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Laboratory ManualStevens High School

Physics

Currently in the Possession of:

Table of Contents:

General Guidelines

How to Write a Formal Laboratory Report……….……….3Laboratory Report Scoring Rubric……….……….4

How to Excel! ……….……….5How to Word! ……….……….9

Example Formal Report……….……….11

Lab Procedures:

Lab 1: The Speed of a Runner ……….……….13

Lab 2: Reaction Time ……….……….16Lab 3: Projectile Range ……….……….18

Lab 4: Inclined Plane ……….……….20Lab 5: Friction ……….……….22

Lab 6: Collisions ……….……….25Lab 7: Specific Heat ……….……….28

Lab 8: g ……….……….31Lab 9: Bungee Jump ……….……….34

Lab 10: Speed of Sound ……….……….36Lab 11: Simulated Circuits ……….……….39

Lab 12: Ohm’s Law – Part 1 ……….……….45Lab 13: Ohm’s Law – Part 2 ……….……….47

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How to Write a Formal Report(A guide for Physics students)

Understanding how to write a quality scientific report is very important because a great deal of scientific work’s value comes from communicating it to others. Over time, a general outline for formal laboratory reports has evolved, and will be the format we use most-often in this class. Here is a guide to this format.

Lab TitlePrimary Investigator: (your name here) Date: day/month/year or day-month-year

Secondary Investigators: (Lab SI’s). E.g., Jeff Whetzal, Sandy Richards, Tom Keck, Amy Weiers

Introduction: This should include the purpose of the laboratory and a brief statement of the approach to the problem and expected results.

Procedure and Materials: This section should allow a reader to reproduce the laboratory experiment without any additional information. Try to strike a balance between adding unnecessary detail and a procedure which lacks critical details. It may be listed numerically, bulleted, or written in a clear paragraph. Do NOT plagiarize the lab procedure.

Results: This section contains the observations/measurements from the laboratory. Note that all figures and tables should be labeled and a brief description should be included in the body of the report. For example, “Note that the velocity increases markedly after 2.3 seconds, as shown in Figure 1.”

Data Analysis: Here is where you can answer questions about the laboratory including results obtained via calculation using the raw data presented in the results section. The majority of your plots will be here.

Conclusions: This allows for a final interpretation of the data. Was the experiment successful? Did the experiment match expectations? Where were errors caused, and to what extent did they impact the lab. How could this lab be done differently to improve the results?

Style notes: Traditionally, scientific papers always avoided the use of first-person writing (e.g., “I turned the car on and then caught it before it fell off the table.”), in lieu of the third-person (e.g., “The car was switched on and caught before it fell off the table.”). However, some journals and editors prefer a bit of first-person voice, especially in the introduction and conclusions sections. Be judicious with your use of personal pronouns.

Typically, size 11 or 12 font, single-spaced is preferred. Make sure to label the sections of your report. A typical lab report will be 2-5 pages, depending on the number of figures and tables present.

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Physics Laboratory Report Scoring RubricAll physics lab reports are worth 35 points (or more if big lab), and I use this rubric when I grade. Use this form to self-correct any mistakes and maximize your score! Note: multiple mistakes can result in multiple deductions. If you score below a 28/35 on the on-time report you have three days to rewrite it for a max score of 28/35.

Appearance of your lab report: You receive an automatic 5 points for typing/printing your lab report.-2 Report is hand-written, but is legible, organized, and written in black ink.-5 Report is ILLEGIBLE (illegible). You will have two days to rewrite it for a maximum score of 31/36.

Heading: You should include your name first, then the first and last names of your partners, the date the lab was conducted, and the title of the laboratory (from the lab packet).

-1 Wrong title, name(s) or partner(s) missing, incorrect date.

Purpose: You must write the purpose of the laboratory in your own words, using full sentences in correct English – do not copy the lab packet, please.

-2 Purpose is missing or largely copied.

Procedure: Your procedure must be written so that someone could replicate the laboratory by reading your report. You’ll only be allowed to use the procedure you write up for lab day (this will be homework), so make sure that you write it carefully. Do not copy the lab packet verbatim, write out the procedure in your own words. Sometimes, you’ll omit steps from the lab packet, or an additional step will be necessary in class.

-1 Detail in procedure is missing (e.g., one step is missing).-4 Entire procedure is missing.

Data: You need to include a typed table of your data, labeled with correct units. -1 Data table is complete, but hand-written neatly in black ink, with straight lines.-2 Some portion of data is missing from table-6 Data table is missing

Calculations: In many of the lab reports, you’ll have to analyze your data to reach a conclusion. In such instances, you need to show the formula you use, as well as at least one sample calculation.

-1 Formula missing or minor calculation error-3 Calculations are not included.

Graphs: Many of the labs will also require graphs to express or interpret data and/or results. Your graphs should be made using a plotting program (e.g., Microsoft Excel or Open Office’s Spreadsheet) with labels.

-1 Graph is missing a title or axis labels (or other minor errors in the graph)-2 Graph is missing

Analysis/Summary Questions: Usually, you will be asked to answer a few questions regarding the interpretation of your results. Please answer these questions in complete sentences with some depth of reasoning (i.e., usually, a “yes” or “no” answer is not sufficient). No names or pronouns in scientific writing here.

Partial credit Lacks thoroughness in answer to question or answer is not consistent with resultsNo credit Question is not answered

Conclusion: This is one of the most important components of your laboratory report, and is one of the first parts read in scientific literature. Your conclusion needs to include a summary of the results, a statement about whether or not the purpose was achieved, and a discussion of sources of error in the experiment.

-1 Either the purpose or experimental accuracy is not addressed -1 lack evidence to back up claim

-3 Conclusion is missing or not relevant to lab.

Miscellaneous: Laboratory reports need to be written in proper scientific English. -1 Spelling or grammatical errors or errors in sentence structure.

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-1 Personal pronoun - max of -2 (e.g., I, we, they, our) use (except in personal conclusion)

How to Excel!(pun intended)

In Physics, actually in all of science, you must concisely communicate laboratory findings. Readers of technical documents often skip all of the hard work you’ve put into the text and go straight to the figures you’ve made. Then, if they are interested, they will read further. So, here’s a basic guide to creating a beautiful plot. I’ll use Excel here since many of you will have access to that program, but the same basic guidelines are fairly universal.

Let’s plot the following hypothetical data for the period of oscillation for a spring with a weight attached to one end (called a spring-mass system).

To make this table, I opened Excel, and entered the values for oscillation time and mass. To make the first row labels fill two lines, I highlighted those cells and clicked on ‘Wrap Text’. Be sure to include the units of your measurements in brackets, parentheses, or something similar.

To ensure that all data values had the same number of decimal points (for appearance and sometimes for significant figures), I highlighted the data and went to ‘Number’, clicked on ‘Number’ (again), and then set the decimal places to ‘2’.

Ok, now you want to plot this data. Well, when you do, you want to highlight the cells that represent the desired x-axis (here, mass), followed by the desired y-axis (here, oscillation time). If you make your tables so that the x-column is the first column, and the y-column is the second column, you can just highlight both of them all at once. I did this in the table above.

So, highlight your data (not the cells with labels), then click on ‘insert’, ‘charts, ‘X Y scatter’, and click on the cell that has dots without any connecting lines.

The result will be a plot-in-progress that looks like this figure to the left.

Believe it or not, people turn in plots like this with otherwise quality work! Well, it’s hard to know what’s going on; it needs labels on the x- and y-axes, and it needs a title.

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Mass [kg]

Oscillation Time [s]

0.10 0.530.20 0.730.25 0.790.40 1.010.50 1.120.65 1.270.70 1.390.75 1.410.80 1.470.90 1.581.00 1.63

To add axes labels, navigate to the upper left corner of your excel sheet, and locate two little buttons: Add Chart Element and Quick Layout. I have the best luck using ‘Add Chart Element’, but you might have success with ‘Quick Layout’ after a little practice.

