Appendix 1

Appendix 4: Measuring Instruments

The Metric Ruler: The scale of this metric measuring instrument is divided into centimeters and millimeters. Since the millimeter is the smallest division on the scale, the accuracy with which an object can be measured with this instrument is limited to one millimeter. A reading to tenths of a millimeter can only be estimated.

The English Ruler: The smallest division on the scale of an English ruler is one-sixteenth of a inch. Therefore, length an accuracy of one-sixteenth of an inch.

The Vernier Caliper:

The Vernier caliper is a metric measuring device which consists of a fixed part (a fixed jaw and the main scale) and a movable jaw, which has a vernier scale engraved on it. The vernier slides along the main scale so that the graduations of the two scales can be compared. The fixed scale is divided into centimeters and millimeters. The vernier scale is divided so that ten divisions on it correspond to nine divisions on the main scale. Therefore, the length of each vernier division is nine-tenths the length of a main-scale division. (See illustrations.) When the jaws are closed, the zero line on the vernier (the first line on the left end) coincides with the zero line on the main scale. In this position, it can be seen that the first vernier division is 0.1 mm away from the first main scale division, the second vernier division is 0.2mm away from the second main-scale division, and so forth. If the jaws are opened slightly, one can tell what fraction of a main-scale division the vernier index (zero line) has moved by noting which vernier division coincides with a main-scale division.

In making a measurement with the vernier caliper, the jaws are dosed on the object to be measured, and the position where the zero line of the vernier falls on the main scale is noted. This reading gives a measurement that is accurate to one millimeter. To obtain the fractional part of the main-scale division, the line on the vernier which coincides exactly with a line on the main scale is read. (See illustrations.) Therefore, the auxiliary scale of the vernier enables one to make a measurement which is accurate to one tenth of a millimeter.

If the vernier does not read zero when the jaws are completely closed, a zero correction -- either positive or negative -- must be applied to every reading. The zero correction is always made be subtracting the zero reading from the final reading.

The micrometer caliper is an instrument used to make precise measurements of short lengths. It consists of a carefully machined screw which is mounted in a C-shaped frame. (See illustration.) By rotating the screw, the jaws can be opened or closed. The object to be measured is placed between the end of the screw and the projecting end of the frame, called the anvil. The screw is then advanced until the object is gripped firmly between the jaws of the instrument. Use of the ratchet (located on the far end of the screw) makes it possible to tighten the screw by the same amount each time, and to avoid forcing the screw once the object has been secured in the jaws. NOTE: If the ratchet is absent, care must be taken not to force the screw as this can damage the instrument.

The micrometer caliper you will be using consists of a screw with a pitch of 0.5 mm (the distance advanced by the screw in turning through one revolution), a longitudinal scale engraved along a barrel containing the screw, and a circular scale engraved around a thimble which rotates with the screw and moves along the scale on the barrel. The longitudinal scale is divided into millimeters, while the circular scale has 50 divisions. Since the pitch of the screw is 0.5 mm, if the thimble is rotated through one scale division, the screw moves a distance of one-fiftieth of 0.5 mm, or 0.01 mm. Therefore, measurements can be made with an accuracy of 1/100 of a millimeter. Readings can be estimated to 1/1000 of a millimeter by estimating tenths of a thimble-scale

division.

The micrometer is read by noting the position of the edge of the thimble on the longitudinal scale (giving measurement to the nearest whole main-scale division) and the position of the axial line of the barrel on the circular scale (giving the fractional part of the measurement). The two readings are then added together. since two revolutions of the screw are required for an advancement of one millimeter, it is necessary to be careful to note whether the reading on the circular scale refers to the first half or the second half of the millimeter. (In the illustration, the reading is 7.75 mm.)

If the micrometer does not read zero when the jaws are completely closed, a zero correction -either positive or negative -- must be applied to every reading. The value of the zero reading is made by noting the reading on the circular scale when the screw is in contact with the anvil.

Formulas

DENSITY: The density of a substance is defined as its mass per unit volume. Density can be calculated mathematically using the formula:

where m is the mass (which will be in grams for the Measurement Lab), V is the volume (in cubic centimeters), and D is the density (in units of grams per cubic centimeter).

VOLUME: Volume can be defined as the measure of the capacity or space occupied by a three dimensional figure (i.e.: a solid). Therefore, measurements of volume are made in cubic units. The correct formula for finding the volume of an object depends on the shape of the object. The volume of a cylindrical object is given by the formula: where r is the radius, d is the diameter (2 r), and L is the length (height) of the object being measured.

The volume of a spherical object is given by the formula:

The volume of an irregularly shaped solid can be determined by measuring the volume of liquid that it displaces.

AREA: Area is a measure of the size of a closed region, and is expressed as the number of square units contained in the region. To find the area of a square or rectangular shaped region, one simply multiplies its length times its width, or: A = LW

To find the surface area of an object with a curved surface (i.e.: a right circular cylinder), one would use the formula: A = 2x rL

The volume of an irregularly shaped solid can be determined by measuring the volume of liquid that it displaces.

To find the surface area of an object with a curved surface (i.e.: a right circular cylinder), one would use the formula: A = 2x rL

2-D Geometric Shapes:

Rectangle: Parallelogram Circle