, adjust the power

supply to produce a 10 volt reading. 2. Attach a sheet of paper to the top. Disconnect one of the voltmeter wires from the mapping board. Plug the “wand” onto the

end of this wire. Slide the bottom of the wand under the mapping board and the top of the wand onto the top of the mapping board. Using the voltmeter locate and mark all the points at 1 Volt potential. Try to find points that are about 1 cm apart and draw a smooth line connecting the points. Label this line “1 volt”. Repeat for the 3 Volt, 5 Volt, 7 Volt, and 9 Volt equipotentials. How precise are your lines?

3. Remove the sheet of paper and sketch in the electric field lines. (Remember: electric field lines have direction.) 4. Repeat steps 1-3 with another electrode configuration. 5. Repeat steps 1-3 for a third configuration.

6. Explain how your voltage maps illustrate the properties of E-Fields.

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Capacitors Concepts: • Capacitance • Charging and Discharging a Capacitor

Pre-Lab Questions: 1. How does the capacitance of a parallel plate capacitor depend upon the area and separation of the plates? 2. What is the equation that contains capacitance, area and distance between plates? Show the equation and explain each term. 3. Predict what will happen if a capacitor, a light bulb, and a battery are hooked together in series. Describe what you will see

happen to the light bulb from the moment the circuit is completed.

Procedures: In your experiment description start by showing the equation that has capacitance, area and distance. Identify each variable in the equation and then explain what your units will be for each in this lab. Make sure to make a drawing of each setup. Make sure your data page is well organized. Compare your pre-lab predictions (question 3) with your lab group. Come up with a group prediction and write it down.

A. Parallel Plate Capacitors 1. Construct a parallel plate capacitor from two rectangles of aluminum foil. Make each rectangle the same size. Make them just

smaller than the size of your text book pages. Record the length, width and area of the rectangles. Place them inside your text book, separated by one page. Make sure no part of the aluminum foil hangs outside the page. Tape one end of a small piece of wire to the shiny side of each foil sheet and let the other ends hang outside the book to connect to the multimeter. Weight the textbook with two 2½ kg masses. Connect the wires to the capacitance connections on the multimeter and set the multimeter to one of the capacitance ranges.

2. Measure how the capacitance of your parallel plate capacitor depends on the spacing of the foil sheets. Make measurements of the capacitance for the following page-spacings: 1, 2, 3, 4, 5, 7, 9, 11, 15, 18

3. Plot your data on a graph of Capacitance vs. Spacing. Is your graph linear? Should it be linear? If not, what relationship should you see? Remember to use more than half of the graph sheet while using an appropriate scale.

4. Determine a way to measure how the capacitance of your parallel plate capacitor depends on the area of the foil sheets. Make measurements of the capacitance for at least 5 different areas. For the first measurement use the largest possible area and the smallest possible page separation. For each new area reduce your plates’ area by 15 percent each time. Make sure to record the length, width and area of each set of plates.

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Capacitors (Continuation) 5. Plot your data on a graph of Capacitance vs. Area. Is your graph linear? Should it be linear? If not, what relationship should

you see?

B. Charging and Discharging a Capacitor

Note: Make sure you always discharge the capacitor by connecting its terminals together with a piece of wire before you handle it. This will prevent you from getting a shock. 1. Hook up the battery, light bulb, capacitor, and switch (keep the switch OPEN) in series. Close the switch and observe what

happens. Discharge the capacitor and repeat several times. Now write a description of what happens. 2. Discharge the capacitor. Hook up the capacitor, the light bulb, and the switch (OPEN) in series (without the battery, this time).

Use the battery to charge the capacitor by hooking the one terminal of the battery to one terminal of the capacitor and the other terminal of the battery to the other terminal of the capacitor. Remove the battery. Close the switch and observe what happens. Repeat this several times then write a description of what happens. After you describe what you see happening, offer an explanation for what happened.

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Batteries and Bulbs Concepts: Schematic diagrams

Complete circuits

Current

A. Series and Parallel Circuits • Two light bulbs can be hooked to a battery in two different ways: series or parallel. • Two batteries can be hooked to a light bulb in two different ways: series or parallel. • The light bulbs in series (#1,#2) are drawn schematically as • The light bulbs in parallel (#3,#4) are drawn schematically as

Pre-lab Questions: 1. If a light bulb is hooked up to batteries, do you think the brightness of the bulb will depend on how many batteries you use?

Explain why or why not. 2. If two identical bulbs are hooked up in series and two more identical bulbs are hooked up in parallel as shown, rank the four

bulbs (by number using the locations in the circuits above) from brightest to the least bright. Explain the reasons for your rankings of all four bulbs.

Note: Never use more than two batteries. The light bulbs can’t take it.

Procedures: 1. Discuss your pre-lab prediction #1 with your lab partners. Come up with a group prediction and write it down. 2. Attach a round light bulb to one battery and then to two batteries. Describe what you observe and how it relates to your

prediction. 3. Discuss your pre-lab prediction #2 with your lab group. Come up with a group prediction, including a sketch of the two circuits

with the bulbs carefully labeled. 4. Test your prediction using two batteries and two round bulbs in series. Describe your observations. Hook up the two round

bulbs in parallel. Describe your observations.

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Ba<ery

Ba<ery

#1 #2

#3 #4


Batteries and Bulbs (Continuation)

5. Write a brief explanation of what is happening to produce the results you observed and reconcile them with your prediction.

6. Predict what will happen if you have the two round bulbs in series and you unscrew one bulb from its socket. Does it matter which bulb you remove?