So, click on ‘Add Chart Element’, then ‘Axes Titles’. You will have to select a ‘Primary Horizontal Axis Title’ and then go through the same process to select ‘Primary Vertical Axis Title’. I like to go with the option of ‘Rotated Title’ - It looks best.

Then, in the same tab click on ‘Chart Title’, and select ‘Above Chart’. In my class, I require chart titles, but some journals and other professors may not want them as long as the figure is labeled in a caption. Here’s what you have now.

This is getting there. Now, just click on the axes labels and chart title and fill them in. Make sure to include labels, and remember that charts are usually titled in a ‘y-axis vs x-axis’ format. You can also stretch the plot window in Excel just by clicking and dragging the edges, and I eliminated the ‘Series 1’ label which is unnecessary unless you have multiple lines on the same graph. Sometimes Excel doesn’t even include it. Here’s what you have below.

This is a fairly nice plot. Generally, I will ask that you also include a trend line with a best-fit equation. You can do it! It’s easy after you have done it a couple of times.

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Advanced Stuff:1. Adding a trendline: This is easy. Now, beware of the following caveat: it is important to linearize

your graphs whenever possible. Depending on your current mastery of physics, you may not realize that the oscillation period for a

spring-mass system is given by: T=2 π √ mk

.

This is not a linear equation. So, if we fit the data in the plot with a straight line as T vs. m, we’re making a mistake. Just right-click on the data points and select ‘Add Trendline’, scroll down and select ‘linear’, and then click on the two boxes that say ‘Display Equation’ and ‘Display R2’. You can drag the equation box around and resize the font so that it looks readable.

More Advanced Stuff:2. Linearizing! Generally, I will help suggest ways to linearize your data in the lab manual, but AP

students especially will have to look for necessary linearization and take care of them on their own. In this case, plotting the oscillation period squared versus mass (or, alternatively, the oscillation period versus square-root of mass) makes MUCH more sense because the result is a straight

line. E.g. T 2=4 π2

km. Here, I grouped the

‘k’ term with the 42 so that you can see this equation is just y = mx if you let y be T2

and x be m.

So, make a column for oscillation period squared, and plot it versus mass. Follow all of the other steps listed, and you get a plot like that shown on the next page.

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Now this is nice! Note that I also enlarged the axes labels a bit, and filled in the data points with white. You can experiment and make some really nice plots!

Also note how nice the R2 value is. This is a great fit, and from the equation of the best-fit line’s slope, we know that:

slope of line=4 π2

k

2.5813 [ s2

kg ]=4 π2

k

k= 4 π2

2.5813[ s2

kg ]

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Mass, m [kg]

Oscillation Period, T [s] T2 [s2]

0.10 0.51 0.2580.20 0.71 0.5000.25 0.81 0.6540.40 1.01 1.0190.50 1.17 1.3800.65 1.34 1.8070.70 1.40 1.9460.75 1.37 1.8740.80 1.42 2.0250.90 1.52 2.3221.00 1.60 2.564

k=15.3[ kgs2 ]∨[ N

m ]

You will impress your college professors with plots like this. The first couple of times you make one, it takes a while, but you’ll quickly get the hang of it. It’s easy after a few tries!

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Stevens High School Physics Laboratory Manual

How to WORD!(Written by Robert ‘Bob’ Julius)

In Physics and many of your other science classes, you will get the wonderful opportunity to write lab reports: both memo and formal reports. As the “How to Excel” document states, many of your superiors will skip most of the written work and go straight to the figures. This is most likely what many of you will end up doing with this document. Another element that is required in reports is the use of equations.

Equations in Microsoft Office Word can be very pleasing to the eye when done correctly; the problem is that many of the parts of the equation, subscripts, superscripts, Greek letters, degree symbols, etc., can be quite difficult to insert. This can cause students to take the easy route while leaving a mess for the grader to decipher. Let’s look at an example:

Many times, a student will use this as an equation:

Q = Q0+W0*t+0.5*a*t^2

This looks very unprofessional and is very hard to understand what you are talking about. A step up from this equation would be to start inserting Greek symbols instead of English letters. The result would be this:

ϴ=ϴ0+ω0t+1/2αt2

Now this looks much better, but it can still get even more appealing and professional by using the equation editor.

θ=θ❑0+ω0t +12

α t 2

Now that’s an equation!

Normally, to insert this equation, you would have to click INSERT, NEW EQUATION, then INSERT, SYMBOL, MORE SYMBOLS, and then search through the hundreds of symbols in the database for theta, lowercase omega, and lowercase alpha. After most of those variables, you would also need to click the subscript and superscripts buttons in the equation editor bar. FEAR NOT, PHYSICS STUDENTS!!!! There is a much easier way to insert these symbols.First we need a new equation. STOP! Don’t you dare click insert. Instead, all you must do is click “alt+(=)”. This will open a new equation. Now, we need a theta; yes, this can be taken from the symbols, but it is much easier to just use the shortcut, “\theta”. After pressing space, the symbol appears. This shortcut works for all Greek letters in equation editor! Subscripts and superscripts are also much easier to insert simply by using “_” for subscripts and “^” for superscripts. Fractions are made simple by using “/”.

Now that you know how to insert an equation in less than 10 seconds, maybe, you need to know how to insert variables. Luckily, Mr. Julius II found a great article online that he will now summarize for your benefit. For any Greek character in equation editor, just use the shortcut from before. To use them outside of equation editor, follow the table below:

Insert Equation Alt + =


Greek Letters Type the English letterHighlight that letterUse Ctrl + Shift + Q

Get back to English letters after using the Greek letter shortcut (Change Back to Original Font)

Ctrl + Space

For Greek letters, capital and lowercase letters in English translate to capital or lowercase in Greek

To Save a Document Ctrl + STo Bold Type Ctrl + BTo Underline Ctrl + UTo Insert a New Line in a table TAB (use while in the cell to the farthest right)To Type in Italics Ctrl + ITo Print Ctrl + PTo Create a Bulleted List Ctrl + Shift + LTo Change the FontQuite helpful when changing from Greek letters back to English

Ctrl + Shift + F

To Delete Whole Words to LEFT of Cursor Ctrl + BackspaceTo Delete Whole Words to RIGHT of Cursor Ctrl+ DeleteTo Spell/Grammar Check F7To Insert the Current Date Shift + Alt + DTo Insert the Current Time Shift + Alt + T Bigger Font Ctrl + Shift + >Smaller Font Ctrl + Shift + <Left Justify Ctrl + LCenter Justify Ctrl + ERight Justify Ctrl + RSuperscript Ctrl + Shift + (+)Subscript Ctrl + (=)

Here is a beautiful example of a formal laboratory report!


Refraction Laboratory ReportPrimary Investigator: Grace E. Hofmann Date: March 3rd, 2017Laboratory Partners: M. Holt, J. Oleson

Introduction: The purpose of this laboratory is to deduce the index of refraction of water and confirm the critical angle (for total internal reflection) for a transition between water and air.

Materials:• Clear, semicircular plastic dish with water• Laser pointer• Protractor• Paper and pencil

Procedure:1. Using paper and pencil, draw an outline around the clear, semicircular plastic dish and mark the center point

on the flat side of the dish.2. Fill the dish with water and set it back on the outline.3. Using the laser pointer, shine a laser beam through the center point on the flat side of the dish so that θa ~0o.

Mark (in a corresponding fashion) the laser pointer location and the angle at which the laser beam emerges on the curved side of the dish.

4. Shift the laser pointer approximately 5o then repeat steps 3 for 12+ data points (0 ≤ θa ≤ 90o).5. Using the laser pointer, shine a laser beam through the curved side of the dish toward the center point on the

flat side of the dish. Vary θw until the refracted beam has θa ~90o. Mark this angle and label it “CRITICAL ANGLE.”

