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Sample Lab Report - Lab Material
General Physics I (PHY 1420)
Baylor University
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Guidelines for a Physics Lab Reports
A laboratory report has three main functions: (1) To provide a record of the experiments and raw data included in the report, (2) To provide sufficient information to reproduce or extend the data, and (3) To analyze the data, present conclusions and make recommendations based on the experimental work.
General Comments: The single most important requirement for a laboratory report is clarity. Imagine that your audience is one of your classmates who missed that experiment. If you are using a word processor for your lab report, then use the spelling and grammar checkers. The grammar check can be annoying because often technical sentences are wordy and complex, but it will help you avoid using too many passive sentences. In general, passive sentences are less understandable. However, grammar check will not assess clarity, and it will ignore simple errors. (I do not doubt there are still mistakes in this document I have run it through spelling and grammar checks.) Many technical writers prefer to write sentences with passive verbs. A simple example: “The spring constant k was found from the slope to be 3 N/m.” If you run this sentence through the grammar check, it will tell you that “was found” is a verb in the passive voice. To change this to an active voice you could write: “The spring constant k is the slope, 3 N/m.” Not every sentence has to be in an active voice. What you want is a report that is readable.
Lab Report Structure: I. Cover Sheet: This page has the course number and assigned lab section, the title of the experiment, your name, your lab partner’s names, the date that the lab was performed and your TA’s name. II. Abstract: The purpose of an abstract in a scientific paper is to help a reader decide if your paper is of interest to him/her. (This section is the executive summary in a corporation or government report; it is often the only section that a manager reads.) The abstract should be able to stand by itself, and it should be brief. Generally, it consists of three parts which answer these questions: What did you do? – A statement of the purpose of the experiment, a concise description of the experiment and physics principles investigated. What were your results? – Highlight the most significant results of the experiment. What do these results tell you? – Depending on the type of experiment, this is conclusions and implications of the results or it may be lessons learned form the experiment. Write the abstract after all the other sections are completed. (You need to know everything in the report before you can write a summary of it.)
III. Data Sheets: For each experiment, the lab manual has one or more data sheets for recording raw data, as well as, intermediate and final data values. These are not for doodling, but for recording your data. Record the data neatly in pen. If your data values are so sloppily recorded that you have to recopy them, then the accuracy of the data is questionable. This fact will be reflected in your laboratory performance score. If there is a mistake, then draw a single line through that value. “White-Out” and similar covering agents are expressly forbidden.
The values that you record on your data sheet must have: Units (such as kg for kilograms) Reasonable uncertainty estimates for given instruments and procedures Precision consistent with uncertainty (proper significant digits) Propagation of error for calculated quantities Your lab instructor’s initials.
If you happen to forget your lab manual, then you will take your data on notebook paper. Your lab instructor will initial that as your data sheet and you will turn that in with your lab report as well as your own data sheet from the lab manual. You may not use your lab partner’s datasheet and then make a photocopy.
IV. Graphs: You must follow the guidelines in the lab manual for all graphs. The first graphs of the semester must be made by hand, not computer software. After your lab instructor gives permission, you may use computer software to make graphs. Those graphs must also conform to the guidelines in the lab manual. Remember that when plotting data with units, both the slope and intercept of a graph also have units. V. Sample Calculations : Show calculations in a neat and orderly outline form. Include a brief description of the calculation, the equation, numbers from your data substituted into the equation and the result. Do not include the intermediate steps. Numbers in the sample calculations must agree with what you recorded in your data sheet. For calculations repeated many times, you only include one sample calculation. Answers should have the proper number of significant figures and units. (It is not necessary to show the calculation for obtaining an average, unless your TA requests that you do so.) Typing the equation into the lab report is not required; it is easier and faster to print these calculations neatly by hand. If you wish to type this section, then use the equation editor in Microsoft Word. Your lab instructor can give you information on using the equation editor.
VI. Discussion of Results: This is the most important part of the lab report; it is where you analyze the data. (In the future, you may not actually collect data; a lab technician or other people may collect the raw data. Regardless of your discipline, the most challenging and rewarding part of your work will be analyzing the data.) Begin the discussion with the experimental purpose and briefly summarize the basic idea of the experiment with emphasis on the measurements you made and transition to discussing the results. State only the key results (with uncertainty and units) quantitatively with numerical values; do not provide intermediate quantities. Your discussion should address questions such as: What is the relationship between your measurements and your final results? What trends were observable? What can you conclude from the graphs that you made? How did the independent variables affect the dependent variables? (For example, did an increase in a given measured (independent) variable result in an increase or decrease in the associated calculated (dependent) variable?) Then describe how your experimental results substantiate/agree with the theory. (This is not a single statement that your results agree or disagree with theory.) When comparison values are available, discuss the agreement using either uncertainty and/or percent differences. This leads into the discussion of the sources of error. In your discussion of sources of error, you should discuss all those things that affect your measurement, but which you can't do anything about given the time and equipment constraints of this laboratory. Included in this would be a description of sources of error in your measurement that bias your result ( e. friction in pulleys that are assumed frictionless in
Hooke’s Law Experiment
Objective: To measure the spring constant of a spring using two different methods.
