Physical Quantities & Measurement
Section: Motion, Forces & Energy | Syllabus: Cambridge AS Level Physics 9702
Measuring Length In the laboratory, lengths are measured using a ruler (such as a metre ruler). Although this seems straightforward, careful technique is needed to get a reliable measurement. The object must be straight and laid closely alongside the ruler - a bent wire, for example, must be straightened first Look carefully at the ends of the object - are they neat, or ragged?
It may be difficult to judge exactly where the object begins and ends Ruler markings are typically 1 mm apart but the marks themselves have some width, which affects where you line up the zero end Line one end of the object up against the zero mark on the ruler Read the other end of the object at eye level , looking perpendicular to the scale, to avoid parallax error Figure: Using a Ruler Correctly A ruler lying flat with a piece of wire placed alongside it.
The left end of the wire aligns with the 0 cm mark. At the right end, two eye positions are shown: (1) correct - eye level with the scale, looking straight down, giving a reading of 6.4 cm; (2) incorrect - eye at an angle above or below the scale, giving a different apparent reading due to parallax.
The correct reading position is labelled "Eye at scale level - no parallax error". The incorrect position is labelled with a cross "Parallax error". Measuring a Small or Curved Length Multiple measurements: for a very small length (e.g.
the thickness of one sheet of paper), measure a stack of many sheets together and divide. For example, measure 500 sheets at once and divide by 500 to find the thickness of one sheet Thread method: for a curved length (e.g.
the circumference of a cylinder), lay a thread along the curve, mark both ends on the thread, then straighten the thread against a ruler to read the length Measuring Volume Regular Shapes For a cuboid (rectangular block), measure the length, width and height with a ruler and multiply them together: Volume = length × width × height For other regular shapes (e.g.
a sphere or cylinder), measure the relevant dimensions and use the appropriate equation for the volume of that shape. Liquids - Using a Measuring Cylinder Pour the liquid into a measuring cylinder and read the scale.
Important technique points: Look at the scale horizontally (not at an oblique angle from above or below) Read the level at the bottom of the meniscus - the meniscus is the curved upper surface of the liquid (water curves downwards in a glass cylinder) Choose a cylinder of an appropriate size - using a 1-litre cylinder to measure 5 cm³ gives a very inaccurate result; use a 10 cm³ cylinder instead for small volumes Figure: Reading a Measuring Cylinder A measuring cylinder containing water.
The water surface is curved (meniscus), dipping downward in the centre. The eye of the observer is shown level with the bottom of the meniscus. A horizontal dashed line marks the correct reading point at the base of the curve.
A label reads "Read at the bottom of the meniscus". A second inset shows the wrong technique - eye above the meniscus level, reading the top of the curve - labelled "Wrong: parallax error gives reading that is too high".
Irregularly Shaped Solids - Displacement Method Most objects do not have a regular shape. To find their volume, use the displacement method : Select a measuring cylinder that is about three or four times larger than the object Partially fill it with water - enough to cover the object - and note the initial volume Carefully immerse the object in the water (lower it on a thread if needed) The water level rises because the object displaces (pushes aside) the water Volume of object = final reading − initial reading Figure: Measuring Volume by Displacement Two side-by-side measuring cylinders.
Left cylinder: water only, reading at 40 cm³, labelled "Initial volume = 40 cm³". Right cylinder: the same cylinder with an irregular stone fully submerged on a thread, water level now at 55 cm³, labelled "Final volume = 55 cm³".
Below both: "Volume of stone = 55 − 40 = 15 cm³". The stone is shown as an irregular shape beneath the water surface in the right cylinder. Measuring Time Different instruments are used depending on the length of the time interval and the precision required.
Instrument How it works Precision Limitation Analogue stopclock Hands move around a clock face; read by looking at where the hands point ~1 s Low precision; affected by human reaction time Digital stopwatch Displays time directly as numerals; started and stopped by pressing a button 0.01 s Still affected by human reaction time (~0.2 s) Electronic timer with light gate Timer starts and stops automatically when an object breaks a light beam 0.001 s Requires light gate setup; used for fast-moving objects Key Point An analogue clock has hands that move around a dial - it can measure time to no better than the nearest second.
A digital clock or stopwatch displays time in numerals and can measure to at least 0.01 s. For very short time intervals (e.g. a fast-moving trolley passin…
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