6. Using the protractor, measure the angles (from ‘normal’ / 90o from horizontal) of all the marked points.

Results:

θa (o) θw (o) sin(θa) sin(θw)0 1 0 0.0174…5 4 0.0857… 0.0697…10 7 0.1736… 0.1218…15 10 0.2588… 0.1736…20 15 0.3420…. 0.2688…25 17 0.4226… 0.2923…30 21 0.50 0.3583…35 26 0.5735… 0.4383…40 28 0.6427… 0.4694…45 31 0.7071… 0.5150…50 35 0.7660… 0.5735…55 38 0.8191… 0.6156…60 40 0.8660… 0.6427…65 44 0.9063… 0.6946…

CRITICAL ANGLE (θc): 51o

Table 1: Raw data and calculated values for Refraction Laboratory.


Data Analysis:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.2

0.4

0.6

0.8

1f(x) = 1.34376193742814 x

sin(θa) vs. sin(θw)

sin(θw)

sin(

θa)

Graph 1: Calculated values for Refraction Laboratory.

na sin(θa) = nw sin(θw)na = 1.00 ∴ sin(θa) = nw sin(θw)nw = sin(θa) / sin(θw)nw = slope = 1.3438% error = (|a – t| / t) 100 = (|1.333 – 1.3438| / 1.3438) 100 = 0.80%

θc = sin-1 (na / nw) = sin-1 (1.00 / 1.3438) = 48.09o

% error = (|a – t| / t) 100 = (|48.09o – 51.00o| / 51.00o) 100 = 5.71%

Conclusion: Based on laboratory procedure and results, the index of refraction of water (nw) was deduced to be 1.3438 via ratios of sin(θa) and sin(θw) [see Graph 1]. This yielded a 0.80% error from the accepted index of refraction of water (nw) of 1.333 [see “Data Analysis”]. Secondly, the theoretical critical angle (for total internal reflection) for a transition between water and air was measured to be 51o. The calculated critical angle (for total internal reflection) for a transition between water was confirmed to be 48.09o which yielded a 5.71% error [see “Data Analysis”]. The minimal error that occurred in this laboratory resulted from the fickle nature of the laser beam; thus, allowing accurate, but not precise, results to be obtained.


Purpose: The purpose of this lab is to analyze the motion of running Homo sapiens using position- and velocity-time graphs.

Concept: Uniform motion is one of the most fundamental forms of movement encountered in physics. It implies constant speed, that is, that the same amount of distance is covered in successive time intervals. Accelerated motion, on the other hand, implies that the velocity of the object is changing in successive time intervals. In this laboratory, you will record a sprinter’s time to various positions and analyze the data to see if uniform or accelerated motion is occurring at different portions of a 100 m sprint.

Materials: Stop watch (phones are fine) Long measuring tape and set of marking flags (one per class) Suitable garb for being outdoors/ Skin protection for ~40 min of UV exposure. Paper and a writing implement

Procedure: 1. Determine who will serve as a runner for the class. It is ideal to have at least three people per class run.2. Mark a starting line and the following positions: 10 m (32’ 10”), 20 m (65’ 7”), 30 m (98’ 5”), 40 m (131’

3”), 50 m (164’ 1”), 60 m (196’ 10”), 70 m (229’ 8”), 80 m (262’ 6”), 90 m (295’ 3”), and 100 m (328’).3. Next, fan out, so that two people are standing at each marked location with their stop watches ready.

These are the timers. One person, the ‘starter’ should be standing next to the runner ready to start them with the wave of their arm and a shout of ‘Go’. Overall, we will need 22 people. If we have fewer, some positions will have to have one timer only. See Figure 1 below.

4. The runner should prepare at the starting line, and the timers should all prepare as well. 5. When timers are ready, raise one hand. The starter must wait for this signal before the run begins.6. Start your stopwatch the moment the starter waves their hand.7. Stop your stopwatch the moment the runner passes your position. Both timers at a given position need

to record their own times. This will allow us to average the times for better accuracy.8. Record your position, the runner’s name, and your stopwatch time (e.g. 40 m, Doctor Smith, 6.43 sec)9. Repeat steps 4-

8 for three runners, then copy every timer’s data using a table like that shown on the next page.

1 Uniform & Accelerated Motion:The Speed of a Runner


Data: Record your raw data in a data table. It should look something like the table below. Dr. Smith Mrs. Richards Mrs. Weiers Position

(m)Time (s) Time (s) Time (s)1 2 Avg. 1 2 Avg. 1 2 Avg.0 0 0 0

1.85 1.81 1.83 103.22 3.16 3.19 204.48 4.37 4.43 305.74 5.72 5.73 406.92 6.86 6.89 508.23 8.18 8.21 609.49 9.43 9.46 70

10.64 10.58 10.61 8011.83 11.75 11.79 9013.05 12.98 13.02 100

Table 1: Raw position versus time data for three runners.

Data Analysis: 1. Calculate the average time at each position for each runner as shown in Table 1 above. 2. Using Excel (See the ‘How to Excel’ Guide for help), plot position on the vertical axis versus time on the

horizontal axis for all three runners on the same plot. An example of just the ‘Dr. Smith’ data is illustrated below. Be sure to include linear trendlines with equation set to a y-intercept of zero.

3. Are there any portion of the run in which you observe uniform motion (see ‘concept’ section). What about accelerated motion? What aspects of the position vs. time plot tells you this? Be sure to answer these questions for all three runners.

4. Determine the overall average velocity for each runner by dividing their total displacement (100 m) by the average time. Express your answers in both meters per second and miles per hour. The Dr. Smith example above gives an average velocity of 7.68 m/s. Show your work.

5. Is the runner’s instantaneous velocity ever greater than their average velocity? Explain.


Figure 2: Position versus time plot.

Jensen Extension: Choose a runner. Neglecting stops for rest, food, calls of nature, etc., how long would it take them to

run from Rapid City to Denver? How long would it take them to run to the Sun if there was a bridge to it? Feel free to use the web to help you find the relevant distances, but cite your sources and show your calculations.


Purpose: The purpose of this lab is to determine the reaction times of your peers using kinematics. Concept: Human reaction times vary greatly among individuals for many reasons. Fundamentally, your reaction will be dependent on the time light takes to reach your eyes, the time it takes the nervous impulse to reach your brain, the time your brain takes to process the visual stimulus and send a signal to your muscles, and the time it takes for your muscles to contract. In this laboratory, you will measure how quickly you and your classmates can catch a falling object.

Materials: Ruler (at least 30 cm long) Paper and a writing implement

Procedure: Note: Individual ‘A’ is the person whose reaction time is being tested. Individual ‘B’ is the person doing the testing.

10. Have A face B with their thumb and forefinger open 1.0” as shown in Figure 1 below. 11. B should hold the ruler so that the bottom is even with the mid-point of the thumb and finger of A. 12. WITHOUT counting down (e.g., 1…2…3), B should drop the ruler and A should catch it immediately!13. Record the ruler measurement at the midpoint of the thumb/forefinger where A caught the ruler. 14. Repeat steps 1-4 seven times. Repeat any obvious outliers (e.g., if A isn’t looking when B drops the

ruler, etc.).15. Repeat steps 1-5 for all lab partners.

Figure 3: Sketch of the experimental setup showing proper gap. Note that the ruler is shown already falling.

Data: Record your raw data in a data table, then, throw out the lowest/highest values before averaging.

Name Reaction Measurement (cm)1 2 3 4 5 6 7 Avg.

A. Smith 4.5 4.7 1.2 8.4 7.3 5.7 8.9 6.1A. Ninja 1.3 2.1 0.8 2.4 1.6 1.4 0.9 1.5Some Guy 8.6 9.5 11.3 10.5 21.1 9.8 14.2 11.1

Table 2: Raw reaction time data (in terms of distance) for three people.

2 Reaction Time


Data Analysis: 6. Using kinematics, calculate the ‘reaction time’, tR, based on each of the average reaction measurements

in your table. Consider that the initial velocity of the ruler was zero (Voy = 0). Also take the thumb/forefinger to be yo = 0, and the bottom of the ruler is ‘y’ (be sure you use the proper sign). Show your work as you would in any other problem. Equation 1 will help.

y= y0+v0 yt +1

2ay t2 (Eq. 1)

7. Next, get the list of all reaction times for your classmates. Who had the best reaction time? Can you give any possible reasons for their quick time? How does it compare to your time?

