Mechanics & Materials 2015 AQA A Level Physics Vectors 9/17/2018

Physical Quantities 17/09/2018 Scalars Vectors Physical Quantity

Vectors and Scalars Physical Quantity 17/09/2018 Scalars Vectors Scalars have magnitude (size) but no direction Physical Quantity Vectors have both magnitude and direction

Vector or scalar? Vector Scalar ?? weight velocity mass displacement speed acceleration distance energy force

Vector or scalar? Vector Scalar ?? Weight velocity mass displacement speed acceleration distance energy force

Resultant of two Vectors The resultant is the sum or the combined effect of two vector quantities Vectors in the same direction: 6 N 4 N = 10 N 6 m = 10 m 4 m Vectors in opposite directions: 6 m s-1 10 m s-1 = 4 m s-1 6 N 10 N = 4 N

Combining vectors When two vectors are joined tail to tail Complete the parallelogram The resultant is found by drawing the diagonal When two vectors are joined head to tail Draw the resultant vector by completing the triangle

Combining perpendicular Vectors 17/09/2018 15km 10km 100ms-1 6ms-1 100.1ms-1

Combining Vectors 15km 10km 100ms-1 6ms-1 17/09/2018 15km 10km 100ms-1 6ms-1 Find the magnitude of the resultant vectors using PYTHAGARUS 100.1ms-1

Combining Vectors 15km 10km 18km 100ms-1 6ms-1 17/09/2018 15km 10km 18km 100ms-1 6ms-1 Find the magnitude of the resultant vectors using PYTHAGARUS 100.1ms-1 100.2ms-1

Resolving Vectors θ Consider a diagonal push: This force is given by: 17/09/2018 Consider a diagonal push: This force is given by: F1 = F sin θ F1 F θ θ F2 This force is given by: F2 = F cos θ

Resolving Vectors – example questions 17/09/2018 Calculate the horizontal and vertical components of the following: 1) 2) 20N 10N 35O 45O Work out the size and direction of the resultant force: 3) 4) 8N 12N 40O 80O

Resolving Vectors – example questions 17/09/2018 Calculate the horizontal and vertical components of the following: 20sin45 =14.12N 1) 2) 20N 10N 5.74N 35O 45O 20cos45 =14.12N 8.19N Work out the size and direction of the resultant force: 3) 4) 8N 12N 40O 80O

Resolving Vectors – example questions 17/09/2018 Calculate the horizontal and vertical components of the following: 20sin45 =14.12N 1) 2) 20N 10N 5.74N 35O 45O 20cos45 =14.12N 8.19N Work out the size and direction of the resultant force: 3) 4) 16.94N 11.8N 8N 17.41N 5.14N tan θ = 4.05/16.94 θ = 13.40 12N θ 40O 80O 6.13N 4.05N 2.08N

More questions on vectors 17/09/2018 Joe hikes 5km north and then 9km east. This journey takes him 2 hours. Draw, on graph paper, a scale diagram to show this movement and calculate: The displacement at the end of the journey His average speed His average velocity An aeroplane takes off with a velocity of 110ms-1 at an angle of 25O to the horizontal runway. Calculate the horizontal and vertical components of the plane’s velocity. A coin is flicked off a table with a horizontal speed of 2ms-1. Calculate its new speed 1 second later.