7. Test your prediction and record your observations.

8. Predict what will happen if you have the two round bulbs in parallel and you unscrew one bulb from its socket. Does it matter which bulb you remove?

9. Test your prediction and record your observations.

10.Sketch a schematic circuit that has bulbs in both series and parallel. Gather the extra parts you need and build the circuit. You may work with another group and their bulbs if you like. Describe what you see when the circuit is hooked up.

11.If you had unlimited time, what further questions related to the material would you like to explore? How would you build on this experiment to learn more about batteries, bulbs, and circuits?

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Resistance, Voltage and Current in Circuits Pre-lab Questions: 1. Give a mathematical equation that indicates how the voltage drop across a resistor and the current flowing through the resistor

are related to the resistance. 2. Sketch a diagram indicating how a voltmeter would be wired into a circuit of a battery and one bulb in order to measure the

voltage drop across the bulb. 3. Sketch a diagram indicating how an ammeter would be wired into a circuit of a battery and one bulb in order to measure the

current flowing through the bulb.

Note: Verify your pre-lab answers before wiring the circuits. When wiring the circuits, have your instructor check your circuit before you make the last connection.

Procedures: Every time you connect the ammeter to measure current, draw a diagram showing exactly where the ammeter is placed in the circuit. Make sure this goes on your data page with the appropriate data.

A. Finding the Resistance of each bulb 1. Hook up a round bulb to two batteries. Measure the voltage drop (potential difference) across the bulb. Measure the current

on both sides of the bulb. Is the current the same on both sides of the bulb? Calculate the resistance of the round bulb using V=IR.

2. Repeat Step 1 for a long bulb hooked to two batteries. You will use these resistance values for the two bulbs when calculating the equivalent resistances (number 3 and number 7 below) in the circuits.

B. Series Circuit 3. Calculate the series equivalent resistance of the long bulb and the round bulb hooked up in series from the values found in

part A. Predict the appearance (brightness) of each bulb when they are wired in series.

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Resistance, Voltage and Current in Circuits (Continuation)

4. Wire the circuit (Series) shown in the figure: a round bulb and a long bulb in series with two batteries. Describe what you see; is it what you predicted? Why or why not?

5. Measure the current on each side of each bulb. Measure the voltage across each bulb. 6. Calculate the resistance of each bulb in the circuit using the values measured in (5). Use the formula to find the total resistance

in series to find the total experimental resistance in the circuit. Compare the experimental resistance with the calculated resistance (number 3) by finding the percent difference.

C. Parallel Circuit 7. Calculate the parallel equivalent resistance of the long bulb and the round bulb from the values found in part A. Predict the

appearance of each bulb when they are wired in parallel. 8. Wire the circuit (Parallel) shown in the figure: a round bulb and a long bulb in parallel with two batteries. Describe what you

see; is it what you predicted? 9. Measure the voltage across each bulb. Measure the current on each side of each bulb. 10.Calculate the resistance of each bulb in the circuit using the values measured in (9). Use the formula to find the total

resistance in parallel to find the total experimental resistance in the circuit. Compare this with the value you calculated in Step 7 by finding the percent difference.

D. Summary 11.Describe the characteristics of a series circuit and of a parallel circuit. (Think in terms of voltage, current, and resistance.)

Compare what you observed in the series circuit to what you observed in the parallel circuit. 12. How do your measurements relate to the appearance of the bulbs?

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Series Parallel

R1 R2 R3 R4


Magnetic Field Mapping Concepts: • Permanent Magnets • Magnetic Fields due to Current Carrying Wires

Pre-Lab Questions: 1. How can you map a magnetic field using a compass? 2. Sketch the expected magnetic field lines around a single, straight, current-carrying wire.

Procedures:

A. Permanent Magnets Make sure that your magnets do not reverse your compass direction! 1. Set up two bar magnets with the north pole of one facing the south pole of the other. Leave a gap of about 1-2 cm between the

magnets. Cover the magnets with a piece of paper and gently sprinkle on the iron filings. Make a detailed full-size sketch of what you see on a second sheet of paper on which you have traced the magnets. Return the iron filings to their container.

2. Place the magnets on another sheet of paper (keeping the magnets in the same positions and orientations) and trace around them. Label the north and south poles. Use a compass and sketch a number of field lines.

3. Repeat steps 1 and 2 for the bar magnets arranged so that the two north poles are facing each other. 4. Repeat steps 1 and 2 for the horseshoe magnet. 5. Describe the similarities and differences between what you see in your iron-filing pictures and what you see in your magnetic

field lines determined by the compass. Provide specific details.

B. Current-carrying Wires 1. Investigate the magnetic field around a single current-carrying wire that is set up for you. (Keep the current less than 2.5

amps.) Use the compass to map out the field lines. The easiest view to draw will be the view looking straight down along the wire. Make a sketch of the magnetic field lines. (Do not touch the bare copper wire!)

2. Investigate the magnetic field around a coil of wire carrying current. (Keep the current at less than 1 amp.) Use the compass to map out field lines. Draw a sketch of the field lines as you look straight down from above the coil.

3. What similarities and differences do you see between the single-wire magnetic field and the coil’s field? Provide specific details.

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Magnetic Induction Concept: • Magnetic Induction

Pre-Lab Question: 1. What is electro-magnetic induction and how does it produce current? 2. Upon what physical quantities does electro-magnetic induction depend? 3. Print the tables to complete the exercise (pp. 34)

Procedures: 1. Set up the wire coil and attach it to the ammeter as shown in the diagram.