Jensen Extension: First, measure the length of your arm and express it in meters. Consider your own reaction time as

measured in the lab. Neglecting the time that it takes light to reach your eyes (which is probably about 3 ns), and assuming that processing speed in your brain is instantaneous, how fast do the nervous system impulses travel from your eyes to your brain then hands? Express your answer in both meters per second and miles per hour.


Students: This will be a memo laboratory report. In this report, you will not include the typical procedure section or the purpose section. Instead, please write up your data analysis questions and include the plot. You should write up your results as you would if you were emailing it to a busy boss who need to know the highlights of your experiment, but is already familiar with physics. Use your ‘How to Write a Memo Lab Report’ handout.

Purpose: The purpose of this lab is to determine the launch angle that maximizes distance and to compare the range given by complimentary launch angles. Concept: When a projectile is launched at some angle from horizontal, it possesses two components of velocity, one horizontal and one vertical (see diagram). These components of velocity are independent! This means that gravity affects only the vertical component of velocity, and any kinematics equations we might apply cannot mix ‘x’ and ‘y’ variables. Time is the connection between ‘x’ and ‘y’ variables. At shallow angles, the horizontal component of velocity is much larger than the vertical component. At steep angles, the opposite is true. In this lab, you are to plot the range of a projectile launched at a fixed speed across level ground to determine which angle maximizes the range and whether complimentary angles (e.g., 30o and 60o) yield identical ranges.

Figure 4: Illustration of horizontal and vertical components of velocity and their dependence on angle, .

3 Projectile Range


Figure 2: Sketch of the experimental setup showing projectile launcher and a hypothetical launch.

Materials: Projectile launcher and projectile Meter stick Paper and a writing implement

Procedure:

16. Set your projectile launcher, and test fire it a few times to ensure that you have adequate space to test the range at a variety of launch angles.

a. Ensure that you have two desks, one that the launcher is mounted to, and another for the projectile to land on.

17. Next, make a table like that in the data section below. 18. Fire the projectile launcher two or three times at each angle, and calculate the average distance the

projectile travels BEFORE BOUNCING! 19. Repeat for at least 4 sets of complimentary angles (remember, complimentary angles add up to 90o).

Note that I have included some in the table, but you are free to choose your own. 20. Be sure to include one set of trials at 45o as well.

Data: Record your raw data in a data table, then, throw out the lowest/highest values before averaging.

(o)Range measurements (m)

1 2 3 Avg.10 20 30 40 45 50 60 70 80

Table 3: Projectile range data.

Data Analysis: 8. Plot the average projectile range versus angle. Describe the curve in a few sentences. 9. Based on your data, what angle appears to give the greatest range? 10. Does the hypothesis that complimentary angles give the same range hold up in your experiment?11. Give a detailed explanation for one reason why the angle which maximizes range may not be 45o in this

experiment.

Jensen Extension:1. If not for drag, one could, in theory, fire a projectile fast enough that it would circle the Earth and return

to the starting point! In fact, we do this all the time for spacecraft in orbit. So, how fast would you have to shoot something horizontally for it to fall 7.98 inches for every 1.00 miles travelled horizontally? Note: These numbers are accurate for the curvature of the Earth, and a typical orbital velocity is 7.8 to 8.0 km/s near the surface.


Students: This will be an in-class report. You will turn in the plot I ask for at the end of class, or you may bring it the next day.

Purpose: Your objective is to plot the component of the gravitational force acting parallel to an inclined plane as a function of the angle the inclined plane makes with horizontal.

Concept: On an inclined plane, it is often convenient to ‘decompose’ the force of gravity, the weight (Fg), vector into two components: one parallel to the surface of the inclined plane, F ∥=Fg sin θ and one perpendicular to the surface of the inclined plane, F⊥=Fg cosθ.

Figure 5: Illustration of parallel and perpendicular components of weight on an inclined plane.

Materials: A cart, with a mass you can determine. A spring scale capable of reading up to 10.0 N. A book, or something else smooth that the cart can sit on. A protractor (or the inclinometer on your phones – it’s more accurate, and the apps are free)

Procedure:

1) Determine the mass (m) of your cart (in kg). 2) Next, determine the weight of the cart (Fg = mg) (in Newtons). Is your scale calibrated (does it read

exactly zero when nothing is attached to it)?3) Using a book or another smooth surface, come up with a method for precisely measuring the angle that

the surface makes with horizontal. This will be critical to your success. I recommend your phone.4) Set the inclined plane angle to 5o, and measure the weight of the cart parallel to the surface of the

plane. Be sure to hold the spring scale PARALLEL to the inclined plane. Not doing so will greatly impact your error.

5) Record this force, along with the angle. 6) Repeat for every 5o increment, up to 90o.

4 Inclined Plane


7) On a sheet of paper, carefully draw axes for force versus angle. Plot the component of the weight parallel to the ramp as a function of the angle, . Your y-axis should be in Newtons, and the x-axis should be in degrees. Note that I have included a hypothetical plot on the next page.

8) Give a few-sentence explanation of the results you see in the graph.


Students: This will be a formal report. It will be due in approximately 1 week (Dr. Smith will give you the exact details). Refer to your ‘How to Write a Formal Report’ for guidance.

Purpose: The purpose of this laboratory is to provide students with the opportunity to investigate friction between various materials and to determine coefficients of friction for wood, Teflon, and rubber on an anodized aluminum ramp.

Concept: Ah, friction. The bane of all moving objects (to varying degrees – deep space is relatively free from friction, though it is still present). Typically, friction is the term used to describe a motion-resisting force which arises between two solid objects sliding past one another, but it may be extended to include drag in fluids/gases (a property known as viscosity). Friction reduces the efficiency of power-generation turbines and vehicles, unfortunately slows you down on the ski hill, fortunately stops your car when you hit the brakes, causes your hands to warm when you rub them together, allows you to walk uphill on a smooth floor, or start a fire with a stick…et cetera. Many people are familiar with friction, but do not understand how it works. It may be difficult to slide two rough surfaces past each other because they actually become mechanically stuck as small ridges grind against others. However, even on two atomically smooth (very smooth, indeed) surfaces, friction exists. Friction is due to electromagnetic forces between atoms in the two objects being slid past each other. Essentially, friction between solid objects is due to weak bonding between the objects in contact. An object placed on an inclined plane may or may not slide. If the angle between the inclined plane and horizontal (, see Figure 1) is small enough, the object will not slide, but eventually, as the angle increases, the object will start to slide. Take a look at the free-body diagram in Figure 1 showing a block on an inclined plane. Note that there are three forces acting on the block. The first is gravity, Fg (i.e., the object’s weight). The second is the normal force, FN, that is keeping the block from falling into the ramp. Finally, friction, Ff, is keeping the block from sliding down the ramp (note, friction opposes motion). As we have seen, it is helpful to decompose the object’s weight into two forces, one that acts down the ramp, F∥=Fg sin θ, and another that acts perpendicularly into the ramp, F⊥=Fg cosθ. Taken together, these two forces represent the weight of the object; they are the vector components of the weight.

On an inclined plane, it is often convenient to ‘decompose’ the force of gravity, the weight (Fg), vector into two components: one parallel to the surface of the inclined plane, F∥=Fg sin θ and one perpendicular to the surface of the inclined plane, F⊥=Fg cosθ.

5 Friction


Figure 6: Free-body diagram of an object on an inclined plane. Inset shows Fg decomposition.

Once the object starts to slide, if it slides at a constant speed (no acceleration), Newton’s 2nd Law tells us that there is no net force on the object. This is true both along the inclined plane and into the inclined plane (an odd concept, for sure). For the sliding object, F f =μk FN , where μk is the coefficient of kinetic (i.e., sliding) friction. Note that this coefficient is independent of the object’s mass or surface area. By balancing the forces, we find:

Perpendicular direction:F⊥−FN=0

mg cosθ−FN=0FN=mg cosθ

Parallel direction: F ¿∨¿−Ff =0¿

mg sin θ−μk FN=0mg sin θ−μk (mg cosθ )=0

μk=sin θ

cosθ =tanθ

(1)

Equation (1) shows us that we have an incredibly simple way to find the coefficient of kinetic friction for an object. We merely find the angle at which is slides at constant speed, and then take the tangent of that angle!

