How to Write a Good Lab Report .pdf - Yidnekachew

**How** **to** **Write** a **Good** **Lab** **Report**

Sample **Lab** Instruction

Experimental Investigation of C/D

Introduction: **How** is the circumference of a circle related **to** its diameter? In this lab, you design

an experiment **to** test a hypothesis about the geometry of circles. This activity is an introduction

**to** physics labora**to**ry investigations. It is designed **to** give practice taking measurements,

analyzing data, and drawing inferences without requiring any special knowledge about physics.

Equipment (per group):

• Metric ruler

• Vernier calipers

• At least 5 objects with diameters ~1 cm **to** ~10 cm: (penny, marble, “D” cell, PVC

cylinders)

Procedure:

Design an experimental procedure **to** test the following hypothesis:

Hypothesis: The circumference (C) of a circle is directly proportional **to** its diameter (D).

Make sure you record what you do as you do it, so that the procedure section of your report

accurately and completely reflects what you did. Some helpful hints for taking and recording

data are in the lab tips and in the grading rubric.

Analysis:

Note: As the semester progresses, you will be expected **to** take more and more responsibility for

deciding how **to** analyze your data. Drawing valid inferences from data is a vital skill for

engineers and scientists. The instructions for analyzing data for most labs will not be as detailed

as the instructions below.

• Numerical Analysis: Calculate the ratio C/D for each object. Estimate the precision of

each value of C/D.

• Graphical Analysis: Use Excel **to** construct a graph of C versus D. Use Excel **to** display

the equation of the best fit line through your data. Use the LINEST function **to** estimate

the uncertainty in the slope and intercept of the best fit line. Make sure you interpret the

meaning of both the slope and intercept. A checklist for graphs is in the grading rubric.

• Questions **to** consider:

o

o

o

**How** do your calculations and graph support or refute the hypothesis?

Does your graphical analysis agree with your calculations?

Do your results for the C/D ratio agree with accepted theory?

**Report**:

A sample lab report for this activity is provided as an example for you **to** follow when writing

future lab reports.

Sample **Lab** **Report**: Experimental Investigation of C/D

Abstract

In this investigation, we examined the hypothesis that the circumference (C) and diameter (D) of

a circle are directly proportional. We measured the circumference and diameter of five circular

objects ranging from 2 cm **to** 7 cm in diameter. Vernier calipers were used **to** measure the

diameter of each object, and a piece of paper was wrapped around each cylinder **to** determine its

circumference. Numerical analysis of these circular objects yielded the unitless C/D ratio of 3.14

± 0.03, which is essentially constant and equal **to** pi. Graphical analysis lead **to** a less precise but

equivalent estimate of 3.15 ± 0.11 for this same ratio. These results support commonly accepted

geometrical theory which states that C = pD for all circles. **How**ever, only a narrow range of

circle sizes were analyzed, so additional data should be taken **to** investigate whether the constant

ratio hypothesis applies **to** very large and very small circles.

Introduction

Procedure:

Five objects were chosen such that measurements of their circumference and diameter could be

obtained easily and would be reproducible. Therefore, we did not use irregularly shaped objects

or ones that could be deformed when measured. The diameter of each of the 5 objects was

measured with either the ruler or caliper. The circumference and diameter of each object was

measured with the same measuring device in case the two instruments were not calibrated the

same. The circumference measurement was obtained by tightly wrapping a small piece of paper

around the object, marking the circumference on the paper with a pencil, and measuring this

distance with the ruler or caliper. The uncertainty specified with each measurement is based on

the precision of the measuring device and the experimenter’s estimated ability **to** make a reliable

measurement.

Equipment used:

• “D” cell battery, 2 short pieces of PVC pipe, **to**ma**to** soup can, penny coin

• Metric ruler with millimeter resolution

• Vernier caliper with 0.05 mm resolution

Analysis:

Object Description Diameter(cm) Circumfer(cm) Measuring Device

Penny coin 1.90 ± 0.01 5.93 ± 0.03 Vernier caliper, paper

“D” cell battery 3.30 ± 0.02 10.45 ± 0.05 Vernier caliper, paper

PVC cylinder A 4.23 ± 0.02 13.30 ± 0.03 Vernier caliper, paper

PVC cylinder B 6.04 ± 0.02 18.45 ± 0.05 Plastic ruler, paper

Toma**to** soup can 6.6 ± 0.1 21.2 ± 0.1 Plastic ruler, paper

The C/D value for the penny is (5.93 cm)/(1.90 cm) = 3.12 (no units). The precision of the ratio

can be estimated using the error propogation formula:

Results for all five objects are given in the table below.

Object Description Diameter(cm) Circumference(cm) C/D calculated (no units)

Penny coin 1.90 ± 0.01 5.93 ± 0.03 3.12 ± 0.02

“D” cell battery 3.30 ± 0.02 10.45 ± 0.05 3.17 ± 0.02

PVC cylinder A 4.23 ± 0.02 13.30 ± 0.03 3.14 ± 0.02

PVC cylinder B 6.04 ± 0.02 18.45 ± 0.05 3.06 ± 0.01

Toma**to** soup can 6.6 ± 0.1 21.2 ± 0.1 3.21 ± 0.05

Average C/D = 3.14 ± 0.03, where 0.03 is the standard error of the 5 values.

From this empirical investigation, the average C/D ratio is 3.14 ± 0.03 (no units). This ratio

agrees with the accepted value of pi (3.1415926…). The uncertainty associated with the average

C/D ratio is the standard error of the five C/D values, which is equal **to** the standard deviation

(0.06) divided by the square root of N, which in this case is 5 since there were five

measurements.