2. Experimentally determine the qualitative effect of moving the magnet in and out of the coil of wire in different ways. For each factor (or way) that determines the current, describe how the current is affected by varying that parameter. Note: you should think about the amount of current (indicated by how far the ammeter needle is deflected) and the direction of the current (indicated by the direction of the ammeter needle’s deflection). Make sure you have investigated the following factors: using the north or using the south end of the magnet, which side of the coil the magnet goes into, the speed of the magnet, and the direction of the magnet (towards or away from the coil.) Make an organized data table to show your findings. For any variable that changes the amount of current produced, record numerical values in a data table.

3. Change the magnet and repeat the ways the magnet can go into the coil. Make a second table. 4. Choose one magnet, one side, north or south of the magnet, and the speed to go into the coil (i.e. these parameters are fixed).

Then, use the coils with different number of turns and record on another table how the current changes with the number of turns.

5. Summarize the results from your observations in Steps 2, 3 and 4 by making a general statement about magnetic induction. (What factors alter the direction of current; what factors alter the amount of current; how would you produce the largest current).

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Coil side/speed Front: North in / South out

Front: South in / North out

Back: North in / South out

Back: South in / North out

Fast

Slow

BIG MAGNET

ONE SET UP WITH DIFFERENT COILS

SET UP:

COIL #1 COIL #2 COIL #3 COIL #4 COIL #5

Coil side/speed Front: North in / South out

Front: South in / North out

Back: North in / South out

Back: South in / North out

Fast

Slow

SMALL MAGNET


Simple Harmonic Motion Concepts: • Simple Harmonic Motion • Period

Pre-lab Questions: 1. Write a complete definition for: amplitude, period, equilibrium position. 2. How would you experimentally determine the period of a pendulum? Of an oscillating mass on a spring? 3. Print the tables to complete the exercise (pp. 36-37).

Procedures: When making conclusions in this lab you must give evidence from your data to support your conclusions. You will determine if the Period of an oscillation has significantly changed. Think about what significant means.

A. Mass on a spring 1. On what variables might the period of a mass on a spring depend? Make a group prediction and write it down. Compare your

answer with the rest of the class or check with the instructor. 2. Test each of the variables in part one by picking one value for that quantity, measuring the time for 10 cycles and calculating

the time required for one cycle. Repeat the measurement three times to find an average period. Then change your variable (keeping the other variables constant) and repeat the process to find another average period. Repeat the process again so that you have three average periods. How good are your data? Does the period depend on that quantity (within experimental precision)? [Note: compare the variation between measurements of the same value to the differences between the average periods.] If so, describe the dependence.

3. Repeat Step 2 for the other quantities you predicted in Step 1.

B. Pendulum 1. On what variables might the period of a pendulum depend? Make a group prediction and write it down. Compare your answer

with the rest of the class or check with the instructor. 2. Test the quantities using the same method as in Part A. You may need to time for less than 10 cycles if the motion changes

significantly in those cycles. Be sure to note how many cycles you used to time the period. How good are your data? On what quantities does the pendulum period depend from your data?

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Set up: Mass, Spring (K):

Displ. x/Time trials Trial #1 Trial #2 Trial #3 Average Period

x1:

x2:

x3:

Set up: Spring (K), Displacement (x):

Mass/Time trials Trial #1 Trial #2 Trial #3 Average Period

Mass #1:

Mass #2:

Mass #3:

Mass #4:

Mass #5:

Periods for Spring (Mass):

Periods for Spring (Displacement):

Set up: Mass, Displacement (x):

Spring/Time trials Trial #1 Trial #2 Trial #3 Average Period

K1:

K2:

K3:

Periods for Spring (Spring):


Set up: Mass, Length (l):

degrees/Time trials Trial #1 Trial #2 Trial #3 Average Period

y1:

y2:

y3:

Set up: Length (l), Displacement (degrees):

Mass/Time trials Trial #1 Trial #2 Trial #3 Average Period

Mass #1:

Mass #2:

Mass #3:

Periods for Pendulum (Mass):

Periods for Pendulum (Displacement):

Set up: Mass, Displacement (degrees):

Length/Time trials Trial #1 Trial #2 Trial #3 Average Period

l1:

l2:

l3:

Periods for Pendulum (Length):


Springs and Simple Harmonic Motion Concepts:

• Hooke’s Law • Simple Harmonic Motion

Pre-Lab Questions: 1. What is Hooke’s law? Define all symbols. 2. From a graph of the force applied to a spring vs. the amount that the spring stretches, how can you determine the spring

constant of the spring? 3. How are the period and the frequency of oscillation related to each other?

Procedures:

A. Spring Constant Determination from Hooke’s Law 1. Hang six different masses from the end of the spring and measure the amount that the spring stretches for each applied force.

(The applied force is equal to the weight of the hanging mass.) Do not over-stretch the spring! 2. Graph the applied force vs. the amount that the spring stretched. On the graph, draw a line of best fit, choose two points that

are not data points, and calculate the slope. What is the meaning of the slope?

B. Observation of Simple Harmonic Motion 1. Find and open the 3-graph motion shortcut on the computer. You will collect data for the oscillations of a mass hanging on your

spring. Be sure that you have recorded several complete cycles (periods of oscillation). Check with your instructor to see if your graph is ready to print. Once it is OK’d you may print the graph (one copy per person). [Note: Keep the graph on the screen, you’ll need it later.]

