## Measurement Techniques (A level Physics)

Learning measurement techniques is an important part of physics since physics is a science of measurement. Measurement techniques involve the ability to use a variety of different measuring instruments.

Below is a table of instruments and measurement techniques that you should to be able to use in order to pass Advanced level physics:

Measurement instrumentMeasured quantity
Ruler, vernier scale and micrometer screw gaugelength
Beam balancemass
Spring balanceweight
Protractorangle
Clock and stopwatchtime interval
Cathode-ray oscilloscopepotential difference, time intervals and frequencies of oscillating voltages
Thermometertemperature
Ammetercurrent
Voltmeterpotential difference
Galvanometerpresence of a current

## Measurement of length

### Vernier scale

A vernier scale is much more accurate for measuring small lengths because, unlike a rulers which can measure to the nearest millimetre, a vernier scale measures to the nearest 1 tenth of a millimetre.

The diagram below shows a reading on a vernier scale. To read the scale, we consider the following:

• The object being measured is between 3.3 cm and 3.4 cm long.
• The following decimal number is the marking on the vernier scale which coincides with a marking on the main scale. They coincide at the fourth marking of the vernier scale which is 0.04 cm.
• This gives a reading of 3.3 + 0.04 = 3.34 cm. ### Micrometer screw gauge To measure very small lengths such as the diameter of a fine wire or thickness of a paper we use a micrometer screw gauge. The micrometer screw gauge has two scales:

• Main scale on the sleeve
• Circular scale on the thimble which has 50 divisions in which one complete turn of the thimble moves the spindle by 0.50 mm.

The following precautions should be taken when measuring length using a micrometer screw gauge:

• Never tighten thimble too much
• Make sure the ends of the anvil and spindle are clean before making any measurements
• Close the micrometer with nothing between the anvil and spindle to check for zero error.
• If there is a zero offset error, adjust the final measurement accordingly. • take the reading on main scale.
• then take the reading on the thimble.

For example to take the reading on the instrument in the diagram above.

• reading on the barrel = 5.5mm
• reading on the thimble = 0.12mm

### Metre rule

We use a metre rule when measuring lengths of around half a metre to a metre. The smallest division on the metre rule is 1 mm which means the metre rule gives a reading with an uncertainty of 0.5 mm. Always be aware of the following sources of errors:

• if the end of the rule is worn out, the reading will be affected by a systematic error.
• sometimes the calibration of the metre rule might not be accurate.
• the reading might be affected by parallax error if you do not take your readings with your eye perpendicular to the meter rule directly above the reading.

## Measurement of mass and weight

The following are instruments for measuring mass and weight:

• top-pan balance
• lever balances
• spring balance

### Spring balance A spring balance measures is used to measure either mass or weight by measuring the effect of the force of gravity on an object. The spring balance uses Hooke’s Law which states that extension of a material is proportional to the load applied to it. In this case, it is the extension of the spring that is proportional to the weight of the object being measured. One thing to note is that even though an spring balance can be calibrated to measure mass in kg, the value of the mass will still be dependent on the value of the gravitational force. This makes not a very accurate instrument for measuring mass.

The following precautions should be taken to maintain the accuracy of the readings:

• be careful of zero error. Most spring balances have a zero error adjustment screw to adjust for the zero error.
• avoid parallax error

### Lever balances and beam balances Lever balances and beam balances are based on principle of moments and the unknown mass is balanced against a calibrated mass. Theses types of balances do not depend on the value of the force of gravity which makes them suitable for measuring mass.

The following precautions should be taken to maintain the accuracy of the readings:

• be careful of zero error. Most spring balances have a zero error adjustment screw to adjust for the zero error.
• avoid parallax error

## Measurement of Time

### Stopwatch

A stopwatch is most suitable for measuring short intervals of time. There are two types of stopwatches:

• digital stopwatch • analogue stopwatch A digital stopwatch is the more accurate of the two because it measures time in intervals of 0.01 seconds whilst an analogue stopwatch measures time in intervals of 0.1 seconds.

Errors in measurement of time usually occur due to reaction time in starting and stopping the stopwatch.

## Accuracy of measurements

There are basically two types of errors that sacrifice the accuracy of a measurement:

• random errors
• systematic errors

### Random errors

A random error is the type of error that causes readings to scatter about the true value. Random errors occur in all measurements and they usually arise from the observer estimating the last figure of an instrument reading. They are unpredictable but can be minimised by averaging a large number of readings.

One example of a random error is the reaction time when using a stopwatch.

Another example of a random error is what happens when we try to read an analogue instrument such as an analogue voltmeter. For example on a voltmeter a reading of 3.0 V usually means that the
voltage is between 2.95 V and 3.05 V.

### Systematic errors

A systematic error is the kind of error which causes readings to deviate from the true value in one direction. Systematic errors are constant and specific to the equipment being used. For example a spring balance with a zero error. They can also be caused by environmental factors such as a ruler expanding on a hot day. Systematic errors cannot be reduced by averaging, but we can eliminate them by solving their source if we know it.

One example of a systematic error is, for example a newton-meter reading 0.1 N with no weights attached to it. The means that all the readings of force measured by it will always be 0.1 N too large.

Another example of a systematic error is when you heat some water and measure the temperature rise. The measured temperature rise will show a smaller value due to the thermal energy being lost to the surroundings.

Ways of reducing the effect of systematic errors:

• eliminate zero errors.
• avoid parallax errors.
• properly design your experiment and apparatus to remove systematic errors.
• use properly calibrated instruments.

## Accuracy and Precision

Precision of an instrument means the exactness to which a measurement can be reproduced. It is limited by the smallest division on the instrument’s measurement scale. Precision is also a measurement of how close the readings are to each other.

Accuracy of an instrument is a measurement of how close the results are to the accepted value.

For example, 3 machines are calibrated to drill 6 holes through the centre of a circular disk. The results are shown below: According to the results:

• Machine A has low accuracy and low precision because its drilled holes are all over the place.
• Machine B has high precision and low accuracy because its holes are grouped together but not through the center.
• Machine C has high precision and high accuracy because its holes are grouped together and also through the centre which is the accepted value.