Length Measurement

Length measurement

The length measuring instruments we will use in this phase are:

1. Ruler

Measurements of less than 30 cm. Features also division in millimeters (mm) where 10 mm = 1 cm

10 mm = 1 cm

2. Retractable ruler

Measurements of more than one meter (m). Features also divisions in centimeters (cm) and millimeters (mm)

10 mm = 1 cm
100 cm = 1 m

3. Caliper

Measurements of centimeters (cm), millimeters (mm) up to the first sub-millimeter (10^-2 mm).

1. Suppose we want to measure the length of the physics book. Which of the following methods will give us a more correct result and why?

A few words about errors

• Each measurement includes an uncertainty which is either due to how it is measured, or due to the accuracy of the measuring instruments.
• For example, if we measure the length of an object with a ruler, the value of the measurement will depend on the exact position that we place the ruler, the assessment we do for the precise indication of the location of the edge of the object, viewing angle, etc. This results in different measurements with each other by a small random amount.

• The effect of random errors is not known in advance, but if we measure the same size many times we can estimate the its true value. This is achieved with the average value of the measurements.
• Similarly, we can estimate the corresponding error of our measurements.

2. Students will measure the length of the physics book using the ruler and will record their results in the table below in centimeters. Then, they will calculate the average (mean) of all measurements.

3. Students will measure the length of the desk using the retractable ruler and will record their results in the table below in meters. Then, they will calculate the average (mean) of all measurements.

• The caliper is an instrument used for accurate measurement of the length. It is used both for external and internal measurements and also for depth, holes, grooves measurements, etc.
• The vernier is a small scale placed on the caliper. Due to the vernier scale we are able to determine accurately sizes of  0.1 mm, 0.05 mm or even 0.02 mm.
• If the vernier is shifted by one space then the 0 of the vernier scale will be pointing the integer part of the measurement in the main scale and at the vernier scale there will be a division between 0 and 10 that will coincide with the division of the main scale or it will be closer than all the others. This division of the vernier is also the corresponding decimal place of the indication.

For example if we want to measure the diameter of a wooden pulley, we open the caliper just over the length to be measured and place the piece in the fixed caliper jaw. Then, we approach the movable jaw and read the value.

In the photo, the 0 of vernier is between 3.9 and 4 of the main scale and the 5 of vernier coincides with the 5.9 of the main scale, so the instrument reading is 3.95 cm or 39.5 mm.

4. Students will measure the length of the desk using the caliper and will record their results in the table below in millimeters. Then, they will calculate the average (mean) of all measurements.