2. On your position vs. time graph that you printed, label the distance that corresponds to the amplitude of the oscillation. Determine and record the value of the amplitude. Show what corresponds to one complete period of the oscillation. Measure and record the amount of time that is equal to the period. Calculate and record the frequency of oscillation. The Analyze option (top menu) will be helpful for getting an accurate answer.

3. Observe the position vs. time graph along with the velocity vs. time graph on the screen. What are the similarities and differences between these graphs?

4. On the position vs. time graph you printed mark and label the points that correspond to the magnitude of the velocity being a maximum, for one complete period of the oscillation. Also mark and label the points that correspond to zero velocity. (It may be helpful to refer to the velocity vs. time graph on the computer screen.)

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Springs and Simple Harmonic Motion (Continuation)

5. Observe the position vs. time graph along with the acceleration vs. time graph on the screen. What are the similarities and differences between these graphs?

6. For one complete period of the oscillation, mark and label (again, on the position vs. time graph) the points that correspond to the magnitude of the acceleration being a maximum. Also mark and label the points that correspond to zero acceleration. (It may be helpful to refer to the acceleration vs. time graph on the computer screen.)

C. Adding force to the equation

1. Ask the instructor to show you how to add the force probe to the setup.

2. Close the position vs. time graph program. Locate the motion and force shortcut and open that program. Collect a graph of the moving mass as you did before.

3. Examine the force graph. What force was measured? How are Force and acceleration related? 4. In reality, there are two forces acting on the hanging mass. Describe each force, and how each force varies according to the where the mass is in the up and down cycle.

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Standing Waves on a String Concepts: • Standing Wave Patterns • Nodes • Linear Mass Density

Pre-Lab Questions: 1. Define node in the context of standing wave patterns. 2. How is the wavelength related to the distance between nodes in a standing wave pattern? 3. How is the wavelength related to the tension of the string? Give an equation.

Procedures: 1. Attach a string to the vibrator and hang a mass hanger on the other end over a pulley. 2. Turn on the vibrator and try to form various standing wave patterns on the string by lifting up or pulling down gently on the

mass hanger. Does the number of loops increase or decrease with decreased tension? 3. Adjust the tension in the string by hanging masses from it until you have a pattern with two or three loops. Record the hanging

mass. Make a table to show the amount of mass needed to create a pattern of loops. Measure the length of the string (from the pulley end of the string to the vibrator). Then, find the relation between the number of loops, the length of the string, and the wavelength. Add on the table a column with a wavelength for each number of loops.

4. Repeat step 3 for 2, 3, 4, 5, 6, and 7 loops, determining the hanging mass and the wavelength for each pattern. 5. The wavelength is proportional to the square root of the tension in the string. Plot the appropriate data in order to obtain the

mass density of the string. The frequency of the vibrator is 120 Hz. Compare your experimental value for the mass density with the expected value by computing the percent error.

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Sound Waves Concepts:

Frequency and wavelength Constructive and destructive interference

Beats Visualization of sound waves

Prelab questions:

1. What is the speed of sound in air? 2. Describe what you would hear if two sounds interfere destructively with each other. 3. What are beats, and what are the conditions needed to hear them?

Procedures:

A. Tuning forks

Start the “Audacity” program on your computer. Click on the microphone and select “Start Monitoring”. Collect data by striking the tuning fork on the rubber bumper and then holding the tuning fork in front of the microphone and click record. Find a way to calculate the frequency of the tuning fork from the graph on the computer screen. Calculate the percent error between this number and the correct frequency stamped on the tuning fork. Repeat this procedure for the second tuning fork.

B. Interference

The two speakers on the front desk are both playing the same signal. If the frequency is 550 Hz, what is the wavelength of the sound waves? Calculate the answer and record on the data page.

1. How far apart must the two speakers be for you to hear destructive interference?

2. For you to hear constructive interference? Draw a diagram on the data page showing the two speaker’s positions and distances between them for each instance.

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Sound Waves (Continuation)

3. Write the general mathematical relation to have constructive interference.

4. Write the general mathematical relation to have destructive interference.

When the same frequency is played in the two speakers placed more than three meters apart, walk around the classroom and find the places where you have ups and downs of the sound. Make a diagram of these points in the classroom considering where the two speakers are and show where the constructive and destructive interference occur.

C. Beats

Describe what happens when the two speakers play frequencies that are very close to each other. Mention the value of the frequencies.

D. Observing different wavelengths

Describe what you hear and see when the speakers play different frequencies, and the frequencies are varied. How does the wavelength changes when the frequency changes? Describe what you see on the screen for each set of sounds that are demonstrated.

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Mirrors Concepts: • Images • Ray Diagrams • Planar and Spherical Mirrors

Pre-Lab Questions: 1. Describe the image characteristics for an object viewed in a plane mirror. (Image characteristics mean: upright or inverted,

enlarged or reduced, and virtual or real.) 2. Describe the image characteristics for an object viewed in a concave mirror. 3. Describe the image characteristics for an object viewed in a convex mirror. 4. Print the diagrams to complete the exercise (pp. 44-45)

Procedures:

A. Observations Observe images in all three mirrors. Describe the types of images (upright or inverted, enlarged or reduced) and their

dependence on the distance between the object and the mirror.

B. Plane Mirror Draw a ray diagram for an object located in front of a plane mirror. Indicate where the image will be located in the mirror.

C. Spherical Mirrors 1. Draw a ray diagram for an object in front of the concave mirror for two cases:

a. the object is located closer to the mirror than the focal point, b. the object is located far from the mirror (outside the focal point).

