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Physics 40 Lab 1: Introduction to Measurement & Error Analysis 
 
Equipment: Clear plastic metric rulers, vernier caliper, digital caliper, magnifying loop,  0-decimal, 1-
decimal, 3-decimal mass scales and cylindrical metals.  
 
Introduction 
This lab is intended to serve as an introduction to error analysis, which we will be using in every lab. 
You will measure the dimensions of a metal cylinder to determine its density using various methods 
with different levels of precision in order to explore measurement and error propagation. This is “cook 
book” lab so be sure you follow the directions closely!!! Make sure you include responses to all 
questions.   
 
This is a group lab. You will hand in one lab report for the group. Make sure you include the following 
at the beginning of your report (you do not need a title page):   
      1.   Printed names of all in group  
2.   Lab Section, number and title  
3. Computer station number you used.  
 
PART 0: Significant Figures Simulations 
  
Before the lab, go to: http://lectureonline.cl.msu.edu/~mmp/applist/sigfig/sig.htm  Try to determine the 
significant figures for 10 numbers. If you are wrong in more than one number, try 10 more. Go here to 
learn how to read a vernier scale: http://www.phy.ntnu.edu.tw/java/ruler/vernier.html  You don’t have 
to turn anything in for this part. Practice makes perfect. 
 
  
PART 1: MEASUREMENT AND ERROR 
In Excel, produce a data table for the measurements and calculations to be made below in each part 
where you will measure a dimension and the error in that measurement. You can keep the table(s) in an 
excel document or copy and paste the tables into your word document lab report. Be sure to include the 
error (uncertainty) for each measuring device. Express errors in absolute form. You must show all your 
error calculations and report your results in standard form for each method as shown:  
 
 
 ρ = 3.25 x 103 +/- 0.04 x 103 kg/m3
 
  
I: Rough Measurement 
1. Using a meter stick measure the height (mm) and the diameter (mm) of the cylinder and record 
these values their uncertainty in your lab datasheet. Convert the units to (m).  
2. Using the 0-decimal setting electronic scale, measure the mass (g) of the cylinder and record its 
value and the error in this measurement in your datasheet.  Convert units to (kg). 
3. Calculate the density, showing all the work, in kg/m3 and record this in your lab report.  
4. Calculate the absolute error for density (kg/m3), showing all your steps. How many significant 
figures are you keeping and why? Which instrument limits your precision? 
5. State your final value for the density and its uncertainty in the standard form in your report.    
6. Calculate the discrepancy and percent difference between your experimental value and the 
‘true’ value for the metal.  
 
   
II: Precise Measurement 
This time repeat the above measurement using the Vernier for measuring the length and diameter and 
the 1-decimal setting electronic scale. Record your data in the lab report, calculate possible errors, 
significant figures, density and state your final value in the standard form.  
  
  
III: More Precise Measurement 
This time repeat the above measurement using the digital Vernier calipers and the 3-decimal setting 
electronic scale. Record your data in the lab data sheet, calculate possible errors, significant figures, 
density and state your final value in the standard form.  
  
 
IV: Conclusions 
What do you think your metal is made of and why? Using the density you calculated, try to determine 
the material your metal is made of from the internet (http://www.simetric.co.uk/si_metals.htm) . What 
is the percent difference between the ‘true’ density and those you calculated from each method? For 
which method, if any, did the true value fall within your experimental uncertainty? Summarize your 
results from the 3 different methods.  Which method gave the best result? What sources of systematic 
and human errors contributed to your experimental results?  
  
 
PART 2: MEASUREMENT AND PERCEPTION 
Our eyes and minds can deceive us and produce errors in our measurements. Print out the following 
activity, do it, and turn it in with your lab report.