Intermediate 2 Physics
In addition to set homework you will be expected to
finish off class notes and regularly review work against
the learning outcomes.
You will be expected to take responsibility for your own
learning and for seeking help when you need it. At the
end of each section, you must ensure all notes are
completed and examples attempted.
In unit 1 we will learn about
the physics of motion.
We will focus on the language,
principles and laws which
describe and explain the
motion of an object. Kinematics
is the science of describing the
motion of objects using words,
diagrams, numbers, graphs
and equations.
The goal is to develop mental models
which describe and explain the motion of
real-world objects.
Key words: vectors, scalars, distance,
displacement, speed, velocity.
By the end of this lesson you will be able to:
Describe what is meant by vector and scalar quantities
State the difference between distance and
displacement
State the difference between speed and velocity
State that force is a vector quantity
Use a scale diagram to find the magnitude and direction
of the resultant of two forces acting at right angles to
each other.
Scalars and Vectors
Imagine a boat
making a distress
call to the
coastguard.
The boat tells the
coastguard he is 60 km
from Aberdeen.
Scalars and Vectors
Is this enough
information for the
coastguard to find
the boat?
Scalars and Vectors
Scalars and Vectors
The coastguard needs both
distance (size)
and
direction
to find the boat.
Scalars and Vectors Definition
A scalar is a quantity which has only
magnitude (size). It is defined by a
number and a unit.
A vector is a quantity which has
magnitude (size) and direction. It is
defined by a number, a unit and a
direction.
Distance and Displacement
How
far has
thefrom
girl walked?
A pupil
walks
her house to her school.
How
has her
brother
Herfar
brother
makes
the walked?
same journey, but via a
shop.
50 m
30 m
40 m
Distance and Displacement
The girl has walked 50 m.
Her brother has walked 70 m.
Distance is a
scalar
quantity – it
can be defined
simply by a
number and
unit.
50 m
30 m
40 m
Distance and Displacement
Distance is simply a measure of
how much ground an object has
covered.
50 m
30 m
40 m
Distance and Displacement
But how far out of place is the
girl? And her brother?
Displacement is a vector which
requires number, unit and
direction.
50 m
30 m
40 m
Distance and Displacement
The girl has a displacement of
50 m at a bearing of 117° East
of North.
50 m
30 m
40 m
Distance and Displacement
What is her brother’s
displacement?
50 m
30 m
40 m
Distance and Displacement
Her brother has a displacement
of 50 m at a bearing of 117°
(117° East of North).
50 m
30 m
40 m
Distance and Displacement
Their displacement (how far out
of place they each are) is the
same.
50 m
30 m
40 m
Speed and Velocity
Speed is a scalar quantity requiring
only magnitude (number and unit).
Velocity is a vector, requiring
magnitude and direction.
Speed and Velocity
Speed tells us how fast an object is
moving.
Velocity tells us the rate at which an
object changes position.
Speed and Velocity
Imagine a person stepping one step
forward, then one step back at a speed of
0.5 ms-1.
What is the person’s velocity? Remember
velocity keeps track of direction. The
direction of the velocity is the same as
the direction of displacement.
Speed and Velocity
distance
Average speed 
time
and
change in position
Average velocity 
time
Key words: vectors, scalars, distance,
displacement, speed, velocity.
By the end of this lesson you will be able to:
Describe what is meant by vector and scalar quantities
State the difference between distance and
displacement
State the difference between speed and velocity
State that force is a vector quantity
Use a scale diagram to find the magnitude and direction
of the resultant of two forces acting at right angles to
each other.
Distance and Displacement
Virtual Int 2 Physics – Scalars and Vectors – Distance and Displacement
Speed and Velocity
Virtual Int 2 Physics – Scalars and Vectors – Speed and Velocity
A physics teacher walks 4 meters East, 2
meters South, 4 meters West, and finally 2
meters North. The entire motion lasted for
24 seconds. Determine the average speed
and the average velocity.
The physics teacher walked a distance of 12 meters in 24
seconds; thus, her average speed was 0.50 m/s.
However, since her displacement is 0 meters, her average
velocity is 0 m/s. Remember that the displacement refers to
the change in position and the velocity is based upon this
position change. In this case of the teacher's motion, there is
a position change of 0 meters and thus an average velocity of
0 m/s.
Scalar
or
Vector?
Virtual Int 2 Physics – Scalars & Vectors - Introduction
Key words: vectors, scalars, resultant, scale diagram
By the end of this lesson you will be able to:
Describe what is meant by vector and scalar quantities
State the difference between distance and
displacement
State the difference between speed and velocity
State that force is a vector quantity
Use a scale diagram to find the magnitude and direction
of the resultant of two forces acting at right angles to
each other.
Vectors
Vectors can be represented by a line
drawn in a particular direction.
The length of the line represents the
magnitude of the vector.
The direction of the line represents the
direction of the vector.
Addition of Vectors
When two or more scalars are added
together, the result is simply a numerical
sum.
For example a mass of 3kg and a mass of
5 kg, when added, make a mass of 8kg.
Addition of Vectors
When two or more vectors are added
together, providing they act in the same
direction, the addition is straightforward.
5N
8N
3N
Addition of Vectors
If they are acting in opposite directions
5N
2N
3N
Addition of Vectors
The resultant of two or more vectors
which act at angle to each other can be
found either using a scale diagram, or by
Pythagoras and trigonometry.
Virtual Int 2 Physics – Scalars and Vectors -Adding Vectors
To find the resultant of a set of
vectors using a scale diagram
1.
2
3
Decide on a suitable scale and write this
down at the start
Take the direction to the top of the page as
North. Draw a small compass to show this.
Draw the first vector ensuring it is the
correct length to represent the magnitude
of the vector, and it is the correct
direction.
To find the resultant of a set of
vectors using a scale diagram
4.
5
6
Draw an arrow to represent the second
vector starting at the head of the first.
Vectors are always added head to tail.
The resultant vector can now be determined
by drawing it on the diagram from the tail
of the first to the head of the last vector.
The magnitude and direction of this vector
is the required answer.
The final answer must have magnitude and direction
– either a bearing from North or an angle marked
clearly on the diagram
Scale Diagrams
1. Scale: remember if the question is in ms-1 then your scale
should be a conversion from cm to ms-1.
