Lab 1:  Precision Measurement of Length

                Measuring length is fundamental to our everyday life, and there are many tools in use to measure length – tape measures, odometers, rulers, ultrasonic sensors, GPS systems, etc.  In this lab you will use three tools for measuring length, a precision rule (ruler), a vernier caliper, and a micrometer caliper.  Since these instruments offer varying degrees of precision (and accuracy), you will also gain insight into making and reporting measurements and calculations with the proper precision (significant digits).

            The precision rule is more commonly known as a ruler.  Most have scales marked off in inches and in centimeters (or millimeters).  In this lab (and all labs) you will make your measurements using metric units.  There are several points to remember while you use the ruler.  First, the object whose dimension you are measuring should be as close to the scale as possible, and your eye should be directly over the scale when you read the scale.  These two things will help minimize parallax error due to the line of sight between your eye, the scale, and the object.  If the end of your ruler is roughed up or if the zero mark on the ruler is not readable, you may want to offset the end of the object being measured from the end to the 1-cm mark or the 10-cm mark.  (Remember to subtract this amount from your measurement.)  Finally, remember to read the scale with the correct number of significant digits – all the digits you are certain of plus one estimated digit.  On most centimeter rulers the scale is marked off in 0.1-cm increments, so in that case you will estimate to 0.01 cm.

            The vernier caliper is an advancement from the precision rule in that it uses a sliding vernier scale to aid in making the estimate of the last digit.  Where with a ruler your estimate may be off by 0.05 cm or more, the vernier scale allows you to make the estimate to better than 0.02 cm.  The “caliper” part of the name indicates that the vernier caliper has one or more sets of “jaws” that you set on either side of the object when making a measurement.  This greatly reduces the parallax error one encounters when using a precision rule.  On most vernier calipers, the jaws are designed to make it easier to measure inside and outside dimensions and depth.  Here are a couple of links with illustrations and instructions on using a vernier caliper.  (These will open in a new window)

            The micrometer caliper (micrometer) is an extension of the vernier caliper which uses a threaded screw to position the scale rather than the sliding scale of the vernier caliper.  This allows the scale to be placed more precisely, and, consequently, the micrometer can be read to a higher precision.  Here are a couple of links with illustrations and instructions on using a micrometer caliper.  (These will open in a new window)

Of the instruments you will use today, the micrometer is the most delicate and the most expensive.  Rough handling can damage it, so treat it with care.  Never force the thimble tight or give it a quick twist to let it spin and “coast.”  Always tighten the micrometer using the ratchet on the end to prevent over tightening.  You should also check your micrometer to see if it is properly zeroed.  When the ratchet is tightened with nothing in the jaws of the micrometer, the scale should read within just a few 0.001 mm of zero.  If not, record this “zero” reading and add/subtract it from your measurements to compensate for it being off-zero.

Procedure

            You will be given several objects whose dimensions you should measure.  Measure three (3) objects using the precision rule, three (3) objects using the vernier caliper, and three (3) objects using the micrometer caliper.  There should be some overlap in the objects you measure; at least one object should be measured using both the ruler and vernier caliper, and at least one object should be measured using both the vernier and micrometer calipers.  At least one object should be cylindrical, and at least one object should be spherical.  Organize your data into a table or tables. 
     Once you have all your dimensions measured, you will make 6 calculations--3 surface area calculations and 3 volume calculations.  Pick one object measured using the precision rule and find its surface area and volume.  Pick a different object measured using the vernier caliper and find its surface area and volume.  Pick another different object measured using the micrometer and find its surface area and calculations.  Put these results in a separate table. As you make your measurements and do your calculations, pay careful attention to significant digits.  Include sample calculations in your report.

Questions

1.  Convert your measurements for the cylindrical object (or one of the cylindrical objects) to inches.  Do this for its dimensions, surface area, and volume.

2.  Of the three instruments (ruler, vernier caliper, micrometer), which is best suited for measuring the diameter of a small sphere?  For measuring the diameter of the hole in a washer?  For measuring a length of string?

3.  Since the micrometer gives much greater precision than either the ruler or vernier caliper, why would one not use it all the time?  Give at least two reasons.

4.  Calculate the number of square millimeters in one square centimeter.

5.  Calculate the number of cubic centimeters in one cubic meter.