2. Draw a ray diagram for an object in front of the convex mirror for two cases: a. the object is located closer to the mirror than the focal point, b. the object is located far from the mirror (outside the focal point).

3. Summarize your observations and relate them to the ray diagrams you drew.

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Ray

Dia

gram

s Fo

r Mirr

ors

(1)

f

f

c

c


Ray

Dia

gram

s Fo

r Mirr

ors

(2)

fc

fc


Lenses

Pre-Lab Questions: 1. Draw a picture of a double convex lens. Show the locations of its focal points. 2. Draw a picture of a double concave lens. Show the locations of its focal points. 3. Use the lens equation to determine the location of the image for both types of lenses when the object is very far away. What are

the image characteristics when the object is very far away? (Image characteristics are upright or inverted, enlarged or reduced, virtual or real.)

4. Print the diagrams to complete the exercise (p. 47)

Procedures:

A. Double Convex Lens 1. Look through the lens at various objects and describe what you observe. How do the types of images depend on the distance

between the lens and the object? How do the images depend on the distance between your eye and the lens? 2. Using the optical bench, set up a light source, object, the lens in a holder, and the screen. Adjust the distance between the lens

and the screen to produce a focused image. Measure the distance from the object to the lens (do) and from the lens to the image on the screen (di). Calculate the focal length of the lens. Move the object to a new position (at least 3 cm from the last) and repeat the measurements and calculation of the focal length. Move the object again and repeat the procedure at least five times. Find the average focal length from your measurements and compare it to the manufacturer’s by calculating percent error. What are some of the sources of error in these calculations?

3. Construct a ray diagram for a double convex lens when the object is located inside the focal point. 4. Construct a ray diagram for a double convex lens when the object is located outside the focal point. 5. How do the ray diagrams correspond to your observations? Provide details.

B. Double Concave Lens 1. Construct a ray diagram for a concave lens with an object located outside its focal point. 2. Construct a ray diagram for a concave lens with an object located between its focal point and the lens. 3. Look through the lens at various objects and describe what you observe. How do the types of images depend on the distance

between the lens and the object? How do the images depend on the distance between your eye and the lens? 4. How do the ray diagrams correspond to your observations of images? Provide details. 5. How are the images from the two lenses different?

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Ray

Dia

gram

s Fo

r Len

ses

F

F

F

F

F

F

F

F


Observation of Interference Patterns Concepts: • Interference Patterns • Diffraction Patterns • Constructive and Destructive Interference

Pre-Lab Questions: 1. In the Young’s double-slit experiment what is the condition for a bright fringe? 2. Is the bright fringe caused by constructive or destructive interference between the waves from the two slits?

Procedures:

A. Double Slits 1. Sketch the set-up. 2. Trace and label the patterns that you see on the screen for three different slit separations. Describe in words the differences

and trends you observe.

B. Single Slits Trace and label the patterns that you see on the screen for three different slit widths. Describe in words the differences and trends you observe.

C. Multiple Slits 1. Trace and label the patterns for at least three different multiple-slit separations. Describe in words the differences and trends

you observe. 2. Look at the overhead lights through at least 2 diffraction gratings. Describe what you see and any differences between the

images formed by the different gratings. 3. Replace the slide with at least two diffraction gratings. Sketch and label the patterns. Describe in words the trends and

differences you observe.

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IV. ADDITIONAL EXPERIMENTS Magnets and Motors

Concepts: • Electric currents produce magnetic fields • Solenoids and electromagnets • Magnetic properties of iron-like materials • Force on an electric current in a magnetic field • Torque on a current loop

Pre-Lab Questions: 1. Explain Faraday’s Law. 2. Mention the variables that the Lorentz Force depend on. 3. Explain the physics of a DC motor.

Procedures:

A. Make an Electromagnet 1. Cut a one meter length of 14 AWG solid core insulated wire. Use a pair of wire strippers to remove about a centimeter of

insulation from each end of the wire. Try not to cut into the wire core itself. 2. Neatly wrap the wire tightly around a 4” 20d iron nail at least 20 times. Make certain that you wrap the wire in one direction

only, and leave enough of the wire unwound so that you can comfortably attach the ends to a D cell battery.

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Magnets and Motors (Continuation) 3. When you press one end of the wire to the positive terminal of a D cell battery and the other end of the wire to the negative

terminal, you should have a working electromagnet (like the figure below). Test this with a few paperclips. Note that the wire quickly becomes hot when connected to the battery due to a large current passing through the low-resistance wire. If you were to use a battery that provided twice the voltage, how much more heat would be generated? Why?

4. Draw a diagram of your electromagnet that clearly shows in which direction the wire is wound about the nail and which terminal of the battery each end of the wire is connected to. Indicate the direction of current flow through the wire and label the north and south poles of the electromagnet.

5. The iron nail within the solenoid of wire you made is not necessary to make the electromagnet work, but it greatly increases the strength of the magnetic field. Explain how this works at the microscopic level.

B. Build a Simple DC Motor 1. Wind 22 AWG magnet wire around a cylindrical object two to four centimeters in diameter. (A D cell battery works nicely.)

Make 8-12 loops and leave a tail of about five centimeters of straight wire at the beginning and end of the coil. Magnet wire is enameled with a very thin layer of insulation and is frequently used in applications that require tight coils of wire. The coil of magnet wire you make here will form the armature or rotor of a simple motor. The tails of straight wire at each end of the armature will form the axle of your motor.

