WJEC Physics for AS Level Student Book 2nd Edition

12 WJEC Physics for AS Level 1.1.3 Scalar and vector quantities Some quantities, e.g. mass, are completely specified by their magnitudes. These are called scalar quantities . Others, e.g. force, have a direction too. These are called vector quantities . Think about the effects of the two forces on the sledge in Fig. 1.1.1(a) and (b). We need to specify a direction for a vector quantity, e.g. F = 25 kN horizontally or F = 25 kN due north. In both cases, the 25 kN is the magnitude, consisting of a number ( 25 ) and a unit ( kN ). (a) (b) F F Fig. 1.1.1 Forces on a sledge (a) Forces and how to add them Scalar quantities are easy to add, e.g. 3.0 kg + 4.0 kg = 7.0 kg and similarly, subtract 4.0 kg – 3.0 kg = 1.0 kg . We just use the normal rules of arithmetic. When we are adding forces, other rules apply. = and = but what about = Fig. 1.1.3 Adding forces The combined effect of two (or more) forces is called the resultant force , F res . We can calculate the sum of two forces using the parallelogram law of vector addition , as shown in Fig. 1.1.4. You could find the resultant force, Ȉ F , by drawing a scale diagram but it is more accurate to calculate it using trigonometry, e.g. the cosine rule or (if the forces are at right angles) Pythagoras’ theorem. Note that for the AS exam you only need to be able to add forces at right angles but if you are going on to higher studies you will need to be able to cope with other angles. Key terms Scalar quantity: Has magnitude only. Vector quantity: Has magnitude and direction. 3.0 kg 4.0 kg 7.0 kg + = Fig. 1.1.2 Adding masses 7N 3N 3N 1N 3N 4N 4N 4N ? Fig. 1.1.4 The parallelogram law of vector addition F 1 F 2 F res Study point What Fig. 1.1.3 means is that the combined effect of a 3 N and a 4 N force on the motion of an object could be the same as a single force of magnitude 7 N (if they are in the same direction), 1 N (if they are in opposing directions) or anything in between if they are at different angles. Study point The resultant force, F res , is often written Ȉ F (read as ‘sigma F ’). Sigma, Ȉ , means ‘the sum of’ so Ȉ F means ‘the sum of the forces’.