Experimental techniques practice questions.

A stroboscope flashes at an adjustable rate and makes a spinning fan appear to stand still. Which quantity is it being used to measure?

• The rotational frequency of the spinning fan
• The linear speed of the tip of one blade
• The angular acceleration of the fan blades
• The moment of inertia of the whole fan

Answer: The rotational frequency of the spinning fan

When the flash rate equals the rotation rate the fan looks frozen, so the strobe reads the rotational frequency directly. The trap is that flash rates of f/2, f/3, … also freeze the image, so one blade is marked and the highest flash rate that gives a single stationary image is taken.

Which instrument is most suitable for measuring the diameter of a wire of about 0.4 mm?

• A metre rule graduated in millimetres along its edge
• A steel tape measure that is graduated in millimetres
• A micrometer screw gauge reading to 0.01 mm
• A digital balance that reads to the nearest 0.01 g

Answer: A micrometer screw gauge reading to 0.01 mm

On a millimetre scale the reading uncertainty (about ±0.5 mm) is larger than the 0.4 mm being measured, whereas the micrometer's 0.01 mm resolution gives about 2.5 %. The usual error is to pick an instrument whose resolution is the same size as the quantity being measured; the balance measures mass, not length.

A student finds the period of a pendulum by timing 20 complete oscillations rather than one. What is the main reason for doing this?

• The reaction-time uncertainty is shared over 20 periods, so its percentage effect falls
• Timing 20 oscillations removes the systematic error caused by a stopwatch that runs slow
• The pendulum swings much more regularly once it has completed several oscillations
• The amplitude of the swing stays constant for far longer when many swings are timed

Answer: The reaction-time uncertainty is shared over 20 periods, so its percentage effect falls

The ±0.2 s or so of reaction time is the same whether one or twenty swings are timed, so dividing by 20 divides its percentage contribution by 20. It does nothing to a stopwatch that is miscalibrated — that is a systematic error.

A sample of water must be held at 60 °C for several minutes. Which technique is the most appropriate?

• Heat the beaker directly with a Bunsen burner and remove it at 60 °C
• Stand the beaker in a thermostatically controlled water bath set to 60 °C
• Heat the water to boiling and then allow it to cool down to 60 °C
• Warm the beaker on a hotplate and stir it continuously with the thermometer

Answer: Stand the beaker in a thermostatically controlled water bath set to 60 °C

A water bath supplies heat at the rate needed to hold the temperature, so the control variable stays fixed. Stirring with the thermometer risks breaking the bulb and still leaves the temperature drifting.

An ammeter and a voltmeter are added to a circuit so that the resistance of a lamp can be found. How should they be connected?

• Ammeter connected in parallel with the lamp, voltmeter in series with it
• Both the ammeter and the voltmeter in series with the lamp
• Both the ammeter and the voltmeter in parallel with the lamp
• Ammeter in series with the lamp, voltmeter in parallel with the lamp

Answer: Ammeter in series with the lamp, voltmeter in parallel with the lamp

The ammeter must carry the lamp current, so it goes in series; the voltmeter must sit across the lamp to read the potential difference, so it goes in parallel. Swapping them short-circuits the lamp through the ammeter.

A digital voltmeter displays 4.28 V. Which statement about the uncertainty of this reading is correct?

• There is no uncertainty, because the display gives an exact numerical value
• The uncertainty is half of the smallest scale division, so it is ±0.005 V
• The uncertainty is taken as ±0.01 V, one unit in the last displayed digit
• The uncertainty cannot be stated at all until the reading has been repeated

Answer: The uncertainty is taken as ±0.01 V, one unit in the last displayed digit

The half-division rule applies to analogue scales that have to be read by eye; a digital display is quoted to ±1 in its last digit. Assuming a digital reading is exact is the classic mistake.