While the five C/D values do not agree within their estimated uncertainties, the variation

between these values is relatively small (only about 0.06/3.14 = 2%), which suggests that the

C/D ratio is a constant value. The reason for the imperfect agreement may be that the individual

uncertainties were underestimated or perhaps is a consequence of the “paper” method used for

measuring the diameters of the object. The paper may have slipped while we made the mark, but

this “slip effect” should only be a random error, which would not affect the average value of our

measurements for C, since there is no reason **to** believe that the paper would have consistently

slipped in the same direction (either **to**o high or **to**o low) every time.

Another way **to** visualize and calculate this constant circle ratio is by graphing the circumference

versus diameter for each object. Graphs are especially useful for examining possible trends over

the range of measurements.

If C is proportional **to** D, we should get a straight line through the origin. From our numerical

results, we would expect the slope of the C vs. D graph **to** be equal **to** pi. The slope of the best fit

line is (3.15 ± 0.11), which is equal **to** pi within its uncertainty. The intercept is essentially zero:

(-0.05 ± 0.5). The R squared statistic shows that the data all fall very close **to** the best fit line. If

all the data lie exactly on the fitted line, R squared is equal **to** 1. If the data are randomly

scattered, R squared is zero. With an R^2 value of 0.997, our linear equation appears **to** fit the

data very well.

Discussion

Our results support the original hypothesis for 5 circles ranging in size from 2 cm **to** 7 cm in

diameter. The C/D ratio for our objects is essentially constant (3.14 ± 0.03) and equal **to** pi. The

specified uncertainty is the standard error of the C/D ratio for the five objects. Graphical analysis

also supports the “directly proportional” hypothesis. The line has an intercept (-0.05 ± 0.5) that is

equal **to** zero within the uncertainty and a slope (3.15 ± 0.11) equal **to** pi . The larger uncertainty

from the graphical analysis suggests that the random measurement errors may be larger than

estimated in the numerical analysis. A more extensive investigation of this C/D relationship over

a wider range of circle sizes should be performed **to** verify that this ratio is indeed constant for all

circles.

The uncertainty in the measurements could be due **to** the paper-wrapping method of measuring

the circumference, circles that may not be perfect, and the limited precision of the measuring

devices. The use of paper **to** measure the circumference was probably the most significant source

of uncertainty. It is unlikely, however, that this measurement technique biased our results, since

the technique probably gave measurements of C that were **to**o high in some cases and **to**o low in

others.

The C/D ratio for a perfect circle was defined long ago by the Greek symbol: pi = 3.14159… Our

measured value appears **to** be consistent with the accepted value of pi within the limits of our

experimental uncertainty. This unique C/D ratio has many important applications wherever

circles or spheres are encountered.

**Lab** **Report** Format

Text:

**Lab** reports must be typed or printed clearly in ink. Each report must include a cover page, an

abstract, a summary of your experimental results (including your original data sheet and any

additional notes, tables, or graphs), and a discussion of your findings. See the descriptions below

for what should be included in each section.

COVER PAGE

• Title of experiment

• **Lab** section

• Date the experiment was performed

• Your name

• Your partner’s name (identified as such)

ABSTRACT

The abstract is a concise summary of the lab report. A good abstract should state the purpose,

procedure, principal results, conclusion, and implications of the lab in a single paragraph that is

generally 100 **to** 200 words in length (use your word processor’s word count **to**ol **to** check

length).

INTRODUCTION

A complete scientific lab report has an introduction that gives the context for the experiment, the

background theory, and a description of the experimental procedure and equipment used. For

simplicity and brevity, you are not required **to** include this section, but you may do so if you

prefer. In cases where a particular lab does not have a prescribed procedure, or you used a

procedure that was significantly different than the one described in the lab manual, you should

clearly explain what you actually did either in the introduction or discussion sections.

DATA AND RESULTS

The results of your experiment must be well organized and easy **to** read. When appropriate,

tables or graphs should be used **to** present data and results. Graphs must be properly constructed

(with a computer or by hand, as directed) with descriptive titles, labeled axes with relevant units,

and calculated parameters properly interpreted (e.g. What do the slope and intercept represent?)

All measured values must have four critical parts:

1. A label (word or symbol) that clearly identifies the measured value

2. The numerical value for the measurement (rounded **to** be consistent with the uncertainty)

3. A reasonable estimate of the uncertainty associated with the measurement

4. An appropriate unit of measure (SI units are usually preferred)

Sample calculations, including an analysis of the experimental uncertainties, should be shown for

any derived or calculated values as appropriate. Your original, unaltered data sheet must be

included either in the data section or as an appendix.

DISCUSSION

In the discussion section, summarize the results you obtained, and then discuss any discrepancies

between your results and what was expected according **to** the given theoretical predictions or

your own hypotheses. Did the experimental results agree with your predictions or the findings

from other lab groups? If not, what is the most likely reason for the discrepancy? Remember **to**

consider the uncertainty of your results when determining agreement. Identify the primary source

of error in your results and justify your answer based on your uncertainty estimates. (Note:

General statements without justification and explanation are not acceptable. “Human error” is

not an acceptable source of error!) **How** could you improve the quality of your measurements

with the available equipment? What did you learn or discover from this lab? The discussion

section for most labs should be about one **to** two pages in length. Remember that your discussion

will be graded on the quality of your explanations, not the quantity.