Measuring

Complutense University of Madrid

physics

Measuring at the lab

Prof. J. Peña

UCM - Faculty of education

essentials of physics

contents

• Introduction
• How to estimate errors
• Accuracy versus precision
• Practical examples
• The vernier caliper
• The screw gauge
• Parallax error

UCM - Faculty of education

essentials of physics

introduction

UCM - Faculty of education

essentials of physics

How to estimate errors

Errors when Reading Scales

(scale in centimeters)

We can state that the length is 128.90 cm ± 0.05 cm. Thus, we call the first term, 128.90 cm, the "central value" and the second term, 0.05 cm, the "error" or "uncertainty".

UCM - Faculty of education

essentials of physics

How to estimate errors

Errors of Digital Instruments

• The error of an electronic device is usually half of the last precision digit.
• Example: the resolution is 0.1 g. In other words, the weight is 138.15 g or 138.25 g. We can assume that the error is 0.05 g. Answer: 138.20 g ± 0.05 g

UCM - Faculty of education

essentials of physics

Accuracy versus Precision

• Accuracy is the degree of closeness of measurements of a quantity to that quantity's actual (true) value.
• Precision, also called reproducibility or repeatability, is the degree to which repeated measurements under unchanged conditions show the same results.

UCM - Faculty of education

essentials of physics

Practical examples

Measuring a small length Measuring volume of irregular and regular solids Measuring volume of an irregular piece of wood Measuring mass and volume (to get density)

More...

Examples

What is density?

UCM - Faculty of education

essentials of physics

the vernier caliper

Info

Thickness of rod =main scale + vernier reading = 35 mm + 0.7 mm = 35.7 mm

This tell you the fraction of a millimetre that you must add to the main scale reading

This tell you the lenght in millimetres

UCM - Faculty of education

essentials of physics

The screw gauge

Example

Thickness of rod: main scale reading + fractional scale reading Main scale = 2.5 mm Fractional scale = 0.17 mm Thickness = 2.67 mm

The fractional scale has 50 divisions: a complete turn represents 0.50 mm

Read the additional fraction of a millimetre from the fractional scale

Read the main scale to the nearest 0.5 mm

UCM - Faculty of education

essentials of physics

parallax error

This is the error/displacement caused in in the apparent position of the object due to the viewing angle that is other than the angle that is perpendicular to the object. The easiest solution to avoiding parallax error is to read the device directly from the front of the unit.

UCM - Faculty of education

essentials of physics

references

• Tipler P.A., Physics, 4th Edition, pp. 1-17
• Sang D., Cambridge IGCSE Physics (2nd Edition), pp. 2-10
• Holzner S., Physics I for dummies (2nd Edition), pp. 15-25
• David B. Newell and Eite Tiesinga. International System of Units (SI). https://physics.nist.gov/cuu/Units/index.html

Please send your comments and suggestions regarding this presentation to jpe01@ucm.es