Objectives

When you have completed this assignment, you will be able to:

1. Use basic instruments for measuring length: the metric scale, Vernier caliper, and micrometer.
2. Compute the volume of an object.
3. Measure the mass of an object and determine its density.
4. Record information to an appropriate number of significant figures.

Figure 1: Instruments of Measurement

Discussion

The following are some standard conversion factors:

1.00 pound (lb) = 4.448 Newtons (N) (exact) 1.00 inch = 2.54 centimeters (exact) 1.00 ft. = 30.48 cm = 0.3048 meter (exact) 1.00 mile = 1.61 10³ m (approximate)

Most metric scales are calibrated in centimeters (cm) and tenths of cm, or millimeters (mm). When measuring length using a metric scale, it is often best not to measure from the end of the scale but to start the measurement at 1.0 cm or another convenient point. The reason for this is that the end of the scale may be worn due to extensive use which might cause an error in the measurement. The following is an example of a measurement using a metric scale.

Figure 2, right: Metric Scale

Left end = 1.00 cm

Right end = 3.45 cm

Length = 2.45 cm

When using this type of metric scale, a measurement can be made accurately to 0.1 cm and can be estimated to one additional decimal place. Thus, your data, using this centimeter scale, should include two places after the decimal point.

A measure of the uncertainty of a measurement with this type of instrument is defined as one-half of the least count where the least count is the smallest measuring increment on the instrument.

Uncertainty = 0.50 (Least Count)

Thus, for a metric scale where the smallest increment is 0.1 cm, the uncertainty is 0.50 0.1 = 0.05 cm.

A more accurate instrument for measuring relatively short lengths is the Vernier caliper. The caliper has a second scale called the Vernier, which increases its measurement accuracy by a factor of 10. A sketch of a Vernier caliper follows.

m

2.92cm =>

Figure 3: Vernier Caliper

The Vernier caliper can measure accurately to 0.01 cm. In the above measurement, the top (main) scale indicates a reading between 2.9 and 3.0 cm. The bottom (Vernier) scale is used to find the next digit by determining which mark on that scale best lines up with a mark on the top scale. In this example, it is the 0.2 mm (or 0.02 cm) mark that lines up. This means that the accurate measurement is 2.92 cm. Note: the least count of the Vernier caliper is 0.01 cm.

The micrometer is the most accurate of our three measuring instruments. It has three scales. A scale on the barrel serves as the main scale, one on the rotating sleeve serves as the second scale, and the Vernier scale in on the left side of the sleeve. There are millimeter and half-millimeter markings on the barrel. One rotation of the sleeve is divided into fifty divisions and the sleeve progresses one-half millimeter during one rotation. Thus, each division on the sleeve is 0.01 mm or 0.001 cm. The Vernier scale is read to 0.001 mm or 0.0001 cm. When using the micrometer, make certain the jaws are not over tightened, but are closed with consistent firmness. A sketch of a micrometer follows.

Figure 4: Micrometer

The reading on this sketch is: Shaft: 6.5 mm Sleeve: 0.21 mm + Vernier: 0.003 mm Total: 6.713 mm

Note: the micrometer readings are in millimeters and this least count is 0.001 mm.

Equipment

The Physics Toolbox app installed on a smartphone or tablet Computer with internet U.S. Dollar bill (any denomination) U.S. Quarter (coin) Metric Ruler

Procedure

1. Length Measurement

1. Open the Physics Toolbox app on your Android smartphone or tablet. NOTE: If you do not have an Android device, please see the Measuring instruments rulers and protractors area in Resources.

2. Tap on the menu button (three parallel lines, also known as the Hamburger button) on the top left, and choose Ruler

3. Place a quarter on the screen, moving the two red lines until they just touch the edges of the coin.

4. Record the width of the coin in centimeters. Then click on the Switch unit and record the coins width in inches.

5. Using the two lengths measured in step 4, calculate and record your conversion for centimeters per inch. Compute and record the percent error for this conversion.

2. Determination of Mass

1. In Data Table 2, record a reasonable estimate of your weight in pounds.

2. Calculate and record your corresponding mass in kilograms = (weight in Newtons) / g; where g = 9.8 m/s². Use a consistent number of significant figures.

3. Length Measurement Using Metric Scale

1. Use a metric scale (ruler) to measure the length (long side) of a U.S. dollar bill of any denomination (e.g., $1 bill, $5 bill, $10 bill, etc.) at three different points. Record both the left and right-side readings (see example in Figure 2) using different left-hand readings for each measurement. NOTE: If you do not have a metric scale, please see the Measuring instruments rulers and protractors area in Resources.

2. Compute and record the average of these three lengths. Your measurements should be recorded to hundredths of a centimeter.

________________ Data Table 3: Length Measurement Using Metric Scale

Average Length. L_ave = (L₁ + L₂ + L₃) / 3 = __[answer]__ cm

Practice Using Highly Accurate Measuring Instruments

Vernier caliper practice certificate

[answer]

Metric micrometer practice certificate

[answer]

Triple beam balance practice certificate

[answer]