Higher Physics

1
Higher Physics Unit 1

• 1.1 Vectors

2
Scalars and Vectors
Scalars
Vectors
3
Here are some vector and scalar quantities
Scalar Vector

time
force
temperature
weight
volume
acceleration
distance
displacement
speed
velocity
energy
momentum
mass
impulse
frequency
power
Familiarise yourself with these scalar and
vector quantities
4
Distance and Displacement
A helicopter takes off from Edinburgh and drops a
package over Inverness before landing at Glasgow
as shown.
Inverness
To calculate how much fuel is needed for the
journey, the total distance is required.
200 km
300 km
If the pilot wanted to know his final position
relative to his starting position, the
displacement is required.
75 km
Edinburgh
Glasgow
5
Distance Distance travelled by the helicopter
Displacement Helicopters final position relative
to starting position
6
Summary
7
Speed and Velocity
Speed is the rate of change of distance Say
the helicopter journey lasted 2 hours, the speed
would be
8
Velocity however, is the rate of change of
displacement So for the 2 hour journey, the
velocity is
9
Worksheet Scalars and Vectors Q1 Q9
10
Vector Addition
Vectors are represented by a line with an
arrow. The length of the line represents the size
of the vector. The arrow represents the direction
of the vector. The sum of two or more vectors is
called the resultant.
11
Vectors can be added using a vector diagram.
Resultant of a Vector
12
Example 1 A man walks 40 m east then 50 m south
in one minute. (a) Draw a diagram showing the
journey. (b) Calculate the total distance
travelled. (c) Calculate the total displacement
of the man. (d) Calculate his average
speed. (e) Calculate his velocity.
(a) Draw a diagram showing the journey.
13
(b) Calculate the total distance travelled.
(c) Calculate the total displacement of the
person.
Size By Pythagoras
displacement
The displacement is the size and direction of the
line from start to finish.
14
Direction
So the total displacement of the man is
(d) Calculate the speed of the man.
15
(e) Calculate the velocity of the man.
16
Example 2 A plane is flying with a velocity of 20
ms-1 due east. A crosswind is blowing with a
velocity of 5 ms-1 due north. Calculate the
resultant velocity of the plane.
Size By Pythagoras
Direction
17
Q1. A person walks 65 m due south then 85 m due
west. (a) draw a diagram of the
journey (b) calculate the total distance
travelled (c) calculate the total
displacement. Q2. A person walks 80 m due north,
then 20 m south. (a) draw a diagram of the
journey (b) calculate the total distance
travelled (c) calculate the total
displacement. Q3. A yacht is sailing at 48 ms-1
due south while the wind is blowing at 36 ms-1
west. Calculate the resultant velocity.
150 m
107 m at bearing of 232.6
100 m
60 m due north
60 ms-1 on bearing of 216.9
18
Worksheet Vector Addition Q1 Q12
19
Vector Addition Scale Diagrams
Vectors are not always at right angles with each
other. To add such vectors together, it is
easiest to use a scale diagram.
Example 1 An aircraft travels due north for 100
km. The aircraft changes its course to 25 west
of north and travels for a further 250 km. Find
the displacement of the aircraft.
20
Step 1 Choose a suitable scale.
25 km 1 cm
Step 2 Draw diagram using a pencil and a
protractor.
13.7 cm
Step 3 Measure the length of the resultant vector
and convert using your scale.
13.7 x 25 km 342.5 km
Step 4 Measure the size of the angle using a
protractor.
21
Example 2 A ship sailing due west passes buoy X
and continues to sail west for 30 minutes at a
speed of 10 km h-1. It changes its course to 20
west of north and continues on this course for 1½
hours at a speed of 8 km h-1 until it reaches
buoy Y. (a) Show that the ship sails a total
distance of 17 km between marker buoys X and
Y. (b) By scale drawing or otherwise, find the
displacement from marker buoy X to marker buoy Y.
(a)
Stage 1
Stage 2
Total
22
(b)
1 km 1 cm
Length of Vector 14.4 x 1 km 14.4 km
14.4 cm
Direction of Vector ? 52
Answer Range 14.5 km 0.4 km 52 2
23
Worksheet Vector Addition (Scale Diagram) Q1
Q3
24
Resolution of Vectors
Horizontal and Vertical Components To analyse a
vector, it is essential to break-up or resolve
a vector into its rectangular components. The
rectangular components of a vector are the
horizontal and vertical components.
V

OR
25
The horizontal and vertical component of the
vector can be calculated as shown.
26
Example 1 A ship is sailing with a velocity of 50
ms-1 on a bearing of 320. Calculate its
component velocity (a) north
40
27
(b) west
28
Example 2 A ball is kicked with a velocity of 16
ms-1 at an angle of 30 above the
ground. Calculate the horizontal and vertical
components of the balls velocity. Horizontal
16 ms-1
VV
30
VH
29
Vertical
30
Slopes Parallel and Perpendicular Components On
a slope, the components of a vector are parallel
and perpendicular to the slope.
?
x
resultant
?
Perpendicular Component
Parallel Component
31
Example 1 A 10 kg mass sits on a 30
slope. Calculate the component of weight acting
down (parallel) the slope.
30
32
Worksheet Resolution of Vectors Q1 Q8