Materials: Adjustable Inclined Plane Wooden Block (bare side and Teflon side) Rubber Block Lightweight String Spring Scale Protractor (or the inclinometer on your phones – it’s more accurate, and the apps are free) Triple-beam balance

Procedure: 1. Measure each object’s mass (in kilograms) and record it in the data table.2. Calculate the weight of the object (Fg = mg, in Newtons)3. Attach the string to the object and tie the string to the spring scale.4. With the inclined plane set at 0o (horizontal, flat), pull the object across the inclined plane using the

spring scale. Do this in a very controlled fashion, keeping the velocity constant and the string parallel to the surface. Record the force.

5. Repeat step 4 three times (filling the required entries in the table under the sliding friction heading).6. Remove the scale from the object and place the object on the end of the inclined plane.


7. Begin raising the plane very slowly until the object spontaneously starts to slide. Repeat this experiment 3 times, and record the inclined plane angle in the kinetic friction column.

8. Repeat steps 2-7 with all three objects.9. Then, tip the rubber block on its side and note if the sliding angle changes. It likely won’t significantly.

Data: Record your raw data in a table resembling Table 1.

Object Bare Wooden Block Teflon Block Rubber BlockMass (kg)

Weight (N)

Force of Kinetic Friction (N)

1 2 3 Avg 1 2 3 Avg 1 2 3 Avg

Kinetic Friction Angle (o)

1 2 3 Avg 1 2 3 Avg 1 2 3 Avg

Table 4: Raw data from the friction lab.

Data Analysis:1. Calculate the coefficient of kinetic friction (k) for each of the objects using the average kinetic friction

angle and equation 1 (see previous page). Make sure your calculator is set in degree mode.2. Next, calculate the coefficient of kinetic friction again, but this time by using the average force of sliding

kinetic friction and the weight of the object. Remember Fg = mg, FN = Fg for the flat surface, and F f =μk FN .

3. Calculate the percent difference between the two values of k for each object. How do the two calculated values of k compare for each object?

Jensen Extension(s):1. Use the web or another resource to explain why teflon has such a low coefficient of friction. Make sure

your response includes the chemical formula (e.g., C6H12O6 for glucose) of Teflon. Include your reference. http:// www.library.cornell.edu/node/148 has great tips for citing sources.

2. A brick is placed on an inclined plane with the largest face touching the plane. The plane is tilted, and the brick slides at an angle 1. Now, the brick is tipped onto its long, narrow face and the experiment is repeated causing the brick to slide at an angle 2. Is 1 > 2? Why or why not?

http://www.library.cornell.edu/node/148

http://www.library.cornell.edu/node/148



Purpose: The purpose of this laboratory is to investigate perfectly inelastic collisions between two massive objects on a nearly frictionless air track.

Concept: One of the most powerful tools in Physics is conservation of momentum:

Δ p⃑=0(1 )

For a system of two objects, 1, and 2, we can expand Equation (1) in a very useful way:

p−p0=0

m1V 1+m2V 2−m1V 01−m2 V 02=0(2 )

where the subscript ‘0’ indicates an initial quantity (before the collision).

In a perfectly inelastic collision, the two objects stick together after the impact, as we have discussed in class. In this case, we may simplify Equation (2) by noting that the final velocities of objects 1 and 2 are equal (V = V1 = V2):

m1V +m2 V−m1V 01−m2V 02=0

or

V=m1V 01+m2 V 02

m1+m2

(3 )

A great deal of energy is transformed in perfectly inelastic collisions. It is transformed from kinetic energy to other forms such as strain energy (deformation), heat (thermal energy), sound, etc.

Materials: Air track, setup as shown in Figure 1 Air pump 2 air track carts or ‘gliders’ Timer and two photogates Paper and a writing implement

6 Collisions


Figure 7: Experimental setup for air track collisions.

Procedure: ---------------------------------------------------setup-------------------------------------------------

21. Make a data table to record speeds before and after each collision, the mass of each cart, etc. 22. Ensure that the air track is extremely level to reduce errors. This is done by setting an air cart on the

track and turning it on. It should remain stationary. If not, gently adjust the feet of the track until it is perfectly level.

23. Attach Velcro to one side of each glider so that the two can stick when the collide.24. Attach an elastic ring bumper to each end of the track using the screws. 25. Place the two photogate timers roughly 40 cm apart from each other near the center of the track. 26. Attach a ‘U-flag’ to the top of one glider (this will be cart 2), and measure the width between the tabs on

the U-flag. Make sure the timer selector matches this spacing.

-----------------------------------------------EXPERIMENT-------------------------------------------27. Use the triple-beam balance to measure the mass of each cart and record it in your data table.28. Set one cart in between the two photogates, and the other near the far end of the air track, before the

first photogate. 29. Turn on the timer and allow it to cycle through all of its options. It should flash through red LED

indicators repeatedly.30. Set the timer to “Interval” mode. 31. Turn on the air track, but hold on to both gliders. Wait until the air track reaches full speed.32. Gently push cart 2 from near the far end of the track towards cart 1 sitting stationary between the two

photogates (it may be helpful to have a lab partner hold it until just before the collision). Make sure to let go of the gliders before either passes through the photogate, and keep the speeds VERY low!

33. Allow the collision to take place, then stop the two connected gliders before they bounce back through a photogate!

34. Turn off the air pump.


35. Press “Stop” on the timer. Next, press “Stop” again. It will give you speeds. Write all speeds down, being mindful of units. The first speed is the speed of cart 2 as it passed through the first photogate. The second speed is the speed as it passed through the second photogate.

36. Move the gliders back to the start position. 37. Repeat steps 9-15 three times.38. Add weight cart 1, record its new mass, and repeat steps 9-16.39. Repeat step 17.

Data: Record your raw data in a table resembling Table 1.

Trial 1

Cart 1 Mass (kg):

Cart 2 Mass (kg):

Trial 2

Cart 1 Mass (kg):

Cart 2 Mass (kg):

Trial 3

Cart 1 Mass (kg):

Cart 2 Mass (kg):

Initial Speed (cm/s)

Final Speed (cm/s)


Final Speed (cm/s)


Final Speed (cm/s)

Table 5: Raw data from the friction lab.

Data Analysis:4. Using Equation (3), the measured masses, and the initial speed for a given experiment, calculate the

expected final speed. You should have three values for each trial.5. How does your expected final speed compare to the experimentally-measured final speed for each

experiment? You should have nine comparisons here. Show the percent error for each.

Jensen Extension:3. In the distant past, it is believed that a Mars-sized (mM=6.4 ×1023 kg) object impacted the early Earth (

mE=5.37 ×1024 kg, before impact), closing in on it at 120 m/s. Assuming that the two objects stuck together after the impact, how much did the Earth speed up as a result of the collision? You may assume that the Earth was initially at rest and the Mars-sized impactor moves toward it at 120 m/s before the collision.



Purpose: The purposes of this laboratory are to measure the heat transfer between two materials using a calorimeter and to measure the specific heat of a metal using thermal equilibrium principles.

Concept: Each material responds to being heated differently. Some materials have many ways to absorb heat (vibrations, rotations, etc.) and thus have a large specific heat. At the deepest level, this is due to quantum mechanics. Atoms and molecules can rotate and spin like a propeller or figure skater, can vibrate like guitar strings, can be electronically excited, etc. This ability to store thermal energy is characterized by the specific heat, usually denoted ‘C’, of a substance.

We measure specific heat in terms of the amount of energy [J] required to change the temperature of 1.0 kg of a substance by 1.0 oC or 1.0 K.