Background: If a weight, W = mg , is hung from one end of an ordinary spring, causing it to stretch a distance x , then an equal and opposite force, F, is created in the spring which opposes the pull of the weight. If W is not so large as to permanently distort the spring, then this force, F, will restore the spring to its original length after the load is removed. The magnitude of this restoring force is directly proportional to the stretch,
F = -kx
The constant k is called the spring constant. To emphasize that x refers to the change in length of the spring we write F = mg = - k ∆ l (1)
In this form it is apparent that if a plot of F as a function of ∆ l has a linear portion, this provides confirmation that the spring follows Hooke's Law and enables us to find k.
An additional approach is possible. One definition of simple harmonic motion is that it is motion under a linear, “Hooke's Law” restoring force. Note that for simple harmonic motion, the period does not depend upon the amplitude of the oscillation. For such a motion, we have
Tm 22 =4/π k (2)
where k again is the spring constant, T is the period of the pendulum and m is the mass that is oscillating. Thus, the mass includes the mass of the spring itself. However, the entire spring does not vibrate with the same amplitude as the load (the attached mass) and therefore it is reasonable to assume that the effective load (m) is the mass hung from the end of the spring plus some fraction of the mass of the spring. Based on similar experiments, one third of the mass of the spring is a good estimation of the effective load due to the spring, thus 1 3
mm =+=+ load m mes load mspring
where mes is the effective load of the spring. Using this in Eq. (2), we find
2 2
4{ mmload 1/3( spring )} k T
####### π +
= (3)
The effective load of the spring can be determined for a particular spring using the following
####### process. The equation for T 2 can be written in terms of mload and mes ; mes can then be
determined from a graph of T 2 versus mload. Note that this assumes that mes is constant.
Eq (3) uses an approximation for the contribution of the mass of the spring to the oscillation. If we rewrite Eq (2) as the effective mass of the spring and hanging mass (load), then
22 22 ES load ES load
44 T4m m k m kk
ππ =π +()/= +
m (4)
where mload is the hanging mass and mES is the effective mass of the spring. If we assume that the effective spring mass is the same for all loads, then a graph of period squared (T 2 ) vs. hanging mass (mload) is a straight line, where 4π 2 /k is the slope and 4π 2 mES/k is the intercept.
Procedure: Part 1
Meter StickMeter Stick
- Hang a spring from a horizontal metal rod.
- Attach a mass hanger directly to the bottom of the hanging spring and record the position of the bottom of the mass hanger relative to a meter stick.
- Add masses to the spring and record the position of the bottom of the mass hanger.
Part 2 1. Hang a mass from the spring and use a stopwatch to time 15 oscillations of the mass and spring. 2. Repeat for other masses.
A Poor Abstract – Too long because it has too much detail and unnecessary information. (The worst problems are in italics.) The purpose of this experiment was to determine the spring constant k of a steel spring using two different methods. First we investigated the relationship between the force applied to a spring and the displacement of the spring from its rest length in order to verify Hooke’s law. We hung masses of 0 kg, 0 kg, 0 kg, 0 kg, 0 kg, 0. kg, 0 kg, and 0 kg from the springs, and recorded the vertical displacements. We made four measurements for each mass hung from the spring and used the average of the four values in order to reduce random error. In this method, the main cause of error was measurement. We found a spring constant of k = 2 ± 0 N/m. Our results confirmed Hooke’s Law, the well known relationship that the magnitude of an elastic restoring force on a spring is directly proportional to the displacement of the spring. This relationship is named after the 17th century scientist Hooke who studied it. Next we measured the period of a mass hung from one end of a spring and set into vertical oscillation. We performed this process using the four different masses 0 kg, 0. kg, 0 kg, and 0. The period of each mass was measured three times using three different amplitudes of oscillation. We found that the spring constant depended on the effective mass of the spring and the period of oscillation. The period of the motion was the same whether the amplitude of the oscillation is large or small. In this method, the main cause of error was reaction time. Using this method we found a spring constant of 2 ± 0 N/m. This value is consistent with the result obtained using the first method. (291 words)
Remember to be concise.
