Objective
The idea of this lab is to use simple measuring tools (a ruler and a Vernier caliper) to measure dimensions of objects in both the English and the Metric units and show that they are equivalent. This exercise requires some unit conversion.

Equipment
Meter rule, Vernier caliper, coins, your textbook, and some rectangular metal blocks. All data and calculations can be recorded using these sheets and your handout.

Definition
The following discussion refers to the divisions on the Meter rule, which are in centimeters and millimeters (Metric units). The rule also has divisions in inches and in 1/16^th of an inch (English units). Since English units are divided into units of 1/16^thinches, measurements in English units are easier to express as fractions rather than as decimals (decimals are the preferred method of expressing metric measurements). Remember: inches are measured in increments of 1/16in = 0.0625in.

A ruler or meter stick has marks on it indicating centimeters (100cm = 1 meter) and millimeters (10mm = 1cm) so it can be used to accurately determine length to the nearest millimeter (for example, an object might be 25cm and an additional 3mm in length which is written 25.3cm). If the length of an object does not come exactly to one of the millimeter marks on the stick, you can "estimate" the distance between the mm marks. For example, if an object is a little longer than 15cm so it ends about midway between the next 4mm and 5mm marks, you would indicate the length as 15.45cm. Because you are estimating (eyeballing) however, you can't be sure whether it's really 15.45cm or 15.44cm or 15.43cm or 15.46cm or 15.47cm. However, you can tell whether the end of the object is nearer to the 15.4cm mark or to the 15.5cm mark and so you would say that the length of the object is either 15.4cm or 15.5cm with an accuracy of + or - 0.05cm. In other words, the rule determines length to the nearest one-tenth (1/10^th) of a centimeter (the nearest millimeter).

If you want a more accurate measurement of the length (in the above example, whether the object is really 14.45cm or 14.46cm) you must use a more accurate tool: a Vernier caliper! This tool will determine a length to the nearest one hundredth (1/100^th) of a centimeter. The attached description of the Vernier and the Java simulation below describe how it is used. Please be sure to read them before you proceed!

Procedure
Part A

Before you start this lab, you must understand how the Vernier works. Please practice using the applet before you start the procedure for this lab.

1. Obtain a dime and a quarter (or any other two coins of different sizes).
2. Have someone measure the diameter of the dime using the vernier caliper. Record this below (Metric measurement only — use cm to be consistent).
3. Pass the dime and the caliper to another person. Record their measurement of the diameter of the dime below, too.
4. Finally, pass the dime to a third person, and record their measurement of the diameter of the dime below.
5. Repeat the above three items for the quarter.
6. Make sure that you have recorded the measurements of six (6) different people (three each for the dime and the quarter) in your handout!
7. Compute an average diameter for both the dime and the quarter:

   
         (1st-Measurement + 2nd-Measurement + 3rd-Measurement)
   AVG = -----------------------------------------------------
                                  3
       

8. Finally, convert the average diameters of both the dime and the quarter to English units by dividing your metric measurements by 2.54cm (since 1inch = 2.54cm). E.g.,

   
           1 inch
   45cm x ---------    =    _____ inches
           2.54 cm
       

Part B
The idea here is to measure something that is too small to record accurately by measuring some other thing which is related to it.

1. Measure the thickness of 1 sheet, 50 sheets, and 250 sheets of your textbook with the Vernier caliper (use Metric units only).
2. Just as in Experiment A, please make sure that three different people measure each of the page denominations. NOTE: To measure 50 sheets, you have to select pages numbered 1-100, not 1-50.
3. Compute the average thickness for each denomination (1 sheet, 50 sheets, and 250 sheets).
4. Now calculate the percent variation for each denomination (1 sheet, 50 sheets, and 250 sheets) using the following formula:

   
                      (Biggest_Value - Smallest_Value)
       % difference = --------------------------------   x 100
                        Average of the three values
       

5. Finally, calculate the thickness of a single sheet for each of the three denominations (1 sheet, 50 sheets, and 250 sheets).

Questions

1. Which of the three measurements do you think gives the best number for the thickness of one (1) sheet? Please record your answers on the fill-in sheet.

Part C
Measure the volume of your textbook (using the meter stick or ruler) in cm³ and in³. Now convert them to the same units and compare (using the fact that 1 inch = 2.54cm).

Questions

1. What is the percentage difference between them?

To observe how the scales are read, click in the "checkbox" by SHOW
and drag the lower scale left or right to observe how the measurement is determined.

Notice that the value for the upper scale is determined by where the 0 on the lower scale lines up with the upper scale and the number on the lower scale is determined by finding which mark on the lower scale best lines up with ANY mark on the upper scale.

To test your ability to read a measurement, leave SHOW unchecked and then drag the lower scale left or right.

The applet will wait for you to enter a value into the TextField and will then tell you whether your answer is correct. (After you type in an answer, press Enter.)

Note: Please note that this applet shows scales in mm (i.e., 0, 10, 20, etc.)! Some verniers will be marked in cm (i.e., 0, 1, 2, etc.).