WJEC Physics for AS Level Student Book 2nd Edition

13 1.1 Basic physics Example Find the resultant of the 3.0 N and 4.0 N forces acting at right angles in Fig. 1.1.3. Answer 3.0 N F res θ 4.0 N Step 1: Draw the parallelogram of the forces, which in this case is a rectangle. [Note the angle, θ ]. Step 2: Use Pythagoras’ theorem to calculate the resultant force. F res 2 = 3.0 2 + 4.0 2 so ) res = 3.0 2 + 4.0 2 = 5.0 N Step 3: Calculate, θ . sin θ = opp hyp = 3.0 5.0 = 0.6 , so θ = sin – 1 0.6 = 36.9 ° \ The resultant = 5.0 N at 36.9 ° to the 4.0 N force Note that the direction given in the example answer does not specify the resultant fully, e.g. the angle could be below the horizontal. However, together with the θ in the diagram, this is enough. Most of the time you will only have to combine two vectors at right angles, which you can do using Pythagoras’ theorem and simple trig, such as sin θ = opposite hypotenuse . Knowledge check 1.1.5 is an example. (b) Motion scalars and vectors Like length, distance is a scalar quantity. The question, ‘What is the distance between Aberystwyth and Bangor?’ doesn’t ask about direction. If you know the answer, it doesn’t help you to navigate from A to B. However, ‘Bangor is 91 km due north of Aberystwyth’ would enable a pilot to fly from one to the other. This quantity, which includes direction as well as distance, is called displacement . The displacement of Bangor from Aberystwyth is 91 km north. Similarly, Flint is 65 km east of Bangor. The displacement of a point B from a point A is the shortest distance from A to B together with the direction. What is the displacement from Aberystwyth to Flint? Fig. 1.1.6 shows how we can add the displacements AB and BF to give the resultant AF displacement (shown in red). You should be able to show that AF ~ 112 km at 35.5° E of N . We calculate speed (strictly, mean speed ) using speed = distance time . Distance is a scalar so speed is as well. The vector equivalent of speed is velocity , which is defined by: velocity = displacement time The next example shows the distinction between the two. Fig. 1.1.6 Adding displacements 65 km 91 km B A F θ N Knowledge check Calculate the resultant force. Remember, magnitude and direction. 1.1.5 120 N 70 N Key term Mean speed: distance time Mean velocity: displacement time Fig 1.1.5 Adding forces at right angles Top tip A force has a direction as well as a magnitude so, if calculating a force, you need to specify the direction. Make sure you make it clear what angle you mean.