Name: ___ _Your Name ________ Date:Date Exp. Performed Partner: ___ Partners Full Name
Hooke’s Law and a Simple Spring
Part 1 Table 1 Position Mass Location of the Mass Hanger Reference in cm ±0 ( g ) ±1%
Trial 1 Trial Trial 3 Trial 4
Reference 0 69 69 69 69. 1 1 69 69 69 69. 2 3 68 68 68 68. 3 5 67 67 67 67. 4 10 66 66 66 66. 5 20 62 62 62 62. 6 40 56 56 56 56. 7 60 49 49 49 49. 8 80 42 42 42 42. 9 100 36 36 36 36. 10 120 29 29 29 29. 11 140 23 23 23 23.
Table 2 Force Displacement ( x 10 -2m ) ( N ) Trial 1 Trial 2 Trial 3 Trial 4 Average ±1% ±0 ±0 ±0 ±0.
Spring Constant (N/m )
0 -0 -0 -0 -0 -0 ± 0 2 ± 0. 0 -0 -1 -1 -1. 03 -1± 0 2± 0. 0 -1 -1 -1 -1. 69 -1± 0 2± 0. 0 -3 -3 -3 -3. 35 -3± 0 2± 0. 0 -6 -6 -6 -6. 62 -6± 0 2± 0. 0 -13 -13 -13 -13 -13± 0 2± 0. 0 -19 -19 -19 -19 -19± 0 2± 0. 0 -26 -26 -26 -26 -26± 0 2± 0. 0 -33 -33 -33 -33 -33± 0 2± 0. 1 -39 -39 -39 -39 -39± 0 2± 0. 1 -46 -46 -46 -46 -46± 0 2± 0.
Average Spring Constant k = _ _ 2 ± 0 N/m _
Spring Constant k from Graph = __ 2 N/m ________
TA’s Initials on data sheet
If the value is four sig figs then include the trailing 0.
If you drop that zero then it is 3 sig figs! This should have been 49!
You can include uncertainty for a tool such as a meter stick in the top of a data table.
Uncertainty can be written as a percentage.
For the subtraction all the uncertainties were the same; thus it was put in the top of a column; that was not possible for the average.
Do you know why there are only 2 sig figs here?
Calculate the standard error.
There is a way to find the uncertainty for slopes of graphs, but we will not do that in this course.
Remember to include units and uncertainty.
Restoring Force vs. Displacement Magnitude
Force = 2 - 0. x = displacemnt
0 0 0 0 0 0 0 0 0 0 0. Displacement Magnitude (m)
Force (N)
Not all graphs will start at zero as this one does. If your data range for the y- axis is from 6 to 20 newtons, then use a graph that starts at 5 and ends on 20 or 25 newtons.
Never force a line to go through the origin. NEVER!!
Your TA may have other information that he/she wants on a graph. Then be sure to include that.
Graphs must conform to all the rules given in lab handbook.
Each graph should be on a separate page.
This graph was inserted into this Word document by a simple “copy and paste” from Excel into Word.
Note that for the first one or two experiments each semester you will be required to make your graphs by hand. After you demonstrate an ability to make a graph by hand, then you may use computer software to make your graphs.
Mass vs. Time Squared
y = 13 + 0. If you use Excel then edit x and y so it looks like this T 2 = 13 +.
y = 13 Dashed curve forced to intercept the origin
0
1
2
3
0 0 0 0 0 0 0 0 0 0 0. Mass
Time
2
Do not force a curve! Error bars were added to this graph to show that when the curve was forced to go through the origin it then did not honor the data collected.
This title is incorrect! Do you know why?
Do not use the default backgound color, use white. It can be difficult to see data points when printed.
Add gridlines for both axes, not just the default as in this plot.
Scale the graph so that the data is spread across the graph. This graph has too much unused space.
Since there are two graphs - each is worth 5 points. I would give this graph only 2 points out of 5.
Sample Calculations
- Displacement: the length that the spring is stretched
22 2
Displacement Location with Mass 1 (0) - Reference Location 66 10 69 10 3 10
x xmmm −− −
== =×−× =−×
- Uncertainty of displacement (∆ l): Propagation of error for addition and subtraction 22
-2 2 -2 2
x = (uncertainty in reference) + (uncertainty in location 1)
x = (0 10 m ) + (0 10 m) x = 0 10 m
×× ×
####### ∆
####### ∆
####### ∆
- Force on spring from the hanging mass
(10 )(1 /1000 )(9 / 2 ) 0.