2.
3.
4.
5.
6.
Direction: draw compass on page
1st vector: length and direction
2nd vector: tail of 2nd starts at tip of first
Resultant vector: tail of 1st to tip of last
Answer must include magnitude
(including units) and direction
Scale Diagrams
Direction should be given as a three
figure bearing from North
e.g. 045° or 175° or 035°
If you give any other angle, you must
clearly mark it on the scale diagram.
Virtual Int 2 Physics – Scalars and Vectors -Adding Vectors 2
Virtual Int 2 Physics – Scalars and Vectors – Example Problem
A car travels 100 km South, then 140 km
East. The time taken for the whole
journey is 3 hours.
Using a scale diagram (and the six step
process) find
(a) the car’s total distance travelled
(b) its average speed
(c) its overall displacement
(d) its average velocity
Scale Diagrams
Scale diagrams are used to find the
magnitude and direction of the resultant
of a number of a set of vectors.
Key words: vectors, scalars, resultant, scale diagram
By the end of this lesson you will be able to:
Describe what is meant by vector and scalar quantities
State the difference between distance and
displacement
State the difference between speed and velocity
State that force is a vector quantity
Use a scale diagram to find the magnitude and direction
of the resultant of two forces acting at right angles to
each other.
Mass
How do you write an
answer which is a
vector?
Kinetic energy
Distance
So you think you know your
vectors and scalars?
Scale
diagram – 6
steps?
Vector definition?
Velocity=
Velocity
Force
Key words: vectors, resultant
By the end of this lesson you will be able
to:
Use Pythagoras and Trigonometry to find
the magnitude and direction of the
resultant of two forces acting at right
angles to each other.
The tropical island of
Sohcahtoa
opp
sin  
hyp
The tropical island of
Sohcahtoa
adj
cos  
hyp
The tropical island of
Sohcahtoa
opp
tan  
adj
The tropical island of
Sohcahtoa
opp
sin  
hyp
adj
cos  
hyp
opp
tan  
adj
adj
cos  
hyp
hyp
opp
θ°
adj
opp
sin  
hyp
opp
tan  
adj
The Old Arab Carried A
Heavy Sack Of Hay
Tan = Opp/Adj; Cos= Adj/Hyp;
Sin=Opp/Hyp
Pythagoras 'Theorem
hyp  adj  opp
2
2
2
hyp
opp
θ°
adj
The squaw on the hippopotamus is equal
to the sum of the squaws on the other
two hides
=
+
N
+ 3 km
North
E
4 km East
N
R  4  3  5 km
2
2
R=?

+ 3 km
North
E
4 km East
 3
  tan    36.90
 4
1
= Bearing of 053.10
6N North, 8N East - what is the
resultant force R ?
6N
We ADD vectors HEAD to TAIL
[tip to toe]
8N
6N

R
R  82  62 10 N
8
tan    1.333
6
  53.1
0
Key words: average speed
By the end of this lesson you will be able to:
Describe how to measure an average speed
Carry out calculations involving distance, time
and average speed.
Which of these are units of
speed?
metres
gallons
miles per hour
minutes
amperes
kilometres per
second
watts
Newtons
seconds
miles
miles per minute
metres per second
Speeds in….
In Physics we normally use units
m/s for velocity.
Average speed (m/s)
Sound
13.4 m/s
Fast jet
10.3 m/s
Air molecule
648 m/s
Olympic
sprinter
340 m/s
Concorde
833 m/s
High speed
train
0.006 m/s
747 jumbo jet
97 m/s
Falcon
7500 m/s
UK motorway
300000000 m/s
Walking speed
1.7 m/s
Snail
270 m/s
UK town
29790 m/s
Earth in orbit
60 m/s
Earth 500 m/s
satellite
Light speed
31 m/s
Average speed ( m/s )
Light speed
300000000 m/s
Earth in orbit
29790 m/s
Fast jet
833 m/s
Concorde
648 m/s
Sound
340 m/s
747 jumbo jet
270 m/s
High speed
train
60 m/s
Olympic
sprinter
10.3 m/s
UK motorway
31 m/s
Walking speed
1.7 m/s
Earth satellite
7500 m/s
Air molecule
500 m/s
Falcon
97 m/s
UK town
13.4 m/s
Snail
0.006 m/s
What is speed?
When we talk about speed we mean…
the distance covered by an object in a
given time.
What is speed?
If Hamish (the dog) runs 10 metres in 2
seconds, what is his speed?
What is speed?
His speed is 5 metres
per second.
So speed is
distance
time
What is speed?
If you forget the formula think of cars
travelling at 30 kilometres per hour
km
Hour
Per
=
distance
time
Key words: average speed
By the end of this lesson you will be able to:
Describe how to measure an average speed
Carry out calculations involving distance, time
and average speed.
distance
speed time
Speed Calculations
A cyclist travels 100 m in
12 s. What is her speed?
Step 1: write down what you know.
d = 100 m
t = 12 s
s=?
Step 2: write down your formula. You can
use the triangle to help you but
remember you get no marks for this!
d = 100 m
t = 12 s
d=sxt
s=?
Step 3: substitute in your values.
d = 100 m
d=sxt
t = 12 s
s=?
100 = s x 12
Step 4: rearrange
d=sxt
d = 200 m
t = 40 s
100 = s x 12
s=
100
12
v=?
Step 5: calculate
d=sxt
d = 100 m
t = 12 s
100 = s x 12
s=
100
12
= 8.33
v=?
Step 6: units!!!!
d=sxt
d = 100 m
t = 12 s
100 = s x 12
s=
100
12
s=?
= 8.33 m/s
Key words: average speed, instantaneous
speed
By the end of this lesson you will be able to:
Describe how to measure instantaneous speed.
Identify situations where average speed and
instantaneous speed are different.
Instantaneous and average speed
Are instantaneous and average speed the same?
Instantaneous or average?
A car’s speed between Arbroath and
Dundee
Average
Instantaneous or average?
The speed read from a car’s speedometer
Instantaneous
Instantaneous or average?
A tennis ball’s speed as it crosses the net
Instantaneous
Instantaneous or average?
A racing car’s speed over a lap of the
track
Average
Instantaneous or average?