A calorimeter is an insulated device, in this case a coffee cup, that allows measurement of specific heat by preventing heat loss to the environment. In this lab, a hot piece of metal (m) will be placed in a room-temperature water (w) bath. In the insulated calorimeter, we can say that energy is conserved. Neglecting any kinetic or gravitational potential energy:

Q=0.(1 )

Since there are two substances, this expands to include the metal and water:

Qm+Qw=0.(2 )

Since neither the water nor the metal undergo a phase change during this experiment, we can say that each heat term expands ed to include the mass of the material, the specific heat, and the change in temperature of each substance:

mm Cm ΔT m+mw Cw ΔT w=0.(3 )

You will heat a metal sample with a known mass to a known temperature, and then place it into a known mass of water at a known temperature. After a couple of minutes, the two materials will come to equilibrium, and the final temperature will be measured. The specific heat of the metal sample is found by algebraically rearranging equation (3) to solve for Cm:

Cm=−mwCW ΔT w

mm ΔT m

(4 )

7 Specific Heat


Note: The specific heat of water is Cw = 4180 J/kgK.

Materials: Calorimeter (Insulated cup with lid) Digital Thermometer Metal Sample Scale

The entire class will share:

Hot Plate Boiling Water Bath Room-temperature Water Bath Small Beaker (for adding Room-temperature water to cups)

Procedure: 10. Use the balance to measure the weight of the empty cup (and lid), and record your measurement in the

table below as mcup. Be sure to measure in kg!11. Add just enough room-temperature water to eventually cover a metal sample.12. Reweigh the cup with the water, and deduct the mass of the empty cup. Record the mass of the water

in your table as mwater. 13. Use the thermometer to measure the temperature of the room-temperature water. Typical values are

around 20 oC. This is T0,water. 14. Now, one person from your group should take the cup of water over to the how water bath and quickly

transfer a metal sample into the cup. Place the lid on the cup quickly, then insert the thermometer.15. Another person from your group should record the temperature of the water bath. This is the initial

metal sample temperature, T0, metal.16. The temperature will change quickly, and you should gently swirl the cup to ensure that the metal

sample transfers its thermal energy to the water uniformly. Record the highest temperature you measure in the water bath before it starts to cool back down. This is the final temperature, T. Be careful not to let the thermometer touch the metal sample as this will give a spurious reading.

17. Now, weigh the cup with the water and metal sample. Deduct the mass of the water and cup to obtain the metal sample mass (mmetal), and record this in your table.

18. Finally, check the metal sample to determine its identity, and add it to your table.

Data: Record your raw data in a table resembling Table 1 on the next page.

T0, water (oC) T0, metal (oC) T (oC) mcup (kg) mwater (kg) mmetal(kg) Identity

Table 6: Raw data from the specific heat lab.


Figure 8: Diagram of the experimental boiling water bath. The calorimeter used by individual groups is not shown.

Data Analysis:6. Using equation (4), calculate the specific heat of your metal sample. Be careful of your signs, and

remember that DT always means ‘final’ temperature minus ‘initial’ temperature. 7. Using the internet, look up the expected specific heat for your metal sample. Note, many times values

given online will be in different units like J/gK or J/goC. You may have to do a conversion to get the same units as you measured in this lab (J/kgK or J/kgoC).

8. Calculate the percent error in your own measurement using equation (5).

% Error= Experimental−TheoreticalTheoretical

(5 )

Here, the theoretical value is the one you look up.

Jensen Extension(s):Do a bit of research. Give at least three examples of substance with a high specific heat (e.g., C > 2000 J/kgK). Does any substance have a higher specific heat than water? State your sources, please.



Purpose: The purposes of this laboratory are to measure the acceleration due to gravity and to observe the factors that affect the period of a pendulum.

Concept: A pendulum’s period, Tp, depends only on the apparent acceleration (usually just gravity, g) and the length of the pendulum, L. It does not depend on the azimuthal angle from equilibrium nor the mass hanging from the end of it, at least theoretically:

T p=2 π √ Lg

.

(1 )

In this laboratory, you will be determining the acceleration due to gravity using a plot, but it is helpful to linearize and rearrange equation (1):

T p2=4 π2 L

g,

¿

L=g( T p2

4 π2 ) .

(2)

Materials: Ring stand and attachments String 100 g or 200 g mass Meterstick Writing substrate and implement

Procedure: 19. Setup your experiment as shown in Figure 1 below. Be careful not to let the ring stand tip over!20. Measure the length, L. Measure to the center of mass of the weight! Measure in METERS.21. Pull the mass back slightly (10o is plenty) while a group member readies a stop watch. 22. Start the stop watch and release the mass at the same instant. Time 20 oscillations of the mass.

Remember, full oscillations return the mass to the release point!a. Divide your answer by 20 and record it in the table as the pendulum period, Tp.

23. Record your data in a table like that shown below.24. Repeat steps 2-5 for lengths varying from almost brushing the floor to as high as you can still accurately

measure the period. I expect at least 10 data points.

8 g


25. Next, hang a different mass from the string, and readjust it to match one of your longer pre-recorded lengths. Note the time required for 20 oscillations.

Figure 9: Diagram of the experimental setup.

Mass, m (kg) Period, Tp (s) T p2

4 π2 (s2)Length, L (m)

Table 7: Raw data from the pendulum period lab.

Data Analysis:

1. Fill in the third column of your data table, T p

2

4 π2 .

2. Plot length, L, on the vertical axis versus the T p

2

4 π2 value. Refer to your ‘How to Excel’ for guidance. The

result should look reasonably linear.

This row is for the alternate

mass


3. Add a best fit line and equation to your graph. Don’t forget axis labels and a title. Figure 2 gives you an idea of what I expect. Take your time and be professional.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.2

0.4

0.6

0.8

1

1.2

1.4

f(x) = 9.94071078026301 x − 0.00089351636743995R² = 0.990831597626136

Pendulum Length , L, versus Tp2/4p2

Tp2/4p2 (s2)

Leng

th, L

(m)

Figure 10: Plot of pendulum length versus scaled period squared.

Jensen Extension(s):Let’s say you have a pendulum that has a period of 1.0 seconds while you are standing still. If you take

this pendulum into an elevator, describe how the pendulum period will vary while the elevator moves from the ground floor up to the top floor. Specifically, how does the pendulum period compare to 1.0 seconds while the elevator is accelerating moving upwards, is moving at constant speed, then is decelerating to a stop at the top floor.


Students: This will be an in-class report.

Purpose: The purpose of this laboratory is to experimentally determine the spring constant for rubber bands and then to use this information to predict the correct number to use to allow an action figure to bungee jump to within 3.0 cm of the ground (without hitting it).

Concept: Springs are characterized by their resistance to being stretched or compressed. Each spring has a particular ‘spring constant’, k [N/m], which is the ratio of the spring force to the displacement from equilibrium (the point there the spring is neither stretched nor compressed:

|F⃑ s|=k|⃑x|(1 )

Theoretically, a perfect spring will follow the relationship implied by equation (1) indefinitely, but in reality a spring will eventually stretch to the point of being very stiff before finally breaking. Connecting multiple springs in series lowers the effective spring constant because they each have to stretch a smaller amount for a given overall displacement.

Materials: Action Figure (medium sized) Ring Stand with horizontal beam Mass Set Meterstick Triple Beam Balance Rubber Bands Jumping Platform (1 per class)

Procedure: 1. Hang a single rubber band over the ring stand, then measure its unstretched length.2. Add a small mass to the rubber band, and measure the stretched length of the band. Calculate the

resulting displacement of the band, and enter it in the table below. See Figure 1 ‘Testing Spring Constant’ above for guidance.

3. Use your measurements to estimate the spring constant for a single rubber band.4. Connect two rubber bands, and repeat steps 1-3. 5. Continue adding bands until you have sufficient information to predict the spring constant and

unstretched length for any number of bands.6. Mass your action figure and enter this information in the table.7. Using your data, estimate the number of rubber bands you should attach to an action figure so that,

when dropped from a height of approximately 2.0 m above the floor (you may measure the apparatus), they will just barely miss the floor. The goal is to come within 3.0 cm without hitting. See Figure 1 ‘Bungee Jump!!’ for guidance.

