MEASUREMENT TOOLS.doc

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MEASUREMENT TOOLS

Meter stick.The simplest way to measure length is to use an ordinary meter stick. In thelaboratory, our meter sticks are carefully calibrated in centimeters with a millimeter least

count. That is, the millimeter is the smallest subdivision on the meter stick, which can beseen in Figure 1. This means the millimeter is the unit of the smallest reading that can bemade without estimating.

Figure 1.This meter stick is calibrated incentimeters (shown as the numbered majordivisions with a least count of millimeters.

Figure 2.!n e"ample of a meter stickreading. The object#s length is measured tobe $1.%$ cm. (&ee te"t for description.

! measurement reading usually has one more significant figure than the least countreading of the scale. The least count of our laboratory meter sticks is '.1cm and thereforea reading can be made to '.'1cm. Figure above shows a meter stick being used to

measure the length of a plastic strip. The meter stick is calibrated in centimeters, so weknow that the strip is between $1 and $ cm. The least count of this meter stick is onemillimeter, so we know with absolute certainty that the object is between $1.% cm and $1.)cm. *e then estimate the object#s length to the fractional part (doubtful figure of the leastcount subdivision. In Figure , it we may estimate that the strip is closer to $1.% cm than itis to $1.) cm and report the length to be $1.%$ cm or '.$1%$ m.

Vernier caliper.! vernier caliper (or vernier, shown in Figure +, is a common tool used inlaboratories and industries to accurately determine the fraction part of the least countdivision. The vernier is convenient when measuring the length of an object, the outerdiameter (- of a round or cylindrical object, the inner diameter (I- of a pipe, and the

depth of a hole.


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Figure 3.The vernier caliper. ! common instrument used to measure lengths, depths

and diameters. (&ee te"t for description.

*hen using a meter stick to measure length, for e"ample, it is necessary to estimate themeasurement#s final digit (tenths of a millimeter. From the above e"ample, the object#slength was determined to be '.$1%$ m, but the final digit of that measurement is doubtfulsince that digit was estimated. nlike a meter stick, the vernier caliper allows the fractionalpart of the smallest division to be accurately determined, not merely estimated.

The vernier consists of a main scale engraved on a fi"ed ruler and an au"iliary scaleengraved on a moveable jaw (see Figure +. The moveable jaw is free to slide along the

length of the fi"ed ruler. The main scale is calibrated in centimeters with the smallestdivision in millimeters. The moveable au"iliary scale has 1' divisions that cover the samedistance as / divisions on the main scale. Therefore, the length of the au"iliary scale is /mm. *hen the vernier is closed and properly 0eroed (see Figure $, the first mark (0eroon the main scale is aligned with the first mark on the au"iliary scale. The last mark on theau"iliary scale will then coincide with the /mm mark on the main scale.

! reading is made by closing the jaws on the object to be measured. 2ake a note ofwhere the first mark on the au"iliary scale falls on the main scale. In Figure 3, we see thatthe object#s length is between 1. cm and 1.+ cm because the first au"iliary mark isbetween these two values on the main scale. The last digit (tenths of a millimeter is found

by noting which line on the au"iliary scale coincides with a mark on the main scale. In oure"ample, the last digit is + because the third au"iliary mark lines up with a mark on themain scale. Therefore, the length of the object is 1.+ cm.


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Figure 4.*ith the jaws closed, this is whata properly 0eroed vernier caliper shouldlook like. 4lick on the image to enlarge it.

Figure 5.!n e"ample of a vernier reading.The object#s length is measured to be 1.+cm. 4lick on the image to enlarge it.

4are must be taken to insure that the vernier caliper is properly 0eroed (see Figure $.(*ith misuse, it is possible that the vernier will not read 0ero when the jaws are closed,thus leading to systematic errors. The vernier in Figure % is improperly 0eroed. To correctthis, a 0ero correction must be made. ! correction may be either positive or negative. Ifthe first mark on the au"iliary scale lies to the right of the main scale, then the reading istoo large and the error is positive. The 0ero reading in Figure % is 5'.'3 cm and should besubtracted from any measurement reading. &imilarly, if the first mark on the au"iliary scalelies to the left of the main scale 0eromark, then the error is negative and the correctionshould be added from the measurement reading.

Figure 6.!n improperly 0eroed caliper. Inthis case, the error is positive (5'.'3 cmand is to be subtracted from themeasurement reading. 4lick on the image toenlarge it.

Triple-beam balance.The triplebeam balance, or laboratory balance, measures themass of an object by balancing the unknown mass with sliding masses of known values.The triplebeam balance is usually calibrated in grams with a least count of '.1g. !measurement, then, can be made to '.'1g. It is important to note that laboratory balances

are used to make measurements of an object#s mass, not weight. (The weight of anobject, as you will learn, is the product of the object#s mass, m, and the acceleration due to
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gravity, g, or * 6 mg.

7efore the triplebeam balance is used to make a measurement, verify that the balance isproperly 0eroed. Fine adjustments may be made by turning the knob under the balancepan.

Graduated cylinder.The volume of an irregularly shaped object may be determined withthe use of a graduated cylinder. To do so, fill the cylinder with water or other li8uid andcompletely submerge the object in the li8uid. The volume of the object is measured bycalculating the difference in the water level before and after the object was submerged.9raduated cylinders are usually calibrated in milliliters or cubic centimeters (1ml 6 1cc 61cm+ but their least counts vary from 1ml to 1'ml depending on the si0e of the vessel.

1. 4lear the balance pan of any debrismake sure it is clean.

. :;ero balance: the balance.

+.


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MEASUREMENT TOOLS.doc