A parachutist’s speed as he/she lands
Instantaneous
Key words: acceleration, velocity
By the end of this lesson you will be able to:
Explain the term “acceleration”
State that acceleration is the change in
velocity per unit time
Carry out calculations involving the relationship
between initial velocity, final velocity, time and
uniform acceleration.
Measuring Acceleration
Activity 3
What do you expect to happen to the value of acceleration as the light gate is moved
further up the slope?
Position of light gate from bottom of slope
Acceleration
(m/s2)
1st attempt
2nd attempt
3rd attempt
Average acceleration
(m/s2)
Position 1
Position 2
m
m
Position 3
m
Position 4
m
What is acceleration?
Acceleration is the change in
velocity of an object per
second (in one second).
Is acceleration a vector or
scalar quantity?
Acceleration
What is the definition of acceleration?
Acceleration is the rate of change
of velocity per unit time OR change
in velocity per unit time.
Is it a vector or a scalar?
Vector – since velocity is a vector.
What is acceleration?
The rocket starts off at 0 m/s and 1
second later is travelling at 10 m/s.
What is its acceleration?
10 metres per second per second
10 m/s2
change in speed
in one second
Calculating acceleration
We need to know…
the change in velocity so…
initial velocity (u)
final velocity (v)
and…
time (t)
change in velocity
accelerati on 
time
final velocity (v) - initial velocity (u)
accelerati on 
time
v -u
a
t
change in velocity
v u
a 
t
in one second
Acceleration
a = acceleration measured in m/s2
u = initial velocity measured in m/s
v = final velocity measured in m/s
t = time measured in s
Units of acceleration
a=
final velocity – initial velocity
time
acceleration is measured in m/s2
If the speed is measured in kilometres per
hour, acceleration can be measured in
kilometres per hour per second.
Acceleration p4
An object accelerates at a rate of 4 m/s2.
What does this mean?
The object goes 4 m/s faster each
second.
Acceleration p4
The object goes 4 m/s faster each
second.
If the object is initially at rest, what
is its velocity after:
1s? 4 m/s
2s? 8 m/s
3s? 12 m/s
4s? 16 m/s
Acceleration
What does it mean if an object has a negative
value of acceleration?
It means that it is slowing down.
For example: an object which has an
acceleration of -2 m/s2 is becoming 2 m/s
slower each second.
Acceleration Calculations
A car, starting from rest, reaches a
velocity of 18 m/s in 4 seconds. Find the
acceleration of the car.
What do I know?
Initial velocity u = 0 m/s
Final velocity v = 18 m/s
time t = 4 s
Acceleration Calculations
What do I know?
Initial velocity u = 0 m/s
Final velocity v = 18 m/s
time t = 4 s
Formula?
v  u 18  0
2
a

 4.5m / s
t
4
Acceleration Calculations
A cheetah starting from rest accelerates
uniformly and can reach a velocity of 24
m/s in 3 seconds. What is the
acceleration?
Use technique and show all working!
Units!!
Acceleration Calculations
A student on a scooter is travelling at
6 m/s. 4 seconds later, she is travelling at
2 m/s. Calculate her acceleration.
Use technique and show all working!
Units!!
What do you notice about her change in
velocity?
Rearranging the acceleration
equation
v-u
a
t
Rearranging the acceleration
equation
v  u  at
v  u  at
v u
t
a
v-u
a
t
Key words: acceleration, velocity
By the end of this lesson you will be able to:
Explain the term “acceleration”
State that acceleration is the change in
velocity per unit time
Carry out calculations involving the relationship
between initial velocity, final velocity, time and
uniform acceleration.
Graph results
Acceleration using two light gates
http://www.crocodile-clips.com/absorb/AP5/sample/media/010102AccnApp.swf
The length of the mask is 5 cm. Calculate
the acceleration.
Remember calculate u (initial velocity) and
v (final velocity) and use
v -u
a
t
Acceleration using a double mask
http://www.crocodile-clips.com/absorb/AP5/sample/media/010102AccnApp2.swf
The length of each section mask is 4 cm. The
gap is also 4 cm. Calculate the acceleration.
Remember calculate u (initial velocity) and
v (final velocity) and use
v -u
a
t
Key words: acceleration, velocity, displacement
By the end of this lesson you will be able to:
Draw velocity-time graphs of more than one
constant motion.
Describe the motions represented by a
velocity-time graph.
Calculate displacement and acceleration, from
velocity-time graphs, for more than one constant
acceleration.
Graphing Motion
Information about the motion of an
object can be obtained from velocity-time
graphs.
Similarly, we can graph motion based on
descriptions of the motion of an object.
Velocity-time graph
The motion of a moving object can be
represented on a velocity – time graph.
Virtual Int 2 Physics – Mechanics and Heat – Velocity and
Acceleration – Velocity Time Graphs
Vectors and Direction
When dealing with vector quantities we
must have both
direction.
magnitude and
When dealing with one-dimensional
kinematics (motion in straight lines) we
use + and – to indicate travel in opposite
directions. We use + to indicate acceleration
and – to indicate deceleration.
Velocity-Time Graphs
Describe the motion of this object.
v (m / s )
0
Constant velocity – does not
change with time
0
t (s )
Velocity-Time Graphs
Describe the motion of this object.
v (m / s )
0
Increasing with time –
constant acceleration
0
t (s )
Velocity-Time Graphs
Describe the motion of this object.
v (m / s )
0
Decreases with time –
constant deceleration
0
t (s )
Velocity-Time Graphs
Describe the motion of this object.
v (m / s )
0
0
t (s )
Speed-Time Graphs
speed (m / s ) Calculate the distance covered by the object
in the first 10 s of its journey.
2
The area under the graph tells us the distance
travelled.
0
0
10
t (s )
Speed-Time Graphs
speed (m / s ) Calculate the distance covered by the object
in the first 10 s of its journey.
2
The area under the
graph tells us the
distance
travelled.
0
0
10
t (s )
Key words: forces, newton balance, weight, mass, gravitational field strength.
By the end of this lesson you will be able to:
Describe the effects of forces in terms of their ability to
change the shape, speed and direction of travel of an object.
Describe the use of a newton balance to measure force.
State that weight is a force and is the Earth’s pull on an
object.