2. Ensuring that the tails are exactly opposite one another on the circle of wire, tightly wrap each tail once or twice around the circular bundle of wire to make the coil secure. Straighten the axle tails and make sure they are parallel to each other by making it rotate with your fingers. An example is shown in the figure below:

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Magnets and Motors (Continuation)

3. Lay the coil flat on a table and use sandpaper or a knife to scrape off the enamel coating of the top half of both tails. The function of the motor depends critically on removing all of the enamel from ONLY the top half of the axle. Scrape from the very edge of the coil to the end of each tail.

4. Strap a large safety pin to each end of a D cell battery using a rubber band. The heads of the safety pins should be in good electrical contact with the battery terminals, and the safety pin loops should stick up from the battery opposite one another. The safety pins will support the axle while simultaneously conducting electricity to the armature.

5. Insert the axle tails through the safety pin loops, sandwiching the armature between the pins above the battery. You may need to squash the coil loop a bit so that it can turn freely.

6. Stick the ceramic magnet on the battery to one side of the armature so that a long side is in contact with the battery and one of the large faces points toward the coil. Place the magnet close to the coil, but not so close that it impedes the turning of the armature. The armature should now start turning – perhaps after some fine-tuning and a gentle kick start. Check your on motor with the one in the figure below:

7. Make a sketch of the DC motor. There are two magnetic fields interacting, draw both in your sketch. 8. How does the motor work? Why is it important to scrape only one side of the axle? Briefly explain the principles of operation

of the motor. 9. Without changing the orientation of the battery, how could you reverse the direction in which the armature spins? 10. List at least three modifications to the design of this motor that would increase the rate at which the armature spins.

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Mirrors and Lenses

Concepts: • Planar and Spherical Mirrors • Double Concave and Double Convex Lenses

Pre-Lab Questions: 1. Describe the image characteristics for an object viewed in a plane mirror. (Image characteristics mean: upright or inverted,

enlarged or reduced, and virtual or real.) 2. Draw a picture of a double convex lens. Show the locations of its focal points. 3. Draw a picture of a double concave lens. Show the locations of its focal points. 4. Print the diagrams to complete the exercise (p. 54)

Procedures:

A. Observations with Mirrors Observe images in all three mirrors. Describe the types of images (upright or inverted, enlarged or reduced) and their

dependence on the distance between the object and the mirror.

B. Double Convex Lens 1. Look through the lens at various objects and describe what you observe. How do the types of images depend on the distance

between the lens and the object? 2. Using the optical bench, set up a light source, object, the lens in a holder, and the screen. Adjust the distance between the lens

and the screen to produce a focused image. Measure the distance from the object to the lens (do) and from the lens to the image on the screen (di). Calculate the focal length of the lens. Move the object to a new position (at least 3 cm from the last) and repeat the measurements and calculation of the focal length. Move the object again and repeat the procedure at least five times. Find the average focal length from your measurements and compare it to the manufacturer’s by calculating percent error. What are some of the sources of error in these calculations?

3. Construct a ray diagram for a double convex lens when the object is located inside the focal point. 4. Construct a ray diagram for a double convex lens when the object is located outside the focal point. 5. How do the ray diagrams correspond to your observations?

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Mirrors and Lenses (Continuation)

C. Double Concave Lens 1. Construct a ray diagram for a concave lens with an object located outside its focal point. 2. Look through the lens at various objects and describe what you observe. How do the types of images depend on the distance

between the lens and the object? 3. How do the images you observe correspond to your ray diagram?

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Ray

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Measurement of Interference Patterns Concepts:

• Interference Patterns • Destructive and Constructive Interference • Wavelength of Laser Light


Procedures:

A. Double Slits 1. Sketch the set-up. 2. Trace what you see on the screen. 3. Measure the distances from the central maximum to the first bright fringe on either side of it. Average these values. Compute

the wavelength using this average distance to the first bright fringe. 4. Compare the wavelength you calculated with the expected value of 6.33 x 10-7 m (i.e., compute the %error). What are the

sources of error? How could you improve your measurements? 5. Look at patterns for at least two other slit separations. Trace and label the different patterns on the screen. Describe in words

the differences and trends you observe.

B. Single Slits Trace and label the patterns that you see on the screen for three different slit widths. Describe in words the differences and

trends you observe.

C. Multiple Slits Replace the slide with at least two diffraction gratings. Sketch and label the patterns. Describe in words the trends and differences you observe.

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Double-Slit Interference Concepts: • Young’s Double Slit Experiment • Interference Pattern • Wavelength


Procedures: 1. Sketch the set-up. 2. Trace what you see on the screen. 3. Measure the distances from the central maximum to the first bright fringe on either side of it. Average these values. Compute

the wavelength using this average distance to the first bright fringe. 4. Measure the distances from the central maximum to the second bright fringe on either side of it. Average these values.

Compute the wavelength using this average distance to the second bright fringe. 5. Average the values for the wavelength of the light from steps 3 and 4 and compare (i.e., compute the %error) with the expected

value of 6.33×10-7 m. What are the sources of error? How could you improve your measurements? 6. Look at patterns for at least two other slit separations. Trace and label the different patterns on the screen. Describe in words

the differences and trends you observe.

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Single and Multiple Slit Diffraction Concepts: • Diffraction Patterns • Single Slits • Multiple Slits • Diffraction Gratings.

Pre-Lab Questions: 1. What is the condition for destructive interference in a single slit diffraction pattern? 2. How is the angle subtended by the central maximum related to the positions of the first minima and the distance between the

screen and the slit? Describe in words and give an equation.

