A basic course in vectors in preparation for A level physics.

1. 1.1 Forces and Vectors

2. Forces
• What is a force?
• A force is a PUSH or PULL experienced by an
object.
• The ‘F’ in F=ma represents ‘Force’
• What different types of forces are there?

3. The Earth PULLS the moon
The moon PULLS the Earth
The shoe PUSHES the ground
The ground PUSHES the shoe
The man PUSHES down on the chair
The chair PUSHES up on the man

4. Vectors
• To understand a force’s influence on the
world, you need to know two qualities about
the force …
• 1. Its magnitude (or size)
• 2. Its direction
• Quantities whose magnitude and direction are
important are called VECTORS
• Quantities whose magnitude only is important
are called SCALARS

5. Vectors and Scalars
Vectors
• Force
• Velocity
• Acceleration
• Displacement
• Field Strength
Scalars
• Mass
• Speed
• Length
• Distance
• Energy

6. Velocity and speed
• Bill runs at a speed of 4m/s
• Brian runs at a speed of 6m/s
• Who will win the race?
• It depends which direction each is running in.
• VELOCITY is important
• While running, both athletes run into a tree.
• Who feels the most pain?
• Brian
• Here, only SPEED is important.

7. More on Vectors
• For objects moving in opposite directions …
• One direction will be seen as POSITIVE
• The opposite direction will be see as …
– NEGATIVE
• Quantities acting neither in the same direction
nor the opposite direction will require the
help of SINE and COSINE.

8. Question
• Tony lives 2km away from his work. In the
morning, he leaves home at 8.30am and
arrives at work at 9am. In the evening, he
leaves work at 5pm and returns home at
5.30pm.
• Over the course of the day, what is
Tony’s:
– Total distance? (Scalar)
– Total displacement? (Vector)
– Average speed? (Scalar)

9. • Draw a graph showing how each of these 4
quantities change with time.
Distance
Time
Displacement
Time
Speed
Time
Velocity
Time

10. Adding Scalars
A man drives from his home 3km to the
nearest KFC. After collecting his meal, he then
drives another 2km. How far has he driven in
total?
5km
• Adding scalars is very easy
• You just need the normal rules of arithmetic
• (ie: ‘+’).

11. Adding Vectors
• A man drives from his home 3km to the
nearest KFC. After collecting his meal, he then
drives another 2km. How far is he from his
home?
• Assuming that he drives in a straight line
before and after KFC …
• His displacement depends on which direction
he drives after KFC
• The solution could be anything between …
• 1 and 5km

12. • The sum of two or more vectors …
• Is the SINGLE vector …
• Which would have the same effect as the two or more
original vectors.
• Draw arrows to represent each vector
• Align arrows into a ‘snake so that one tail starts where
another head finishes
• Join the head and tail of the snake
• This is the SUM of your vectors, or RESULTANT
vector.
Home KFC
New
positionMagnitude
angle

13. Question
• What is the SUM of the
forces, or RESULTANT
force on this crate?
• Move the arrows and draw
in the RESULTANT vector.
70 N
50 N

14. Answer
70 N
50 N
m
a
m =
(70^2 + 50^2)^0.5
=86 N
a =
inv. tan (50/70)
=35.5 deg.

15. Question 2
• What is the SUM
of the forces, or
RESULTANT force
on this crate?60 60
• In a closed loop,
the RESULTANT
vector is zero.

16. Resolving Vectors
In the same way that two vectors can be combined
into one
It can also be useful to …
Divide one vector into two COMPONENTS
This is called RESOLVING
a
VSinea
V Cos a
The component next to the angle
is ‘Cosine (a)’
The component far from the angle
is ‘sine (a)’
V

17. Resolving Vectors
In the same way that two vectors can be combined
into one
It can also be useful to …
Divide one vector into two COMPONENTS
This is called RESOLVING
a
VSinea
V Cos a
The component next to the angle
is ‘Cosine (a)’
The component far from the angle
is ‘sine (a)’
V

18. Resolving Vectors
In the same way that two vectors can be combined
into one
It can also be useful to …
Divide one vector into two COMPONENTS
This is called RESOLVING
a
VSinea
V Cos a
The component next to the angle
is ‘Cosine (a)’
The component far from the angle
is ‘sine (a)’

19. Resolving Vectors
In the same way that two vectors can be combined
into one
It can also be useful to …
Divide one vector into two COMPONENTS
This is called RESOLVING
a
Sinea
Cos a
The component next to the angle
is ‘Cosine (a)’
The component far from the angle
is ‘sine (a)’

20. Question
• A boat intends to take
the shortest route
across a river (AB)
• However, it is pushed
sideways by the
current at an angle of
15 degrees
• If the boat’s actual
velocity is 10 m/s…
• What velocity is due to:
– The boat’s engine?
– The current?
A
B
1510m/s

21. Homework
AS & A2 Success Physics
Page 29
Questions 1 & 2