Distinguish between mass and weight.
State that weight per unit mass is called the gravitational
field strength.
Carry out calculations involving the relationship between weight, mass and
gravitational field strength including situations where g is not equal to 10
N/kg.
What effect can a force have?
Force is simply a push or a pull.
Some forces (e.g. magnetic repulsion, or
attraction of electrically charged
objects) act at a distance.
What is force?
A force can
change the shape of an object
change the velocity of an object
change the direction of travel of an
object
Virtual Int 2 Physics – Mechanics & Heat – Forces - Introduction
Units of Force?
Force (F) is
measured in
newtons (N).
Measuring Forces
A Newton (or
spring) balance can
be used to measure
forces.
Mass and Weight
We often use the words mass and weight
as though they mean the same…
but do they?
Mass and Weight
An object’s mass is
a measure of how much “stuff” makes up
that object – how much matter, or how
many particles are in it.
Mass is measured in
grams or kilograms.
Mass and Weight
An object’s weight is
the force exerted by gravity on a mass.
Since it is a force, weight must be
measured in
newtons.
Investigating the relationship
between mass and weight
How can we find the relationship between
mass and weight?
A newton balance can be used to find the
weight of known masses.
Results
Mass
100g
200g
300g
400g
500g
1kg
2kg
5kg
Weight in N
Relationship between mass and
weight
From this we can see a relationship
between mass and weight
100g = 0.1 kg -> 1 N
1kg -> 10 N
To convert kg -> N multiply by 10
To convert N -> kg divide by 10
Gravitational Field Strength
(g)
Gravitational field strength on Earth is
10 N / kg
What is gravitational field
strength?
This is the pull of gravity on each
kilogram of mass.
So on Earth, the pull of gravity on a 1kg
mass is
10 N
What is gravitational field
strength?
and the pull of gravity on a 2 kg mass is
20 N
Definition
A planet’s gravitational
field strength is the
pull of gravity on
a 1 kg mass.
Gravity in the universe
Is gravitational field strength always the
same?
No! It varies on different planets.
http://www.exploratorium.edu/ronh/weight/index.html
Your weight on different planets
Use the website to find your weight on
different planets for a mass of 60 kg (a
weight of 600 N on Earth).
From this calculate the gravitational field
strength for each planet.
Mass on Earth = 60 kg
Weight on Earth = 600 N
Gravitational field strength =
Weight
Weight
Weight
Weight
Weight
Weight
on Mercury = 226.8 N
on Venus = 544.2 N
on the Moon = 99.6 N
on Mars = 226.2 N
on Jupiter = 1418.4 N
on Saturn = 549.6 N
600
 10
60
g=
g=
99.6
g = 60  1.66
g = 22660.2  3.77
.4
 23.64
g = 1418
60
g = 549.6  9.91
226.8
 3.78
60
544.2
 9.07
60
60
Units for g
We found g by dividing weight in newtons
by mass in kilograms.
What are the units for g?
10 N / kg
Which of the planets has the greatest
gravitational field strength?
Why do you think this is the case?
Weight, mass and gravity
We have seen that there is a link between
weight, mass and gravity.
On Earth
1 kg acted on by 10 N / kg weighs 10 N
mxg=W
mass
Gravitational field strength g
weight
Weight, mass and gravity
Why is weight
measured in
newtons?
Gravitational field
strength measured
in N / kg
W = mg
Mass measured in kg
Weight measured in newtons
Key words: friction, force
By the end of this lesson you will be able
to:
State that the force of friction can oppose
the motion of an object.
Describe and explain situations in which
attempts are made to increase or decrease
the force of friction.
Frictional Forces
Virtual Int 2 Physics – Mechanics & Heat – Forces – Friction
Moving vehicles such as cars can slow
down due to forces acting on them.
These forces can be due to…
road surface and the tyres
the brakes
air resistance.
Frictional Forces
The force which tries to oppose motion is
called the force of friction.
A frictional force always acts to slow an
object down.
Increasing Friction
In some cases, we want to increase
friction. Some examples of this are:
• Car brakes – we need friction between
the brake shoes and the drum to slow
the car down
• Bicycle tyres – we need friction to give
• “grip” on the surface
Increasing Friction
On the approach to traffic lights and
roundabouts, different road surfaces are
used to increase friction compared with
normal roads.
Decreasing Friction
In some cases, we want to decrease
friction. Some examples of this are:
• Ice skating
• Skiing
• Aircraft design
Reducing Friction
Friction can be reduced by:
Lubricating the surfaces – this generally
means using oil between two metal
surfaces. This is done in car engines to
reduce wear on the engine – metal parts
aren’t in contact because of a thin layer
of oil between them.
Reducing Friction
Friction can be reduced by:
Separating surfaces with air (e.g. a
hovercraft).
Making surfaces roll (e.g. by using ball
bearings).
Reducing Friction
Friction can be reduced by:
Streamlining. Modern cars are designed
to offer as little resistance (or drag) to
the air as possible, reducing friction on
the car.
Streamlining
Cars are streamlined (that is, have their
drag coefficient reduced) by
Reducing the front area of the car
Having a smooth round body shape
Using aerials built into the car windows
Virtual Int 2 Physics – Mechanics & Heat - Forces – Friction Effects
Key words: force, vector, balanced
forces
By the end of this lesson you will be able
to:
State that force is a vector quantity.
State that forces which are equal in size but
act in opposite directions on an object are
called balanced forces and are equivalent to
no force at all.
Explain the movement of objects in terms of
Newton’s first law.
Force
Force is a vector quantity. What do we
mean by this?
To describe it fully we must have size
and direction.
Balanced Forces
F
F
Balanced forces are EQUAL FORCES
which act in OPPOSITE DIRECTIONS.
They CANCEL EACH OTHER OUT.
If balanced forces act on a STATIONARY
OBJECT, it REMAINS STATIONARY.
F
F
If balanced forces act on a MOVING
OBJECT, it continues moving in the same
direction with CONSTANT VELOCITY.
This is summarised by NEWTON’S FIRST
LAW which states:
An object remains at rest, or moves in a
straight line with constant velocity unless
an UNBALANCED FORCE acts on it.
