Exp.1 Theory

In most physics experiments, we need to make precise measurements. Many accurate, and sensitive instruments have been developed to make measurements of various physical quantities. In this experiment, you will use a meterstick, a vernier caliper, and a micrometer caliper to measure length; a balance to measure mass; and a stop watch to measure time.

Most of the readings in this experiment will be made using the "cgs" system of unit, that is centimeter (cm) for length, gram (g) for mass, and second (s) for time. Some length measurements will also be made by using millimeter (mm) as the unit.

Measurement of Length

Meterstick
The smallest scale division on an ordinary meterstick is a millimeter, which is equal to a tenth of a centimeter, since 1 cm = 10 mm. This means the last accurate digit in a reading is to millimeters. Consequently, the next digit that has to be estimated by interpolation is to tenths of a millimeter. For example, the end of the object to be measured falls somewhere between 1.2 and 1.3 cm.
We estimate that the right end of the object falls 60% of the distance between the 1.2 and 1.3 cm marks. 60% of the distance between adjacent millimeter marks is equal to a distance of 0.6mm, which is equivalent to 0.06 cm. Thus, the reading is 1.26 cm which is the sum of (1.2 + 0.06) cm. We see that the measurements made with a meterstick can be estimated to hundredths of a centimeter.
Vernier Caliper
A vernier caliper consists of a fixed part and a moveable jaw.
The fixed part includes a stem, that has a linear scale (called the main scale) engraved on it. The moveable jaw is free to slide along the fixed stem and has a small auxiliary scale (called the vernier scale) etched on it.

The main scale is 12 cm long, and the numbers etched onto it are in cm unit. For example, the numeral 7 represents 7 cm. Each centimeter interval is divided into 10 smaller divisions. Thus each division is 1 mm long.
The vernier scale, located below the main scale, is 0.9 cm long, and also has ten divisions. Thus each division on the vernier scale is 0.9 mm.
When the jaws of the caliper are closed, the zero line at the left end of the vernier scale (called the index) coincides with the zero line on the main scale. However, the first vernier division is: 1 - 0.9 = 0.1 mm away from the the next main-scale division, the second vernier division is: 2 - 1.8 = 0.2 mm away from the next main-scale division, and so on.

The object to be measured is placed snugly between the jaws. The length to be measured is the distance from the zero line of the main scale to the position of the index. In the figure below, the reading falls between 5.0 and 5.1 cm marks on the main scale. Because of the relationship between the vernier scale and main scale divisions discussed above, the digit in the second decimal place is accurately read as the vernier-scale mark that lines up with any main-scale mark (it is immaterial which main-scale mark it coincides with). In the present example, the 8-mark on the vernier scale coincides with a main-scale mark. Thus, the reading is 5.080. Notice that a zero is added to the third decimal place as the first doubtful figure. Measurements made with a vernier caliper can therefore be estimated to thousandths of a centimeter.
A vernier caliper can be used to measure the inside diameter of a cylinder by inserting the jaws into the cylinder and opening them until they are in snug contact with the inner walls.
A vernier caliper is also useful in determining the depth of an opening in an object, such as the depth of a cup. This is accomplished by first placing the right end of the stem in contact with the top surface of the opening. Then extend the blade (which is protruding out of the right end of the stem) until it is in contact with the bottom of the opening. The depth of the opening is then given by the reading of the vernier caliper.
Micrometer Caliper
A micrometer caliper, commonly called a "mike", is used for making accurate measurements of short lengths (less than 2.5 cm). It consists of a frame, which is semicircular in shape, a moveable rod which fits inside a sleeve (which looks like a barrel), and a thimble which rotates over the sleeve.
A precision thread is machined on one end of the rod, such that the rod is moved by rotating the thimble. The jaws of a micrometer caliper are the anvil (which is a fixed surface) and the left end of the movable rod.
The object to be measured is first placed loosely between the anvil and the rod. The final adjustment is then made by rotating the ratchet at the end of the micrometer. The ratchet allows the screw mechanism to slip in order to prevent too much force from being applied on the jaws, such that no damage is done to the precision threads, jaws, and the object being measured.
A micrometer caliper has a linear scale (horizontal) engraved on its sleeve, and a circular scale (vertical) engraved on the thimble. One interval on the linear scale is 1 mm long. Some of the micrometer calipers have half-millimeter marks etched below the linear scale. The circular scale has 50 divisions, and one complete revolution moves the thimble 0.5 mm along the the linear scale. Thus, one division corresponds to (0.5 mm : 50) = 0.01 mm.
The length to be measured is the distance from the zero line of the linear scale to the left edge of the circular scale. In the figure below, the reading falls between 6.5 and 7.0 mm marks on the linear scale. Notice that the horizontal axis of the linear scale crosses the circular scale somewhere between the 48th and 49th marks; let's estimate it to be 50% of the interval. Therefore, the total reading is (6.5mm + 48.5 x 0.01mm) = 6.985 mm. In cm unit, it reads 0.6985 cm.
Measurements made with a micrometer caliper can therefore be estimated to ten thousandths of a centimeter.
For micrometer calipers that do not have half-millimeter marks etched below the linear scale, the circular scale has 100 divisions, and one complete revolution moves the thimble 1 mm along the the linear scale. Thus, one division corresponds to (1 mm : 100) = 0.01 mm. The reading is determined in a similar way as that discussed above.

Measurement of Mass
In physics, mass of an object represents the quantitative measure of the inertia of the object. Inertia can be thought of the reluctance of the object to have its state of motion changed; in other words, it tends to remain at rest, or if in motion, it tends to keep in motion with a constant velocity. It is important to note that mass of an object is not equivalent to its weight. Weight of an object represents the gravitational force acting on it.

The balance you will use in this experiment consists of a double beam with scales etched on each beam (the lower beam reads up to 200 grams in 10-g divisions, and the upper beam reads up to 10 grams in 0.1-g divisions), a pointer, and two pans attached to either side of the beam, so that the beam and the pans swing freely. The pans should be balance when they are empty, and the pointer should rest on the zero mark etched on the scale located midway between the two pans. An adjustment nut at the end of the beams can be used to calibrate the balance.

To measure the mass of an object, place the object on the left-hand pan of the scale. Slide the movable permanent mass attached to the lower scale until the right-hand side of the balance moves down. This means the mass is too large. Move the permanent mass back one unit on the lower scale such that the balance moves upward, indicating that there is not enough mass to balance the scale. Now move the smaller permanent mass on the top scale to the right until the beam is balanced. The mass of the object is then equal to the sum of the masses indicated on each scale.

The maximum mass that can be measured directly in this fashion is 210 grams. For objects that are over 210 g, a known mass (chosen from a mass set) can be placed on the right-hand pan of the scale (see the figure above). After balancing the scale, the mass of the object is then the sum of the masses indicated on each scale plus the additional mass on the right-pan.

Measurement of Time
A digital timer (a stopwatch) will be used to measure time interval. The timer displays the elapsed time in minutes, seconds, and hundredths of a second. The last digit displayed is the first doubtful figure. For instance, the time displayed is 12.56 s; the first uncertain figure in this reading is the "6" in the hundredths place.