=Fmg Fgkggms N
- Standard Error for Average Displacement for 0 force 2 i
-2 -2 2 -2 -2 2 -2 -2 2 -2 -2 2 1 / 2 2
(x -x) Standard Error = (1) x = {[( 3 10 m ( 3 10 m)) ( 3 10 m ( 3 10 m)) ( 3 10 m ( 3 10 m)) ( 3 10 m ( 3 10 m)) ] /[(4 1)4]} x = 0 10 m
NN ∆
∆ −
− − × −− × +− × −− × +−×−−× +−×−−× − ×
∑
- Using Hooke’s Law (F = - kx) to find the spring constant No units! No credit would be given
for this sample calculation. 2
/ 0/( 3 10 ) 2.
kFx k −
=− =− − × =
- Spring constant uncertainty: Propagation of error for multiplication and division 22
2 2 2 2
k = k ( F/F) + ( x/x)
0 0 0 10 k = 2/m + = 0 N/m 0 3 10
N m N m
####### ∆∆ ∆
####### ∆
− −
⎛⎞× ⎛⎞× ⎜⎟⎜⎟ ⎝⎠⎝⎠×
- Spring constant from period of oscillation
()()
2 2
23 3 2
4{ 1/3( )}
1 4(3) (145 10 10 10 ) / 1. 3 3 N/m
k mmload spring T
kkgkg
k
####### π
−−
- =
=×+×
=
s
- Spring constant uncertainty: propagation of error for T 2
n 22
A = nA( T/T) where A= T 2 T = 2(1) (.002s/1)= 0 s
####### ∆∆ n
####### ∆
=
- Spring constant from the slope from T 2 vs. Mload graph
22
2 2
(2 ) (2 )
(2 3) 3 / 13 s /kg
slope k k slope
kNm
####### π π
==
×- Spring’s Effective Mass, MES, from the intercept
()
()
2 2
22
(2 ) /(2 )
3/m 0 /(2 3) 0.
ES ES
ES
M Intercept M k Intercept k Ms
####### π
kg
####### ==×π
=× ×=
- % difference for spring constant k
Measured Value1 - Measured Value 2 % 100% Measured Value1+Measured Value 2 / 2 2/m - 2/m % 100% 1% 2/m + 2/m / 2
difference
difference
=×
=×=
principle used in the experiment.) The period of a mass oscillating vertically on a spring depends on the spring constant and the mass of the oscillating object, but not on the amplitude of the oscillation. (How the result demonstrated a physics principle.) Our measurements confirmed that the amplitude of oscillation, within experimental uncertainty, did not affect period (Table 3),
To reduce the reaction time, we observed the motion and used the rhythm to start and stop the stopwatch. ( How the independent variables affected the dependent variables.) For small masses, the period of the oscillation is shorter; this is consistent with Eq (2). These shorter periods for the 55g and 25g masses made accuracy in the timing both critical and difficult. The measured times for 20 oscillations of the 55g mass are not as consistent as for the other masses. This was the result of reaction time random error. Two measurements for 20 oscillations of the 25g mass were so different from the other measurements that we made additional measurements and replaced those data points. There was another complication for these smaller mass, large amplitude oscillations caused the slotted masses to bounce on the mass hanger. This meant that we had to use smaller amplitude differences between the large and small amplitude oscillations for the smaller masses.
(You may need to combine two equations.) Using Eq (3), we found k for the four different loads added to the spring. The four values of k for the four different masses were in agreement (Table 3). The average value of k is 2±0 N/m. ( Always include units; 2± 0 without units would be meaningless.)
(Analysis of graph.) A graph of T 2 vs. Mload is a straight line and consistent with the theory that the period is a function of the effective mass of the spring and the spring constant of the spring, Eq, (4). (Important results.) The spring constant k from the slope is 3 N/m; the effective mass of the spring MES from the intercept of the best fit line is 4, which is approximately 40% of the mass of the spring, which is somewhat higher than the fraction used in Eq. (3).
The sources of error in this part of the experiment are due to the accuracy of the slotted weights and the accuracy of the time measurements. (There is no need to repeat what you have already discussed.) As mentioned previously, the reaction time uncertainty is greater for the smaller loads. However, due to the care that taken in the time measurements and the fact that 20 different oscillations were measured, the uncertainty in the time measurements was not as important in this experiment as the uncertainty in the slotted masses. There is uncertainty (1%) in the mass of the slotted weights. It would have been prudent to have measured the masses on the triple beam balance so that we would have less uncertainty in the mass of the oscillating weights; however, we did not make those measurements.
The value of the spring constant found in Part 1 (2±0 N/m) and Part 2 (2± 0. N/m) do not agree. (Discuss how results agree using either uncertainty and/or percent differences.) However, the percent difference between the two values is only 1%. One possible explanation for the small discrepancy may be that the time measurements were precise, but not accurate due to a systematic error in the timing. If our time measurements of the twenty oscillations were low by as little as 0, then the spring constant values would agree.
(A brief conclusion.) Besides measuring the spring constant using two very different methods, we verified Hooke’s law, verified the linear relationship between period squared and load for a vertically oscillating spring, and observed that the amplitude of the oscillations did not affect the period.
Answers to Questions (if any): Answer questions in complete, grammatically correct sentences.
Sample Lab Report - Lab Material
Course: General Physics I (PHY 1420)
University: Baylor University
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