9 Bungee Jump


Figure 11: Schematic of laboratory setup for testing the spring constant of rubber bands (left panel) and the bungee jump (right panel). Note that cephalopod is not assured.

Number of Bands

Unstretched Length [m]

Stretched Length [m]

Displacement [m]

Hanging Mass [kg]

Spring Constant [N/m]

Table 8: Raw data for spring constants of rubber band combinations.

Data Analysis:1. Were you successful? Describe the results of the bungee jump.

2. If so, what factors do you attribute to your success?

3. If not, what factors did you fail to account for sufficiently?


Students: This will be an in-class report. You will be expected to do the calculations prior to the lab as a homework assignment. If you do not have your calculations at the beginning of class on the day of the lab, you will have to make up the lab at 7:30 am the next day.

Purpose: The purpose of this laboratory is to experimentally determine the speed of sound.

Concept: The speed of sound varies depending on the material the pressure wave is travelling through. Sound is a longitudinal wave, and is transmitted by molecules or atoms bumping into one another (the absence of such matter is the reason why sound does not travel through space – at least in the most basic sense). Very roughly speaking, denser, more tightly-bonded materials have higher speeds of sound, but there are many other factors that play a role (e.g., molecular weight for gases). The speed of sound also varies with temperature, especially in a gas due to the higher velocity of the particles at higher temperatures.

Pre-lab:1. Using fn = nv/(4L) where n = 1, 3, 5, 7, … calculate the length (L) of a closed tube needed to produce

the first few harmonics for the tuning fork frequencies on the next page. Use the tuning fork frequency as the resonant frequency, f1, and vary the value of ‘n’ to find different resonant lengths. Assume the speed of sound (v) is 343 m/s.

2. Discard any length values exceeding 50 cm. Record the remaining values in the ‘expected closed pipe lengths’ row of your data table (see next page). Note: one calculation has been done for the 1000 Hz tuning fork. Check your work.

3. The speed of sound is not likely to match the 343 m/s value you used in your calculations during the laboratory. If the speed of sound were to increase, would you expect the length of the tube at each harmonic to increase or decrease? Why?

4. Bring your answers to class.

Materials: Graduated cylinder Dihydrogen monoxide Glass tube Tuning forks Meter stick Rubber block

Procedure: 8. PLEASE! DO NOT HIT THE TUNING FORK AGAINST ANYTHING OTHER THAN THE PROVIDED GREEN

RUBBER BLOCK. DOING SO CAN ALTER THE TUNING FORK’S FREQUENCY. purposes of this laboratory are to measure the acceleration due to gravity and to observe the factors that affect the period of a pendulum.

9. Ensure that you have completed your pre-lab. Failure is imminent if you have not…10. Select a laboratory station, and ensure that it is properly set up by placing the 2.5 cm wide glass tube

into the tall 1-L graduated cylinder and then filling the cylinder with water to nearly the top. Leave

10 Speed of Sound

“Hi. I am a tuning fork. Hitting me against anything beside the provided green rubber block will cause plastic deformation and alter my resonant frequency. This is bad.”


approximately 0.5 cm of air space between the top of the water column and the top of the graduated cylinder.

11. In your data table, record the frequency of the tuning fork at your lab station. The frequency is printed on the fork.

12. Have one group member strike the tuning fork against the green rubber block and hold the ringing tuning fork over the open end of the glass tube.

13. Raise the tube upwards, while holding the tuning fork above it, until you hear a marked increase in the volume of the tuning fork. You may have to restrike the tuning fork every 10-20 seconds to ensure it is still ringing. This should occur when the tube is out of the water by roughly the amount you calculated in the pre-lab.

14. Move the tube up and down slightly until you locate the position where the sound is loudest. 15. Once you have located the loudest point, confirm it by restriking the tuning fork and holding it over the

tube while moving the tube slightly up and down to ensure you have located the maximum resonance. Then have a group member precisely measure the distance from the top of the water to the top of the open glass tube (near the tuning fork). Record this in your data table.

16. Next, raise the glass tube further. Note any other positions where you get an amplification of sound.17. Repeat the experiment at least once to recheck your numbers.18. Move to additional stations and repeat steps 4-11 for two additional frequencies.

Table 9: Data table for Speed of Sound Lab. Fill in shaded portions before the day of the lab.


Data Analysis:4. Calculate the speed of sound given the information in your data table (see a highly-trained physics

teacher if you have questions). Note that the value of ‘n’ is unknown, but if you conducted the experiment carefully, the smallest tube length should be n = 1, the next is n = 3, and so on.

5. Compute your overall average speed of sound using each of your data points. How does this value compare to the expected 343 m/s value?

Average Speed of Sound: ____________________________

6. Discuss at least two reasons why your measured speed of sound did not match the expected speed of sound.

i.

ii.

Jensen Extension(s):The speed of sound tends to increase with temperature because the speed of the air molecules

increases (so they collide more often and can send information more rapidly). How would the speed of sound in a room full of very light-weight hydrogen gas compare to the values you measured in this lab? Assume that the temperature is exactly the same, but think about what that means with regard to kinetic energy and the speed of the light-weight hydrogen. Explain your reasoning


Students: This will be an in-class report. I expect that you will fill in the blank sections with neat work, and I will check it on the next class day. You will be called to the board to present your solutions.

Purpose: The purpose of this lab is to give you some experience with constructing circuits and measuring current (amperage) and electric potential difference (voltage) before working with actual electrical components in follow-up labs. Concept: Electricity, as the term is commonly used, refers to the phenomena associated with the motion of charged particles. Moving charged particles produce an electric current, I [A], and they lose energy as they move through elements of an electric circuit. The degree to which an element of a circuit (a wire, battery, bulb, etc) impedes the flow of current is referred to as the resistance, R []. In electric circuits, energy is measured in volts, which is actually energy per charge [1 V = 1 J/C]. Ohm’s Law gives the relationship between these quantities:

I= ΔVR

(1 )

The basic laws of conservation of charge and energy still apply to electric circuits, and they form very useful tools for analyzing them. For instance, in a series circuit like that shown below, the current through each resistor is the same (no electrons are lost!).

Figure 12: Series arrangement of resistors

In a series circuit, electrons are forced to go through one resistor after another, giving an effective resistance that is the sum of the individual resistances:

Req=R1+R2+…+Rn

or

Req=∑i=1

n

Ri

(2 )

In contrast, in a parallel circuit like that shown below, multiple paths for electrons are available, so the current in each branch is not necessarily the same, but it adds up to the total. In parallel, the potential difference is the same across every branch. This is necessary so that any complete path through an electric circuit gives a net

11

Simulated Circuits


potential difference of zero (energy is conserved). The electrons flow through all paths simultaneously (with the magnitude of each current given by equation (1) above), and the resistance is added as reciprocals:

Figure 13:Parallel arrangement of resistors

1R eq

= 1R1

+ 1R2

+…+ 1Rn

or

Req=(∑i=1

n

Ri)−1

(3 )

You will be investigating the properties of both of these circuits as well as a combination circuit in this lab.

Materials: Computer with connection to the internet Paper and writing implement Calculator

Procedure: 40. Navigate to the Phet simulation: Circuit Construction Kit (DC only). You’ll find it here:

https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc

Series:41. Now, build a series circuit with two light bulbs by dragging circuit elements onto the layout area. The

schematic for what I would like you to build is below along with a screen shot of the simulation in the data section.

42. You can vary the values of each element of your circuit by right-clicking on it. Set the following parameters:

a. Bulb 1: resistance = 10 .b. Bulb 2: resistance = 20 .c. Battery: voltage = up to you! I recommend at least 20 V so that you can see the light bulb

brightnesses. 43. Record your measurements in the data section of this report below. To measure voltage, you will need

to drag a voltmeter onto your work space and place the leads across each bulb, one at a time. Don’t worry about any negative signs – they are merely telling you that the red lead of the voltmeter is at a lower electric potential than the black lead.

https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc


Parallel:44. Now, build a parallel circuit with two light bulbs by dragging circuit elements onto the layout area. The

schematic for what I would like you to build is below in the data section.45. You can vary the values of each element of your circuit by right-clicking on it. Set the following

parameters:a. Bulb 1: resistance = 10 .b. Bulb 2: resistance = 20 .c. Battery: voltage = up to you! I recommend at least 20 V so that you can see the light bulb

brightnesses. 46. Record your measurements in the data section of this report below.