Procedures:

A. Single Slits 1. Sketch the set-up. 2. Trace what you see on the screen. 3. Measure the distances from the central maximum to the first minimum on either side of it. Average these values. Compute the

angle subtended by the central maximum. 4. Given the wavelength of the laser light is 6.33×10-7 m, determine the slit width. 5. Look at patterns for at least two other slits with different widths. Trace and label the different patterns on the screen. Describe

in words the differences and trends you observe.

B. Multiple Slits 1. Trace and label the patterns for at least three different multiple-slit separations. Describe in words the differences and trends

you observe. 2. Look at the overhead lights through at least 2 diffraction gratings. Describe what you see and any differences between the

images formed by the different gratings. 3. Replace the slide with at least two diffraction gratings. Sketch and label the patterns. Describe in words the trends and

differences you observe.

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V. APPENDICES Sample Pre-laboratory Questions

There are one or two questions that the students have to answer ahead of the exercise as a homework. This is an example how to write the pre-lab questions. Do not type it in the computer, do it by hand.

My Name ____________________

Date______________________

Simple Harmonic Motion Lab:

1. Define the following terms:

amplitude; period; equilibrium position

Amplitude is the distance from an equilibrium position to the maximum displacement of an object such as a swinging pendulum. It can also be found by finding the distance between the maximum and minimum wave displacements and dividing by 2.

Period is the amount of time it takes to complete one cycle of harmonic motion.

Equilibrium position is the position of a mass on a spring or of a pendulum mass where no movement happens when the system "runs down". This is where the weight force and tension force in the spring are equal.

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Sample Laboratory Report Energy Conservation Part II

Lab Partners: Zatanna Zatara, Hal Jordan, Arthur Curry, & Oliver Queen

Introduction

In this lab we will find the spring constant of the plunger spring in a metal cart, then calculate the spring potential energy and gravitational potential energy to see if energy is conserved. The physics we used was Hook’s Law, potential and mechanical energy.


Equipment: Dynamics cart, metal track, pulley and mass hanger, rulers and meter stick.

In Part A, a plunger (spring) was attached to the cart, which was attached to the end of the track. On the other side of the cart a string was attached in order to hang masses when this string was passed over a pulley with a hanger. The initial position of the cart was measured and then five different masses were hung. The cart moved to five different positions that were also measured as shown for one mass in the figure below.

In order to calculate the spring constant (k) we had to measure a Force and a displacement. The equation with k is : F = -k x.

This force was a weight force from masses hung on a mass hanger with the string run over the pulley. (The weight was calculated by multiplying the hanging mass times acceleration of gravity.) With five sets of points, a graph with Force on the y-axis and displacement on the x-axis was made. Then a “best fit” line was used through the data points to calculate the slope.

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In Part B of the experiment, the cart was pushed against the spring compressing it. The distance that the cart moved in order to fully compress the spring was measured in order to find the potential energy of the spring. To find the potential energy stored in a spring the equation PE = ½ k x2 was used. The next figure shows the compression.

In the last part of the experiment, the plunger was used as a launcher of the cart when it traveled a certain distance on the inclined track. The vertical distance traveled by the cart on the track was measured several times to find the final potential energy of the cart at the highest point. The initial vertical high of the cart on the track was also measured with the spring fully compressed. The initial and final potential energy can be obtained with PE = mc g h. The following figure explains how the cart traveled on the track.

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Results Data:

Part A, the following table shows the spring compressed with the hanging mass

Part B, spring fully compressed

Initial position (m): 0.015 Final position (m): 0.002

Change in position (spring compression in meters): 0.028 Part C, the table shows the cart traveling up the inclined track: Mass of the cart (Kg): 0.4998

Initial height of the cart (m): 0.050 Final height of the cart (m): 0.098

Trial number Final position along track (m)1 0.9032 0.9513 0.8984 0.9635 0.9546 0.9687 0.9808 0.9649 0.95810 0.94411 0.955Average final position 0.955

Trial Hanging mass Weight Force Initial Pos. Final Pos. Δ-Pos.(kg) =mg (N) (meters) (meters) (m)

1 .150 1.47 0.030 0.028 0.0022 .250 2.45 0.030 0.025 0.0053 .350 3.43 0.030 0.023 0.0074 .450 4.41 0.030 0.020 0.0105 .500 4.90 0.030 0.019 0.011

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Results Graph:

0.0160 0.002 0.004 0.006 0.008 0.01 0.012 0.014

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Calculations:

For Part A, the values of force and distance were plotted as seen in the previous figure. The slope of the best fit line was calculated as

with units of Newtons divided by meters. These are the units of k, the spring constant.

In Part B with the spring all the way in and locked, the displacement of the spring was 2.8 cm or 0.028 m. Then, the potential energy of the spring is

Then, for Part C the cart’s initial gravitational energy was

The average position the cart traveled up the track was to a final position of 95.5 cm. The height of the front of the cart at this position on the track was 9.8 cm or 0.098 m. The cart’s PE at this point was

The ME at the initial position was the sum of the spring PE and gravitational PEi

The MEf at the final position on the track was the same as the potential gravitational energy at the end, that is, MEf = PEf = mghf = 0.480 J. The cart gained 0.08 J of ME, with the average being ME = 0.4 J. The percent difference between initial and final ME is

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Conclusions

For Part A, the sources of error are due to the measurements for the the displacement which are of the order of millimeters. The significant figures come from the measurements in distance which were done using a meter stick. The smallest unit in this instrument is a millimeter. Therefore our significant figures were one after the decimal point for the value of k. As in the previous case, the errors in Part B are due to the measurements in distance when we calculate the compression of the spring. As in Part A, the amount of significant figures for the potential energy of the spring is just one.

