WJEC Physics for AS Level Student Book 2nd Edition

16 WJEC Physics for AS Level Fig. 1.1.11 In all cases the component of A in the direction of the arrow is A cos θ Fig. 1.1.10 Component directions on a slope Example Use components to find the resultant of the forces in Fig. 1.1.12. Answer Total horizontal component = 10 + 12 cos 45° + 15 cos 120° [see Study point] (to the right) = 10 + 8.485 – 7.5 [Note the ‘–’ sign] = 10.99 N Total vertical component = 0 + 12 sin 45° + 15 sin 60° (upwards) = 21.48 N Combine the two components using Pythagoras’ theorem: F 2 res = 21.48 2 + 10.99 2 \ F res = 24.1 N . And θ = tan – 1 21.48 10.99 = 62.9° \ The resultant force is 24 N at 63° to the horizontal (2 s.f.). 1.1.5 Density For a material of uniform composition, the mass of a sample is directly proportional to its volume. Hence the ratio of mass to volume is a constant, which is characteristic of the material. We call this constant the density . Table 1.1.2 contains the densities of some common materials. You should make sure you can make a reasonable estimate of densities if asked. A A A θ θ θ Study point In the example, the angle between the 15 N force and the right horizontal line is 120° . Key term Density = Mass Volume ; ȡ = M V Unit: kg m – 3 F res θ 10.99 N 21.48 N 15 N 12 N 45° 60° 10 N Fig. 1.1.12 Knowledge check 1.1.7 What is the component of B in the y direction? B θ y Top tip Remember that cos ( 90° − θ ) = sin θ and sin ( 90° − θ ) = cos θ