Combination:47. Now, build the circuit with 4 bulbs as shown in the schematic below. You should set the resistances as I

have indicated, but may pick whatever voltage you would like for the battery, then complete the measurements in the data section below.

Data: Record your measurements and observations in the spaces provided on the following pages.


Series

Figure 3a: Schematic of series circuit for the laboratory.

Data:Potential Difference

(V, volts)Current (I, amps)

Resistance (R, ohms)

Bulb 1Bulb 2

Battery/Total n/a

Observations:1. Are electrons ‘used up’ as they flow through the circuit? How can you tell?

2. How do the individual potential differences of the two bulbs compare to the battery voltage you selected?

3. Which bulb appears brighter? Explain why you would expect it to be brighter.

Figure 14b: Screen shot from the simulation.


Parallel

Figure 15: Schematic of parallel circuit for lab.




Bulb 1Bulb 2

Battery/Total n/a

Observations:1. How do the currents through each individual bulb compare to the total current?

2. Which conservation law does your answer to question one verify?

3. How do the potential differences across each bulb compare to the battery voltage?

4. Which bulb appears brighter? Explain why you would expect it to be brighter.


Combination

Figure 16: Schematic of a combination circuit for the laboratory.




Bulb 1Bulb 2Bulb 3Bulb 4

Battery/Total n/a

Observations:1. Explain what you notice about the currents and the potential differences.

Data Analysis: 12. Summarize your results as follows.

a. Resistors (or bulbs) in a series circuit have the same _____________.

b. The brightest bulb in a series circuit is the one with the (circle one): largest/smallest resistance.

c. Resistors (or bulbs) in a parallel circuit have the same ________________.

d. The brightest bulb in a parallel circuit is the one with the (circle one): largest/smallest resistance.


Students: This will be a formal report. Dr. Smith will give you details regarding the due date, and be sure to refer to your ‘How to Excel’ and ‘How to Write a Formal Report’ documents.

Purpose: The purposes of this laboratory are: to test the validity of Ohm’s Law, and to introduce you to multimeters and how to use them to measure electric potential (voltage) and current in circuits. Concept: Recall that our study of circuits relies on three terms: voltage (also called electric potential or just potential), current (the flow of charge through the circuit), and resistance (the extent to which charge is impeded by parts of the circuit. In the previous lab, you constructed circuits in a simulated environment, and now you will have the chance to learn to use a multimeter as well as DC power supplies, resistors, alligator clips, and other equipment.

Ohm’s Law gives the relationship between voltage, current, and resistance:

ΔV =IR(1 )

Plotting voltage versus current across a resistor is expected to produce a straight line with a slope of ‘R’. The exception would be for something considered ‘nonohmic’ which simply means the object being studied does not obey Ohm’s Law.

Materials: Multimeter 4 or 5 alligator-clip wires 3 resistors DC power supply

Procedure: 48. Select one of the three resistors, and wire together a circuit with it and the power supply.49. Set the multimeter probes to measure voltage and connect the meter to your circuit. This entails having

the black probe in the center slot and the red probe in the right slot. If you look closely, you will see that the meter is labeled. NOTE: If the meter beeps, turn off the power supply and double check your setup.

50. Set the power supply control knob to the minimum level, then turn it on.51. Record the voltage reading on the multimeter – note if the display is reading mV or V.52. Turn off the power supply.53. Set the multimeter to measure current – you will also have to rewire your circuit slightly so the meter is

in series. DO NOT change the power supply setting.54. Turn the power supply on and record the current. Immediately turn off the power supply.55. Repeat steps 2-7 for at least 4 more power supply settings, then repeat for all 3 resistors.

Data: Record your measurements and observations in tables like those on the following pages.

12

Ohm’s Law – Part 1


Resistor Label (): Resistor Label (): Resisitor Label ():

Ammeter Reading, I [A]

Voltmeter Reading, V [V]





Table 10: Raw voltage drop and current data for various power supply settings across three different resistors.

Data Analysis: 13. Record your data in a spreadsheet, and plot the voltage versus current for each resistor (an example is

shown below). You will have three plots.14. In your plot, include axis titles, a chart title, and a best fit line with an equation.15. How does the slope compare to the listed resistance of the resistor you used? Compute the percent

difference between the slope and resistor label for each resistor.16. Discuss, using at least two complete sentences, whether Ohm’s Law is obeyed or not.

Figure 17:Plot of voltage drop versus current for a 25 resistor.

Jensen Extension: If a high voltage is encountered by a human body, the body has a resistance of approximately 500 (though dry skin can be much higher). If the maximum safe current through your body is 10 mA, what is the highest safe voltage your body can handle?


Students: This will be an in-class report. Ideally, you will turn in the analysis questions today at the end of the lab, but you may have an extra day if you need it.

Purpose: The objective of this laboratory is to test the basic formulas used when determining equivalent resistance by measure the voltage and current in simple series and parallel circuits of two resistors. Concept: The resistance of a circuit depends on many factors, none more important than the arrangement of individual resistors. If electrons (or other current-carrying particles) are forced to go through multiple consecutive resistors (in series, say), the effective resistance increases:

R s=∑i

❑

Ri

(1 )

If, on the other hand, electrons are presented with a choice of multiple paths to travel between two points in a circuit (as in a parallel circuit), then the equivalent resistance decreases:

Rp=(∑i

❑ 1Ri )

(2 )

All the while, conservation of charge and energy dictate the voltage drop and current through each resistor. The equation which relates current, electrical potential (voltage), and resistance is Ohm’s Law (V = IR), and the validity of this equation will be assessed in this lab.

Materials: Multimeter 6 to 8 alligator-clip wires 2 resistors DC power supply

Procedure: 56. Wire together a circuit (either series or parallel) with your two resistors and connect it to the power

supply. Double check all of your connections. 57. Record your expected total resistance (using the equations for series and parallel resistors) in a data

table similar to Table 2.58. Set the multimeter probes to measure voltage and connect the meter to your circuit so that you are

measuring the total voltage drop across both resistors. This entails having the black probe in the center slot and the red probe in the right slot. If you look closely, you will see that the meter is labeled. NOTE: If the meter beeps, turn off the power supply and double check your setup.

59. Set the power supply control knob to the minimum level, then turn it on.60. Record the voltage reading on the multimeter – note if the display is reading mV or V.

13

Ohm’s Law – Part 2


61. Turn off the power supply.62. Set the multimeter to measure current – you will also have to rewire your circuit slightly. DO NOT

change the power supply setting.63. Turn the power supply on and record the current. Immediately turn off the power supply.64. Repeat steps 1-8 for at least 4 more power supply settings.65. Repeat steps 1-9 for the other circuit type (i.e., series or parallel)

Data: Record your measurements and observations in tables like those on the following pages. Note that you will

Data Analysis: 1. For each row of each table, compute the resistance using Ohm’s Law. Then, average all of the series

values to obtain the average equivalent series resistance.

Series ParallelI [A] V [V] R [] I [A] V [V] R []

Measured Average Resistance []:

Measured Average Resistance []:

Calculated Equivalent Resistance []:

Calculated Equivalent Resistance []:

Percent Error: Percent Error:Table 11: Reduced data showing average measured resistance.

2. Repeat step 1 for the parallel circuit.3. Next, calculate the expected resistance for each circuit using the resistor labels and the equations for

equivalent resistance we used in class.4. Compute the percent difference between the measured average equivalent resistance and the

calculated expected equivalent resistance. 5. Discuss, using at least two complete sentences, the sources of error in your lab.

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