For Part C, the percentage difference shows that the cart actually gained mechanical energy. The experiment should shows a loss in mechanical energy, but the amount of errors involved produced an increase in mechanical energy. The dispersion of the data for the cart going up hill on the track can be calculated using the percentage difference between the highest and lowest value which is

This percentage is lower than 15% which shows that our measurements were precise. But some error was introduced when we measured the height at the average of this distance, that is why our measurements are not accurate. The same happened when the initial height of the cart was measured. That is why our result is off from the expected loss of energy. The significant figures for the gravitational potential energy can be obtained by knowing that there are four significant figures after the decimal point in kg for the mass of the cart since our triple balance measures up to a tenth of a gram; and three significant figures after the decimal point in meters for the height of the cart on the track. Therefore, the significant figures for gravitational potential energy are three.

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Numbers and Scientific Notation Scientific Notation

In physics we run into both very large and very small numbers. Number can range from small values such as the mass of a proton (0.00000000000000000000000000667 kilograms) to the mass of the Sun (19,870,000,000,000,000,000,000,000,000 kilograms). To save paper and ink, write such big numbers in the form of scientific notation. The form of the numbers is:

1.234×10-56 where the first number is multiplied by ten to the power shown. [Practice this notation on the two numbers given above.] If the exponent (the power to which ten is raised) is negative, this indicates a number that is one divided by the power of ten. The power of ten is often called the order of magnitude of a number. On a calculator you can set the mode to scientific notation and the power of ten is usually entered as “EE” or “10x” for “enter exponent.” Thus:

102 = 10 × 10 = 100 10-2 = 1 ÷ 102 = 1 ÷ 100 = 0.01

5.45×106 = 5,450,000 5.45×10-6 = 5.45 ÷ 1,000,000 = 0.00000545

Generally only a single non-zero digit appears before decimal point, the power of ten can always be chosen to make this happen. To convert to “ordinary” numbers simply take the power to which ten is raised and move the decimal point backwards or forwards that many places. Your calculator probably knows how to use scientific notation but you should know yourself so you can have rough idea of the magnitude of the expected answer and notice if you push the wrong button.

To multiply numbers given in scientific notation, you add the exponents (powers) to which ten is raised and multiply the two numbers. Then the decimal point is moved and the power of ten changed until there is only a single digit in from of the decimal point. For example:

4.32×108 • 7.21×102 = 31.1472×1010 = 3.11472×1011 5.45×10-3 • 3.10×104 = 16.895×101 = 1.6895×102

(Note: Significant digits are not properly handled here: we discuss these later. Also your calculator may do much of this work for you.) Similarly to divide numbers, divide the two numbers and subtract the exponent of the denominator (the bottom number) from that of the numerator (the top number).

Adding and subtracting requires that both numbers have the same power of ten: 3.45×103 + 6.47×102 = (3.45 + 0.647)×103 = 4.097×103

3.45×103 – 4.28×106 = (0.00345 – 4.28)×106 = -4.27655×106 Note that for addition or subtraction, unless both exponents are roughly the same, only the larger number contributes significantly to the sum or difference.

213

2

10518.5105518.01044.41045.2 −− ×=×=×

×

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Mathematical Symbols

= ≠ ≈ ~ ∝ > ≥ >> < ≤ <<

is equal to not equal to approximately equal to on the order of is proportional to greater than greater than or equal to is much greater than is less than less than or eqaul to is much less than

Δx |x| ≅ ≡ lim Δt→0 Σ ∏ n! d/dx ∫

a change in x absolute value of x is almost equal to is defined as limit approaches sum product n*(n-1)*(n-2)*… derivative integral

Symbols

Units in the MKS System

Name Abbrev. Type Equivalent

Ampere Coulomb Farad Henry Joule Kelvin Kilogram Meter Newton Pascal Radians Seconds Tesla Volt Watt Ohm

A C F H J oK kg m N Pa Rad Sec T V W Ω

Electric Current Electric Charge Capacitance Inductance Energy Deg. of temperature Mass Length Force Pressure Angle Time Magnetic Field Electric Potential Power Electric Resistance

A=C/sec A⋅sec C/V J/A2 N⋅m = kg⋅m2/sec2

kg m kg⋅m/sec N/m2 Unit-less sec V⋅sec/m2 J/C J/sec = N⋅m/sec V/A

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Conversion Factors Between Different Systems of Units1 m = 39.37 inches = 3.281 feet = 1.094 yards

1 Ångstroms =1Å = 10-10m

1 km = 0.6215 miles

1 mile = 5280 feet = 1.609 km

1 light-year = 9.461×1015m

1 inch = 2.540 cm

1 liter (L) = 1000 cm3 = 10-3m3 = 1.057 quart

1 revolution = 2π radians = 360o

1 slug = 14.59 kg

1 atm = 101.3 kPa = 1.013 bar = 76.00 mmHg = 14.70 lb/in2

1 N = 105 dyne = 0.2248 lb

1 lb = 4.448N

1 J = 107erg = 0.7373 ft-lb = 9.869×10-3 L⋅atm

1 kWh = 3.6 MJ

1 cal = 4.184 J = 4.129×10-2 L⋅atm

1 Calorie = 1000 cal

1 eV = 1.602×10-19 J

1 Btu = 778 ft·lb = 252 cal = 1054 J

1 horsepower = 550 ft·lb/sec = 746 W

1 Tesla (T) = 104 Gauss

1 kilogram weighs 2.205 lb

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