WJEC Physics for AS Level Student Book 2nd Edition

WJEC Physics for AS Level Practical check The results will be most accurate if both x and y are as large as possible. Thus, in Fig. 1.1.33, the known mass should be similar to the unknown mass. 24 1.1.8 Practical work (a) Measuring the density of solids Finding the density of a substance involves measuring the mass and the volume and dividing mass by volume. This practical is often used to test understanding of uncertainties and how to combine them. The mass is usually determined from a single reading electronic balance, so the absolute uncertainty is taken as ±1 in the last digit of the reading; e.g. a reading of 159.73 g would be taken to be ( 159.73 ± 0.01 ) g . The uncertainty in mass is often not as significant as that in the volume. How the volume is determined depends upon whether the solid object has a regular shape, such as a cuboid (e.g. a microscope slide) or a cylinder (e.g. a wire). (i) Regular solids Volume of a cuboid = ƐEK ; volume of a cylinder = $Ɛ = ʌ r 2 Ɛ = ʌ d 2 Ɛ 4 . For lengths up to ~ 15 cm , digital callipers, with a resolution of 0.01 mm are normally used. It is important when using them to check the zero reading, i.e. close the jaws and take a reading. Any reading should be subtracted from the reading with the object being measured. For lengths > 15 cm a metre rule with a resolution of 1.0 mm is normally used. The precision can be improved for a set of identical objects by laying them end to end, e.g. laying 10 microscope slides end to end gives a length of ~ 75 cm ; using a mm scale to measure the length gives a % uncertainty of 0.13%. (ii) Irregular solids The solid, e.g. a rock, is suspended from a thread and lowered into a measuring cylinder of water until it is completely submerged. The increase in volume reading is the volume of the solid. If the solid is too large for a measuring cylinder, a displacement can is used (Fig. 1.1.32) and the water overflow captured in a measuring cylinder. Disadvantages of this method are: (a) the resolution of the measuring cylinder is quite large (typically 1 – 2 cm 3 for a 100 cm 3 cylinder) and (b) the volume of water overflowing is not necessarily exactly the same as the volume of the object. (b) Measuring mass using the principle of moments In Fig. 1.1.33, the long bar is a 1 2 metre or metre rule. The triangle is any pivot – it could be as simple as an outstretched finger. The pivot is placed at the centre of gravity of the rule. When the bar balances, the ACM and the CM about the pivot are equal. \ Mgx = mgy \ Mx = my . We can also use this technique to find the mass, M , of the bar itself. The position of the C of G is found as in the Study point. A known mass, m , is hung near one end of the bar. The pivot point is found and distances x and y measured (see Fig 1.1.34). Then, as above: Mx = my . Fig. 1.1.31 Regular solids l h b d l Link See Chapter 3 for combining and reducing uncertainties. Fig. 1.1.33 Finding an unknown mass unknown mass, M known mass, m x y Mg mg Fig. 1.1.34 ‘Weighing’ a ruler y x Mg Fig. 1.1.32 Measuring the volume of a rock Study point The centre of gravity is not necessarily at the midpoint of the scale. It is a good idea to do a preliminary experiment to find it: The C of G is above the balance point. C of G mg Top tip Remember that you measure the diameter of a wire, not the radius !