WJEC Physics for AS Level Student Book 2nd Edition

17 1.1 Basic physics Study point The usual symbol for density is the Greek letter ȡ (rho). Study point If mass is measured in kg and volume in m 3 , the unit of density is kg m – 3 . For mass in g and volume in cm 3 , density is in g cm – 3 . 1 g cm – 3 = 1000 kg m – 3 . Fig. 1.1.13 Range of densities air ( at sea level ) 9m 1m 0.5m water steel Knowledge check Repeat the calculation in the example using g and cm – 3 . Remember to convert the density from kg m – 3 to g cm – 3 . 1.1.8 Material ȡ / kg m – 3 ȡ / g cm – 3 Material ȡ / kg m – 3 ȡ / g cm – 3 Air* 1.29 0.00129 Steel 7900 7.90 Water 1000 1.00 Aluminium 2800 2.8 Brick 2300 2.30 Mercury 13 600 13.6 Petrol 880 0.88 Gold 19 300 19.3 * At 0°C and atmospheric pressure. Table 1.1.2 Densities The range of densities of materials on the Earth is quite large. The drawings in Fig. 1.1.13 all represent 1 tonne ( 10 3 kg ) of material. But this range pales into insignificance compared with the range of densities in the universe. For comparison, Table 1.1.3 gives the size of 1 tonne ( 1 t ) cubes of various materials outside the Earth. The range of densities shown in the table is ~ 10 33 . Material Width of 1 t cube Interstellar space 10 6 km Red giant star 100 m The Sun 0.89 m White dwarf 8.9 mm Neutron star 15 µ m Problems involving density will usually require you to convert units. Either the density or the volume often needs to be converted. If the volume is given in cm 3 and the density in kg m – 3 then: either convert the volume using 1 cm 3 = 1 × 10 – 6 m – 3 or convert the density using 1000 kg m – 3 = 1 g cm – 3 Example A rectangular block of steel, of density 7900 kg m – 3 , has length 10.0 cm , width 5.0 cm and height 4.0 cm . Calculate its mass. Answer Equation first: ȡ = M V \ M = ȡ V . We’ll use kg and m 3 as the units. Mass = 7900 kg m – 3 ( 10.0 × 10 – 2 m × 5.0 × 10 – 2 m × 4.0 × 10 – 2 m ) = 7900 kg m – 3 × 2 × 10 – 4 m 3 = 1.6 kg (2 s.f.) Fig. 1.1.14 The Cat’s Eye nebula. The white dot in the middle is a white dwarf star with a density of ~ 10 9 kg m – 3 . Table 1.1.3 Density in the universe