Virtual Int 2 Physics – Mechanics & Heat – Forces - Newton’s First Law
To understand NEWTON’S FIRST LAW
remember:
An object tends to want to keep doing
what it is doing (so if it is sitting still it
wants to stay that way, and if it is moving
with constant velocity it wants to keep
going).
This reluctance to change motion is
known as inertia.
The greater the mass, the greater
the reluctance.
Think! Is it easier to stop a tennis
ball travelling towards you at 10 m/s
or to stop a car travelling towards
you at 10 m/s?
Forces and Supported Bodies
A stationary mass m
hangs from a rope.
m
What is the weight of
the mass? In what
direction does
this act?
W = mg
downwards
Forces and Supported Bodies
The mass is stationary.
Newton’s law tells us
that the forces must
be
m
balanced forces.
The weight is
counterbalanced by a
force of the same size
acting upwards due to
the tension in the
string.
Forces and Supported Bodies
A book of mass m
rests on a shelf.
m
What is the weight of
the book? In what
direction does
this act?
W = mg
downwards
Forces and Supported Bodies
The mass is stationary.
Newton’s law tells us
that the forces must be
m
balanced forces.
The weight is
counterbalanced by a
force of the same size
acting upwards due to
the shelf.
What forces are acting on this stationary hovering
helicopter?
lift = W = mg
W = mg
Newton’s First Law
Newton’s first law tells us that when the
forces on an object are balanced, a
stationary object will remain stationary.
But it also says that if when forces are
balanced, an object moving at constant
velocity will continue in the same direction
with the same velocity.
Virtual Int 2 Physics – Mechanics & Heat – Forces - Newton’s First Law
A moving car
If a car moves with constant velocity, then
what forces are acting on it?
Engine force
Friction force
The ENGINE FORCE and the FRICTION
FORCE must be equal.
Newton’s Law & Car Seat Belts
If a car stops suddenly, someone inside the
car appears to be “thrown forwards”.
In fact, they simply carry on moving with
the car’s previous speed.
A seat belt prevents this happening by
applying an unbalanced force to the person,
in the direction opposite to motion. This
causes rapid deceleration.
No seatbelt – what’s going to happen when the car hits the
wall?
Explain this in terms of Newton’s 1st law.
What’s going to happen when the motorbike hits the wall?
Explain this in terms of Newton’s 1st law.
Air bags
Air bags produce a similar effect to
seatbelts. They apply a force which opposes
the motion, causing rapid deceleration.
The large surface area also spreads the
force of impact, reducing the pressure and
reducing injury.
Forces in a Fluid
Terminal velocity
Any free-falling object in a fluid (liquid or
gas) reaches a top speed, called ‘terminal
velocity’.
Terminal velocity
The air resistance acting on a moving object
increases as it gets faster.
Terminal velocity is reached when the airresistance (acting upwards) has increased to
the same size as the person’s weight (acting
downwards)
time = 0s, velocity = 0 m/s, friction = 0 N
Friction Ff(air resistance) = 0 N
a = -10 m/s2
W = weight
Ff
a < -10 m/s2
v
W = weight
Equal & opposite forces
Acceleration
zero
F
Terminal velocity
f
a = 0 m/s2
v
W = weight
Velocity – Time Graph
velocity
(m/s)
Terminal
velocity
0
0
time (s)
Virtual Int 2 Physics – Mechanics & Heat – Forces - Terminal Velocity
air resistance
Terminal velocity is
reached when the air
resistance balances
the weight.
weight
Terminal Velocity
What effect does opening a parachute
have on the terminal velocity?
Virtual Int 2 Physics – Mechanics & Heat – Forces - Terminal Velocity
When the parachute is opened, air resistance
increases a lot. There is now an unbalanced force
upwards, which causes deceleration. The velocity
decreases, and the air resistance decreases until
the forces are balanced again. The parachutist
falls to the ground with a lower terminal velocity.
Key words: Newton’s second law,
unbalanced forces, mass, force,
acceleration
By the end of this lesson you will be able
to:
Describe the qualitative effects of the change of
mass or of force on the acceleration of an object
Define the newton
Carry out calculations using the relationship
between a, F and m and involving more than
one force but in one dimension only
The example of the parachutist accelerating until
the forces are balanced helps us to understand
NEWTON’S SECOND LAW which states:
When an object is acted on by a constant
UNBALANCED FORCE the body moves
with constant acceleration in the
direction of the unbalanced force.
Virtual Int 2 Physics – Mechanics & Heat – Forces - Newton’s First Law
Force, mass and acceleration
Acceleration (m/s2)
F = ma
Force (N) mass (kg)
Virtual Int 2 Physics – Mechanics & Heat – Forces - Force, mass and acceleration
Force, mass and acceleration
One newton (1N) is the force required to
accelerate 1 kg at 1
2
m/s
F = ma
Find the unbalanced force required to
accelerate a 4 kg mass at 5 m/s2
What do I know?
m = 4kg
a = 5m/s2
F = ma
F= 4 x 5
F = 20 N
Key words: free body diagrams, resultant
force
By the end of this lesson you will be able
to:
Use free body diagrams to analyse the forces
on an object
State what is meant by the resultant of a
number of forces
Use a scale diagram, or otherwise, to find the
magnitude and direction of the resultant of
two forces acting at right angles to each
other.
Newton’s First Law
A body remains at rest, or continues at
constant velocity, unless acted upon by an
external unbalanced force.
(that is objects have a tendency to keep
doing what they are doing)
Newton’s Second Law
Newton’s Second Law is about the
behaviour of objects when forces are not
balanced.
The acceleration produced in a body is
directly proportional to the unbalanced
force applied and inversely proportional to
the mass of the body.
Newton’s Second Law
In practice this means that
the acceleration produced increases as
the unbalanced force increases
the acceleration decreases as the mass of
the body increases
Which forces?
An object may be acted upon by a number
of forces but
only an overall
unbalanced force
will lead to acceleration in the direction
of that force.
Forces are measured in…?
Newton’s Second Law
can be written as
F
a 
m
or more commonly
F  ma
Forces are measured in…?
