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Physics 1020 Laboratory 1 Measurement and Uncertainty

Measurement and Uncertainty


Prelab Questions

These questions need to be completed before entering the lab.

Please show all workings.

Prelab 1:

A rectangular object has length L = 25.3 +/- 0.2 cm and width

W = 18.6 +/- 0.5 cm.

What are the absolute uncertainties in length and width?

Find the relative uncertainties in length and width.

Prelab 2:

Given a set of length measurements: 60.4, 60.8, 61.2, 60.0, 60.6 cm.

Find: the average (mean) length

the standard error (refer to the introductory pages of yourLab Workbook).


Contents

I. Experimental uncertainty in a measurement

II. Combining quantities and comparing results

III. Experimental uncertainty in multiple measurements

IV. Conclusion and summary


Objectives

The objectives of this lab are to:

� Learn about the different types of uncertainties.

� Learn more about experimental uncertainties, ways to represent them, and how to assign them.

� Apply these concepts in straightforward measurements and calculations.

� Calculate the perimeter and area of your hand along with the associated experimental uncertainties.


Part I:Experimental Uncertainty in a Single Measurement

In this part of the lab, you will study the concepts of measurement and associated experimental uncertainty by measuring the physical dimensions of your hand with a ruler.


Part I:Estimating Experimental Uncertainty

When a physical quantity is measured, a reading is made with a device.

The number of significant figures in the reading is limited by the device itself and the

size of the smallest division on the measuring device.

The uncertainty is a reflection of the confidence in the measurement and must be

estimated based on the individual experimental setup.

How do you estimate the uncertainty?

Look closely at your experimental setup: Is the metre stick easy or difficult to read?

Are the edges of your object (i.e. a hand for this experiment) sharp and well defined

or are they not clearly defined?

When doing your measurement ask yourself how reliable is your measurement: Are

you confident to 0.2 mm, 0.5 mm, 1 mm, 2 mm, or more? Whatever you decide will

be your uncertainty.

Measurements should have the same number of places after the decimal as the

uncertainty.


Part I: Single Measurements

Carefully lay your hand on the ruler and measure the length of your hand from the

base of your wrist to the tip of your longest finger.

Record this in Table 1 of your Laboratory Workbook.

Be sure to answer all questions with complete sentences!

QUESTION 1: Estimate the experimental uncertainty in your measurements.

You will need to estimate this value! Ask: How reliable is your measurement? How

well can you define the ends of your hand? Are you sure to 0.5mm, 1mm, 2mm, or

more? Your estimate of reliability is your uncertainty.

Reposition your hand and measure the width of your hand.

Record this in Table 1 of your Laboratory Workbook.

QUESTION 2: Record the length and width of your hand in the form x ± δx,

using your estimated experimental uncertainty from Question 1.

Be sure to include units.


Part I: Relative Uncertainty

We will now calculate relative uncertainty as an indicator of precision: The

smaller the relative uncertainty the more precise the measurement is.

In this course, any relative uncertainty that is less than 0.05 is considered

reasonable.

QUESTION 3: Calculate the relative uncertainties for the length and

width of your hand.

Which relative uncertainty is the largest?

QUESTION 4: According to this, which measurement is most precise?

Have your instructor check your measurements and your relative

uncertainties and sign your Laboratory Worksheet.


Part II:Combining Quantities and Comparing Results

QUESTION 5: Treating your hand as a rectangle, calculate theperimeter P of your hand.

Be sure to include units and uncertainty.

Use your length and width measurements from Table 1.

Measure the perimeter of your hand using a string:

Use a string to make an outline of your hand, keeping as close as

possible to the outside of your hand.

Be sure to close the loop across your wrist!

When done, measure the length of the string, i.e. the perimeter, using a

metre stick.

Record the length of the string in Table 2 of your Laboratory Workbook.

Also estimate and record the uncertainty in measuring with the string.


One of the most important things about experimental uncertainties is how we use them to see if two or more quantities can be considered equal.

If you have two quantities for x say x1±δ x1 and x2±δx2 then these two numbers agree within experimental uncertainty if the range x1-δx1 to x1+δx1 overlaps with the range x2-δx2 to x2+δx2.

Example:

Since their ranges overlap, d1 and d2 agree within experimental uncertainty.

QUESTION 6: Does the perimeter you measured with the string agree withthe perimeter you calculated in Question 5? In your answerto this question, be sure to write the range of both quantities.

Comment on any disagreement.

QUESTION 7: Is the absolute uncertainty in perimeter smaller or largerthan the absolute uncertainties in length and width? Is thisan expected result? Comment.

d1 =10.6 ± 0.4cm,

range : d1 =10.2 →11.0cm

10.2cm < d1 <11.0cm

d2 =11.1± 0.2cm

range : d2 =10.9 →11.3cm

10.9cm < d2 <11.3cm



QUESTION 8: Treating your hand as a rectangle, calculate the area A ofyour hand. Be sure to include units and uncertainty.

QUESTION 9: Is the relative uncertainty in area smaller or larger thanthe relative uncertainties in length and width? Is this anexpected result? Comment.

Laying your hand on top of the graph paper in your Laboratory Workbook, have your partner carefully trace your hand.

Determine the area of your traced hand. Count carefully and do your best to

estimate the area in the partially filled squares.

Record this area in Table 3 of your workbook.

Estimate the uncertainty in the area and record this value in Table 3.

QUESTION 10: Does the area you measured with the graph paper agreewith the area you calculated in Question 8? In youranswer to this question, be sure to write the range of bothquantities. Comment on any differences.



Part II:Experimental uncertainty in multiple measurements

In this part of the lab, you will use measurements of many hands to find

the mean and standard error in length and width.

For the first row of Table 4, fill in the values of length and width you

previously measured in this experiment.

The remaining values will come from other students in the lab. Visit other

students sitting close to you and record their values for length and width.

You should record 10 values each of length and width in Table 4.


Use Graphical Analysis to determine the standard error in length:

Click to open Graphical Analysis.

Enter your length values in the table.

Click Analyze then Statistics.

Record the mean, standard deviation, and point count in Table 4.

Calculate the standard error and record your result in Table 4.

Repeat this process to determine the standard error in width, recording

your results in Table 4.



QUESTION 11: Write the average hand length in the form L ± δL

using results from Table 2.

Find the relative uncertainty in length.

QUESTION 12: Write the average hand width in the form W ± δW

using results from Table 2.

Find the relative uncertainty in width.

For this distribution we expect 68.2% of all individual measurements will fall within one standard deviation of the mean, 95.4% of all individual measurements will fall within two standard deviations of the mean and, 99.6% of all individual measurements will fall within three standard deviations of the mean.

QUESTION 13: By how many standard deviations are your lengthand width measurements different from the averagelength and width?



Part V: Conclusion and Summary

QUESTION 14: List at least three sources of uncertainty in thisexperiment.Which is the most significant source of uncertainty?Why? How could you reduce this uncertainty in yourexperiment?

Leave your lab workbook on your assigned shelf and sign out (at thecentre desk) before you leave.

To access your prelab questions for next week:http://www.mun.ca/physics/undergraduates/fylabs/p1020/manual.php

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