9/22/2018

2015 AQA A Level Physics

Vectors

Physical Quantities22/09/2018

Scalars

Vectors

Physical

Quantity

Vectors and Scalars22/09/2018

Scalars

Vectors

Physical

Quantity

Scalars have magnitude (size) but no direction

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

Vectors in opposite directions:

6 m s-1 10 m s-1 = 4 m s-1

6 N 10 N = 4 N

Resultant of two Vectors

Vectors in the same direction:

6 N 4 N = 10 N

6 m

= 10 m

4 m

The resultant is the sum or the combined effect of two

vector quantities

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 Vectors22/09/2018

6ms-1

10km

15km

100.1ms-1

100ms-1

Combining Vectors22/09/2018

6ms-1

10km

15km

100.1ms-1

100ms-1

Find the magnitude of the resultant vectors using PYTHAGARUS

Combining Vectors22/09/2018

6ms-1

10km

15km

100.1ms-1

100ms-1

Find the magnitude of the resultant vectors using PYTHAGARUS

18km

100.2ms-1

Resolving Vectors22/09/2018

Consider a diagonal push:

θ

This force is given by:

F1 = F sin θ

This force is given by:

F2 = F cos θ

F1

F2

θ

Resolving Vectors – example questions22/09/2018

Calculate the horizontal and vertical components

of the following:

1)

3) 4)

2)

45O35O

80O

20N 10N

12N8N

Work out the size and direction of the resultant force:

40O

Resolving Vectors – example questions22/09/2018

Calculate the horizontal and vertical components

of the following:

1)

3) 4)

2)

45O35O

80O

20N 10N

12N8N

Work out the size and direction of the resultant force:

40O

20cos45 =14.12N

20sin45 =14.12N

8.19N

5.74N

Resolving Vectors – example questions22/09/2018

Calculate the horizontal and vertical components

of the following:

1)

3) 4)

2)

45O35O

80O

20N 10N

12N8N

Work out the size and direction of the resultant force:

40O

20cos45 =14.12N

20sin45 =14.12N

8.19N

5.74N

11.8N

5.14N

2.08N

6.13N

4.05N

16.94N

17.41Nθ tan θ =

4.05/16.94

θ = 13.40

More questions on vectors22/09/2018

1) 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:

1) The displacement at the end of the journey

2) His average speed

3) His average velocity

2) 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.

3) A coin is flicked off a table with a horizontal speed of 2ms-1.

Calculate its new speed 1 second later.