F  ma
which gives us the definition of the Newton:
1N is the resultant (or unbalanced)
force which causes a mass of 1kg to
accelerate at 1m/s2
1N  1kgm / s
2
Quick Quiz
Unbalanced
force (N)
Mass (kg)
Acceleration
(m/ s2)
10
2
5
20
2
10
20
4
5
10
2
5
10
1
10
Direction of force
Consider the oil drop trail left by the car
in motion.
In which direction is the acceleration?
To the right
In which direction is the unbalanced
force?
To the right
Direction of force
Consider the oil drop trail left by the car
in motion.
In which direction is the unbalanced
force?
To the left – the car is
moving to the right
and slowing down.
Newton’s First and Second Laws
Remember
Forces do not cause motion
Forces cause acceleration
Free-Body Diagrams
A free body diagram is a special
example of a vector diagram.
They show the relative magnitude
and direction of all forces acting
on an object.
They are used to help you identify
the magnitude and direction of an
unbalanced Force acting on an
object.
Using Newton’s Second Law
In the simplest case
m
FUN
a 
m
Fun
Using Newton’s Second Law
Direction of acceleration?
Direction of unbalanced force?
Formula for calculating acceleration?
F2
m
F1
F1  F2
a 
m
Solving Problems
• Always draw a diagram showing all known
quantities (forces – magnitude and
direction, resultant acceleration and
direction, mass of object(s) )
• Remember that Fun=ma can be applied to
the whole system
• When working in the vertical direction
always include the weight
Key words: acceleration, gravitational
field strength, projectiles
By the end of this lesson you will be able
to:
Explain the equivalence of acceleration due to
gravity and gravitational field strength
Explain the curved path of a projectile in
terms of the force of gravity
Explain how projectile motion can be treated
as two separate motions
Solve numerical problems using the above method
for an object projected horizontally.
Acceleration due to Gravity
Definition:
A planet’s gravitational field strength equals the force of
gravity PER UNIT MASS.
Units?
N/kg
To calculate an object’s weight, use this equation -
W  mg
Virtual Int 2 Physics – Projectiles – Acceleration due to
gravity and gravitational field strength
Acceleration due to Gravity
Near a planet’s surface all objects experience
the same gravitational acceleration.
This acceleration is numerically equal to the
planet’s gravitational field strength.
ag
Acceleration due to Gravity
For example, on Earth –
g = 10 N/kg
A free-falling object will experience
acceleration of a = -10 m/ s2
What does the –ve sign tell you?
Gravitational field strength
Is the gravitational field strength the same on each
planet?
How does distance affect gravitational field strength?
It decreases the further away you are from the planet’s
surface.
What will happen to the weight of an object as it gets
further from the surface? Explain your answer.
It will decrease.
The force of gravity near
the Earth’s surface gives
all objects the same
acceleration.
So why doesn’t the
feather reach the ground
at the same time as the
elephant?
Why are the gaps
between the balls
increasing?
An object is released from rest close to the Earth’s
surface. Which formula can be used to find its velocity
at a given time?
v = u + at
where v = ?
,u=
0
What is its velocity:
At the time of release?
After 1 second?
After 2 seconds?
After 3 seconds?
After 4 seconds?
,a=
,t=
Projectiles
Virtual Int 2 Physics – Projectiles –
Projectile Motion
Forces acting on projectiles
What would happen to a ball kicked off a
cliff, in the absence of gravity?
Forces acting on projectiles
There would be no vertical motion
therefore the ball would continue at
constant speed in a straight
line (remember Newton’s first law)
Objects projected horizontally
Think about…
What is the initial vertical speed of a
projectile fired horizontally?
0 m/s
How will the horizontal speed vary during
the object’s flight?
It will remain the same as
the initial horizontal speed.
Objects projected horizontally
Think about…
Describe the vertical motion of an object
projected horizontally:
It will accelerate downwards
due to gravity.
Projectiles
Virtual Int 2 Physics – Projectiles –
Comparing Projectile Motion with
Vertical Motion
Virtual Int 2 Physics – Projectiles –
Graphs of Projectile Motion
Objects projected horizontally
Think about…
What formula can be used to find the
horizontal displacement of an object
fired horizontally if horizontal velocity
and time of flight are known?
horizontal
displacement (m)
sh = vht
time of flight (s)
horizontal
velocity (m/s)
Which
ball will
hit the
ground
first?
http://www.fearofphysics.com/XYIndep/xyindep_correct.html
Summary
Forces
Are there forces
present? If so, in
what direction are
they acting?
Horizontal
motion
Vertical motion
No
Yes
The force of gravity
acts downward
Acceleration
No
Is there acceleration?
If so, in what
direction? What is
the value of the
acceleration?
Yes
Velocity
Constant or changing?
Changing
Constant
Acceleration = "g" downward
at 10 m/s2
by 10 m/s each second
Solving Numerical Problems
• Always write down what you know – many questions
have a lot of text surrounding the Physics so pick out
the information from the question
• Write down other relevant information you have e.g.
acceleration due to gravity
• Select formula – this isn’t a test of memory so while
you should learn your formulae, don’t be afraid to
check against the data book or text book
• Substitute values and rearrange formula
• Write answer clearly remembering magnitude and
direction, and units.
Example
A flare is fired horizontally out to sea from a
cliff top, at a horizontal speed of 40 m/s. The
flare takes 4 s to reach the sea.
(a) What is the horizontal speed of the flare
after 4 s?
There are no forces acting in the horizontal. The
horizontal speed remains the same = 40 m/s.
Example
(b) Calculate the vertical speed of the flare after 4s
final speed
initial vertical speed
acceleration
time
v = u + at
v = 0 + 10 x 4
v = 40 m/s
v=?
u = 0 m/s
a = 10 m/s2
t=4s
Initial vertical speed is always 0 m/s!
Example
(c) Draw a graph to show how vertical speed
varies with time.
Variation of vertical speed with time
Initial vertical speed = 0 m/s
Final vertical speed = 40 m/s
45
Vertical speed (m/s)
40
35
30
25
20
15
10
5
0
0
1
2
3
Time (s)
4
5
Example
(d) Use this graph to calculate the height of the
cliff.
