Motion 5 vectors introduction (shared)
- 1. A-level Physics Unit G481: Mechanics Vectors - introduction Module 1: Motion
- 2. Vectors and scalars LOs To do - in pairs 1. Explain the difference between speed and velocity. 2. Write definitions for vector and scalar. 3. Give two examples of vector and scalar quantities. Extension Give another pair of quantities that have the same relationship as speed and velocity. Module 1: Motion LO1: define scalar and vector quantities and give examples
- 3. Lesson focus • An introduction to vectors Learning objectives At the end of the lesson you will be able to: • define scalar and vector quantities and give examples; • draw and use a vector triangle to determine the resultant of two coplanar vectors such as displacement, velocity and force; • calculate the resultant of two perpendicular vectors such as displacement, velocity and force. Module 1: Motion
- 4. Learning outcomes All can • explain the difference between a scalar and a vector quantity; • give two examples each of scalars and vectors; • add two vectors using a scale drawing; • add two vectors at right angles using Pythagoras’s theorem. Some can • add components to sum vectors Module 1: Motion
- 5. Vectors and scalars LOs A scalar quantity (‘scalar’) is a physical quantity that can be completely specified by a single number together with an appropriate unit. A vector quantity (‘vector’) is a physical quantity that is completely specified by a magnitude (size) and a direction. Question Which of these quantities are scalars? displacement / kinetic energy / mass / power / velocity / weight Module 1: Motion LO1: define scalar and vector quantities and give examples
- 6. Vectors addition – useful? LOs click to link Module 1: Motion
- 7. How to show and notate a vector LOs E.g. In a diagram B a ‘The vector AB … ’ A Vectors are shown in diagrams as arrows (‘directed line segments’). Vectors are written as a bold, lower case letters in printed text ~ or AB a in handwritten text |a| means the magnitude of a. Module 1: Motion
- 8. How to add two vectors: method 1 LOs 1. parallelogram rule a a+b resultant vector b The two vectors are drawn from a common point. The diagonal of the resulting parallelogram is the vector sum (resultant). Module 1: Motion LO 2 & 3: draw and use a vector triangle to find a resultant
- 9. How to add two vectors: method 1 LOs To do - pairs Work out a method for finding the displacement (distance and angle θ) of the spider. Module 1: Motion
- 10. How to add two vectors: method 1 LOs Question How should these vectors be added? Answer Use Pythagoras’s theorem and trigonometry. OB2 = OA2 + AB2 = 0.82 + 1.22 = 2.08 m OB = 1.4 m tanθ = 0.8 / 1.2 = 0.67 θ = 37.4 ‘The spider undergoes a displacement of 1.4 m along a bearing of 37.4 N of east.’ Module 1: Motion
- 11. 2861 June, 2002 Adding vectors using Pythagoras and trig. LOs Module 1: Motion
- 12. Adding vectors by drawing LOs Module 1: Motion LO 2 & 3: draw and use a vector triangle to find a resultant
- 13. Adding vectors LOs Choose appropriate methods to answer these questions. 1. Two forces act on a wooden block, one to the right of 3 N and the other, to the left, of 5 N. Draw a scale diagram of these vectors. What are the magnitude and direction of the resultant force on the block measured from the diagram? 2. A boat leaves harbour and travels due north for a distance of 3 km and then due west for a distance of 8 km. What is the final displacement of the boat with respect to the harbour? The boat then travels a further 1 km due south. What is the new displacement with respect to the harbour? 3. A helicopter rises vertically from the ground for a distance of 600 m and then moves horizontally for a distance of 1.6 km. Draw a scale diagram to calculate the displacement of the helicopter from its starting point. Module 1: Motion LO 2 & 3: draw and use a vector triangle to find a resultant
- 14. Vectors and scalars LOs Module 1: Motion LO1: define scalar and vector quantities and give examples
- 15. Adding vectors by drawing LOs Methods for adding vectors: 1. Pythagoras theorem & trigonometry 2. scale diagram Which is most appropriate for each of these? Calculate the magnitude and direction of An aircraft has a speed relative to still air the resultant of 55 N and 25 N acting at of 150 ms-1. The pilot wishes to fly due right-angles on a small object. north when the wind velocity is 20 ms-1 towards the north-east. On what bearing should the pilot fly? Two ships, A and B, leave port P at the same time. Ship A travels due north at a A helicopter rises vertically from the steady speed of 15 km h-1 and ship B ground for a distance of 600 m and then travels N 60 E at a steady speed of 10 moves horizontally for a distance of 1.6 km h-1. What is the distance and km. Find the displacement of the direction from A to B after one hour? helicopter from its starting point. Module 1: Motion LO 2 & 3: draw and use a vector triangle to find a resultant