Measurement in Physics

Introduction

Physics depends on measuring quantities accurately. In the Kenyan Senior School CBC (KICD) Physics curriculum, you learn to use instruments, record units correctly and reduce errors in experiments.

Physical quantities and SI units

A physical quantity can be measured.

• Base (fundamental) quantities: length (m), mass (kg), time (s), temperature (K), electric current (A).
• Derived quantities are combinations of base quantities: area (m2), volume (m3), speed (m/s), density (kg/m3), force (N).

Prefixes: kilo (k) = 1000; centi (c) = 1/100; milli (m) = 1/1000; micro = 1/1,000,000.

Measuring length

• Metre rule: accuracy to 1 mm.
• Vernier callipers: accuracy to 0.1 mm (0.01 cm). Reading = main scale reading + (vernier division aligned x 0.01 cm).
• Micrometer screw gauge: accuracy to 0.01 mm. Reading = sleeve reading + thimble reading.

Always check for zero error before use.

Measuring volume

• Regular solid: length x width x height.
• Liquids: measuring cylinder (read at the bottom of the meniscus, with the eye level).
• Irregular solid: displacement method, subtracting the initial volume from the final volume after submerging it.

Measuring mass and time

Use beam balances or electronic scales for mass; use stopwatches for time. For small times such as a pendulum swing, time many oscillations and divide.

Density

Density is the mass per unit volume. rho = m / V Units: kg/m3 or g/cm3. 1 g/cm3 = 1000 kg/m3. Water has density 1 g/cm3 (1000 kg/m3). Objects less dense than water float.

Errors in measurement

• Parallax error - eye not level with the scale.
• Zero error - instrument not starting at zero.
• Random errors - small unpredictable variations; reduce by repeating and averaging. Accuracy is how close a reading is to the true value; precision is how close repeated readings are to each other.

Worked example 1

A stone is lowered into a measuring cylinder holding 40 cm3 of water. The level rises to 55 cm3. Its mass is 45 g. Find its density. Answer: Volume = 55 - 40 = 15 cm3. Density = 45 / 15 = 3 g/cm3.

Worked example 2

A micrometer has a sleeve reading of 5.5 mm and thimble reading of 0.27 mm. Find the diameter. Answer: 5.5 + 0.27 = 5.77 mm.

Worked example 3

Convert 2.7 g/cm3 to kg/m3. Answer: 2.7 x 1000 = 2700 kg/m3.

Try it

• Measure the thickness of a coin with vernier callipers and record the zero error.
• Find the density of a pebble using displacement.
• Convert 0.5 kg/m3 to g/cm3.
• Explain how to reduce parallax error.