Variation of vertical speed with time
Displacement = area under
velocity-time graph
Height of cliff = 80 m
40
Vertical speed (m/s)
½ bh = ½ x 4 x 40
= 80 m
45
35
30
25
20
15
10
5
0
0
1
2
3
Time (s)
4
5
Projectiles
Virtual Int 2 Physics – Projectiles
Example Problem
Virtual Int 2 Physics – Projectiles –
Newton’s Thought Experiment
Key words: Newton’s third law, newton
pairs
By the end of this lesson you will be able
to:
State Newton’s third law
Identify “Newton pairs” in situations involving
several forces
State that momentum is the product of mass
and velocity.
State that momentum is a vector quantity.
Forces acting between objects
Newton realised that
When a body is acted upon
by a force there must be
another body which also has
a force acting on it. The
forces are equal in size but
act in opposite directions.
Newton’s Third Law
If object A exerts a force on
object B, then B exerts an equal
and opposite force on A
Forces always occur in equal and
opposite pairs
For every action there is an
equal and opposite reaction
Firing a gun
Force of GUN
on BULLET
Force of BULLET
on GUN
Starting a sprint
Force of
RUNNER on
BLOCKS
Force of
BLOCKS on
RUNNER
A falling apple
Force of
EARTH on
APPLE
Force of APPLE
on EARTH
A Rocket
Force of GAS on
ROCKET
Force of
ROCKET on
GAS
Key words: momentum, law of
conservation of momentum
By the end of this lesson you will be able
to:
State that momentum is the product of mass
and velocity.
State that momentum is a vector quantity.
State that the law of conservation of linear
momentum can be applied to the interaction
of two objects moving in one direction, in the
absence of net external forces.
Carry out calculations concerned with
collisions in which all the objects move in the
same direction and with one object initially at
rest.
Collisions
When two objects collide, they apply
forces to each other.
What does the size of the force depend
on?
Virtual Int 2 Physics – Mechanics and Heat – Momentum – Momentum defined
Momentum
The momentum of an object is the
mass x velocity
It is a vector quantity.
It has units of kgm/s
Momentum & Collisions
Virtual Int 2 Physics – Mechanics and Heat – Momentum – Collisions
We will consider two types of collision:
1.Vehicles bounce apart
after collision
2.Vehicles stick together
after collision
Collisions Examples
A 2kg trolley travelling at 3 m/s hits a
stationary 1kg trolley.
After the collision the 2kg trolley
continues to travel in the same direction
at 1 m/s. The 1 kg trolley moves off
Separately. Calculate the velocity of the 1kg
trolley after the collision.
How can we find the answer?
Using the Law of
Conservation of
Momentum!
total momentum before
collision =
total momentum after
collision
providing no external forces
are acting.
Collisions Examples
A 2kg trolley travelling at 3 m/s hits a
stationary 1kg trolley.
After the collision the 2kg trolley
continues to travel in the same direction
at 1 m/s. The 1 kg trolley moves off
separately. Calculate the velocity of the 1kg
trolley after the collision.
Collisions where vehicles bounce apart
Before
After
2 kg
1 kg
2 kg
1 kg
3 m/s
0 m/s
1 m/s
? m/s
momentum = mass x velocity
momentum = mass x velocity
total momentum before  m1u1  m 2 u 2
total momentum after  m1v1  m 2 v 2
 (2 x 3)  ( 1 x 0)
 6 kg m/s
 (2 x 1)  ( 1 x v 2 )
 6 kg m/s
Conservation of momentum tells us
momentum before = momentum after
Collisions where vehicles bounce apart
2 kg
1 kg
1 m/s
? m/s
momentum = mass x velocity
total momentum after  m1v1  m 2 v 2
 (2 x 1)  ( 1 x v 2 )  6 kg m/s
2  v2  6
2  v2 - 2  6 - 2
v 2  4m / s
Direction of travel to the right (since positive)
Collisions where vehicles bounce apart
2 kg
1 kg
1 m/s
? m/s
Check does this work?
Conservation of momentum tells us
momentum before = momentum after
total momentum before  m1u1  m 2 u 2
total momentum after  m1v1  m 2 v 2
 (2 x 3)  ( 1 x 0)
 6 kg m/s
 (2 x 1)  ( 1 x 4)
 6 kg m/s
Collisions Examples
A 1kg trolley travelling at 2 m/s hits a
stationary 1kg trolley.
After the collision the trolleys stick together
and continue to travel in the same direction.
Calculate the velocity of the combined vehicle
after the collision.
Collisions where vehicles stick together
Before
After
1 kg
1 kg
1 kg
1 kg
2 m/s
0 m/s
? m/s
momentum = mass x velocity
total momentum after  m1v1  m 2 v 2
momentum = mass x velocity  (1 x v )  ( 1 x v )
1
2
total momentum before  m1u1  m 2 u 2
Since vehicles are stuck toge ther, v1  v 2
 (1 x 2)  ( 1 x 0)
 2 kg m/s
 (1 x v )  ( 1 x v)
vv
 2v
 2 kg m/s
Conservation of momentum tells us
momentum before = momentum after
Collisions where vehicles stick together
1 kg
1 kg
? m/s
momentum = mass x velocity
total momentum after  m1v1  m 2 v 2
 (1 x v 1 )  ( 1 x v 2 )
Since vehicles are stuck toge ther, v1  v 2
 (1 x v )  ( 1 x v)
vv
 2v
 2 kg m/s
2v  2
v  1 m/s
Direction of travel to the right since positive
Collisions where vehicles stick together
1 kg
1 kg
1 m/s
momentum = mass x velocity
Check does this work?
Conservation of momentum tells us
momentum before = momentum after
total momentum before  m1u1  m 2 u 2 total momentum after  m1v1  m 2 v 2
 (1 x 2)  ( 1 x 0)
 (1 x v 1 )  ( 1 x v 2 )
 2 kg m/s
Since vehicles are stuck toge ther, v1  v 2  1m /
 (1 x 1)  ( 1 x 1)
11
 2kg m/s
Key words: work done, energy, force,
distance, power, time
By the end of this lesson you will be able
to:
State that work done is a measure of the
energy transferred.
Carry out calculations involving the
relationship between work done, force and
distance.
Carry out calculations involving the
relationship between work done, power and
time.
Work done?
What is meant by work done in Physics?
When a force acts upon an object to
cause a displacement of the object, it is
said that work was done upon the object.
Work done?
There are three key ingredients to work –
force, displacement, and cause.
In order for a force to qualify as having done
work on an object, there must be a
displacement and the force must cause the
displacement.
Work done?
Formula linking work done, force and displacement?
Ew  Fd
Examples of work done?
a horse pulling a plow through the field
a shopper pushing a grocery cart down the aisle of a supermarket
a pupil lifting a backpack full of books upon her shoulder
a weightlifter lifting a barbell above his head
an Olympian launching the shot-put, etc.
In each case described here there is a force exerted upon an
object to cause that object to be displaced.
Work done
A dog pulls a 4 kg sledge for a distance on
15 m using a force of 30 N. How much
work does he do?
What do I know?
F = 30N
d = 15m
Work done
What do I know?
F = 30N
d = 15m
Formula?
Ew  Fd
Ew  30x 15
Ew  450J
Virtual Int 2 Physics – Mechanics & Heat – Work Done – Example Problem
Power
Power is the rate of doing work i.e. if
work is done then the work done per
second is the power.
Energy in joules
E
P 
t
Power in watts (joules per seconds)
time in seconds
Power
A dog pulls a 4 kg sledge for a distance on
15 m using a force of 30 N in 20 s.
Calculate the power of the dog.
What do I know?
F = 30N
d = 15m
t = 20s
Power
What do I know?
F = 30N
d = 15m
t = 20s
Formula?
Ew  Fd
Ew  30x 15
Ew  450J
Power
What do I know?
F = 30N
d = 15m
t = 20s
Ew = 450J
Formula?
EW
P 
t
450
P 
20
P  22.5W
Key words: gravitational potential energy,
mass, gravitational field strength, kinetic
energy
By the end of this lesson you will be able
to:
Carry out calculations involving the relationship
between change in gravitational potential energy,
mass, gravitational field strength and change in
height.
Carry out calculations involving the relationship
between kinetic energy, mass and velocity.
Gravitational Potential Energy
…is the potential energy
gained by an object when
we do work to lift it
vertically in a gravitational
field.
Gravitational Potential Energy
The work done in lifting an
object vertically
What force is required?
Ew  Fd
Gravitational Potential Energy
To lift the object we
must overcome the
weight W=mg
Ew  Fd
Gravitational Potential Energy
Vertical distance – we
call this height h
E  mgd
Gravitational Potential Energy
EP  mgh
Virtual Int 2 Physics – Mechanics & Heat – Potential Energy – Example Problem
Kinetic Energy
…is the energy associated
with a moving object.
Kinetic Energy
depends on…
The mass of the object
Kinetic Energy
depends on…
The velocity of the object
Kinetic Energy
1 2
E K  mv
2
Virtual Int 2 Physics – Mechanics & Heat – Kinetic Energy – Example Problem
Virtual Int 2 Physics – Mechanics & Heat – Power – Example Problem
Speed and Stopping Distance
The distance required
to stop a moving
vehicle is a
combination of two
things:
Thinking distance
Braking distance
Speed and Stopping Distance
Each driver has a reaction time.
The thinking
distance is the
distance you travel
between realising you
need to stop and
reacting.
Thinking distance =
speed x reaction time
Speed and Stopping Distance
Braking distance
To stop a
vehicle, brakes
do work to
transform Ek
into heat. This
work = braking
force x braking
distance.
This is the distance
you travel between
pressing your brakes
and the car coming
to a stop.
Speed and Stopping Distance
To stop a vehicle, brakes do work to transform Ek into
heat. This
work = braking force x braking distance
Ek = Ew = Fd
The kinetic energy depends on the mass and the square
of velocity of the object so as speed increases kinetic
energy increases and therefore braking distance
increases.
Speed and Stopping Distance
Thinking distance = speed x reaction time
Braking distance = speed x braking time
Total stopping distance = thinking distance +
braking distance
Look at the graph of velocity against time
from the moment the driver first sees a
hazard until the moment the car comes to
rest.
velocity
(m/s)
16
0
0
0.6
3
time (s)
Why is the graph in two distinct sections?
Here, the driver has noticed
the hazard but has not yet
reacted. The distance
travelled is reaction time x
speed.
velocity
(m/s)
16
The reaction time is 0.6 s
0
0
0.6
3
time (s)
Why is the graph in two distinct sections?
Here, the driver is braking to a
stop. The braking distance is the
distance travelled while applying
the brakes.
velocity
(m/s)
16
0
0
0.6
3
time (s)
Use the graph to
- calculate the thinking distance
- calculate the car’s braking distance
- calculate the car’s overall stopping
distance.
How is stopping
distance affected
by speed?
Distance in metres
Stopping distances
500
450
400
350
300
250
200
150
100
50
0
Stopping
distance
Braking
distance
Thinking
distance
0
50
100
150
Speed in km per hour
200
250
Distance in metres
Stopping distances
500
450
400
350
300
250
200
150
100
50
0
Stopping
distance
Braking
distance
Thinking
distance
0
50
100
150
200
Speed in km per hour
Kinetic energy is linked
to the square of the
velocity
250
Key words: gravitational potential energy,
mass, gravitational field strength, kinetic
energy, mass, velocity, input and output
energy and power, efficiency
By the end of this lesson you will be able
to:
Carry out calculations involving the
relationship between efficiency and output
power, output energy and input power, input
energy.
Energy Transformations &
Efficiency
There are many occasions where energy is
transformed from one form to another.
For example: an electric motor
transforms electrical energy in kinetic
energy; a light bulb transforms electrical
energy into light energy.
Energy Transformations &
Efficiency
However, in these examples, not all the
electrical energy is converted into the
useful form we want!
Some energy may be transformed into
heat, due to friction, and sound. Energy is not
lost (the law of conservation of energy) however
it has been “wasted” because it is not in a useful
form.
Energy Transformations &
Efficiency
The efficiency of a machine (or energy
converter) is measured by
expressing the useful energy output as a
percentage of total energy
input.
Energy Transformations &
Efficiency
useful energy output 100
% efficiency 
x
total energy input
1
Power & Efficiency
power output 100
% efficiency 
x
power input
1
Virtual Int 2 Physics – Mechanics & Heat – Work, Energy & Power - Efficiency – Example Problem
Conservation of Energy
Energy can neither be created nor
destroyed – simply transformed from one
form into another.