Intermediate 2 Physics

1
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.

2
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.
3

• 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.

4
Scalars and Vectors

• Imagine a boat
• making a distress
• call to the
• coastguard.
• The boat tells the
• coastguard he is 60 km
• from Aberdeen.

5
Scalars and Vectors

• Is this enough
• information for the
• coastguard to find
• the boat?

6
Scalars and Vectors
7
Scalars and Vectors

• The coastguard needs both
• distance (size)
• and
• direction
• to find the boat.

8
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.

9
Distance and Displacement
A pupil walks from her house to her school. Her
brother makes the same journey, but via a shop.
How far has the girl walked? How far has her
brother walked?
50 m
30 m
40 m
10
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
11
Distance and Displacement
Distance is simply a measure of how much ground
an object has covered.
50 m
30 m
40 m
12
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.
13
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
14
Distance and Displacement
What is her brothers displacement?
50 m
30 m
40 m
15
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
16
Distance and Displacement
Their displacement (how far out of place they
each are) is the same.
50 m
30 m
40 m
17
Speed and Velocity
Speed is a scalar quantity requiring only
magnitude (number and unit). Velocity is a
vector, requiring magnitude and direction.
18
Speed and Velocity
Speed tells us how fast an object is
moving. Velocity tells us the rate at which an
object changes position.
19
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 persons velocity? Remember
• velocity keeps track of direction. The
• direction of the velocity is the same as
• the direction of displacement.

20
Speed and Velocity
21

• 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.

22
Distance and Displacement
Virtual Int 2 Physics Scalars and Vectors
Distance and Displacement
23
Speed and Velocity
Virtual Int 2 Physics Scalars and Vectors
Speed and Velocity
24
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.                                      
                    
25
                                                  
        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.
26
Scalar or Vector?
Virtual Int 2 Physics Scalars Vectors -
Introduction
27

• 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.

28
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.

29
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.

30
Addition of Vectors

• When two or more vectors are added
• together, providing they act in the same
• direction, the addition is straightforward.

5 N
3 N
8 N
31
Addition of Vectors

• If they are acting in opposite directions

5 N
3 N
2 N
32
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.

33
To find the resultant of a set of vectors using a
scale diagram

• 1. Decide on a suitable scale and write this
• down at the start
• 2 Take the direction to the top of the page as
• North. Draw a small compass to show this.
• 3 Draw the first vector ensuring it is the
• correct length to represent the magnitude
• of the vector, and it is the correct
• direction.

34
To find the resultant of a set of vectors using a
scale diagram

• Draw an arrow to represent the second
• vector starting at the head of the first.
• Vectors are always added head to tail.
• 5 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.
• 6 The final answer must have magnitude and
  direction either a bearing from North or an
  angle marked clearly on the diagram

35
Scale Diagrams

• Scale remember if the question is in ms-1 then
  your scale should be a conversion from cm to
  ms-1.
• 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

36
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.

37

• 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
• the cars total distance travelled
• its average speed
• its overall displacement
• its average velocity

38
Scale Diagrams

• Scale diagrams are used to find the
• magnitude and direction of the resultant
• of a number of a set of vectors.

39

• 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.

40
So you think you know your vectors and scalars?
How do you write an answer which is a vector?
Mass
Distance
Kinetic energy
Scale diagram 6 steps?
Vector definition?
Velocity
Velocity
Force
41

• 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.

42
The tropical island of Sohcahtoa
43
The tropical island of Sohcahtoa
44
The tropical island of Sohcahtoa
45
The tropical island of Sohcahtoa
46
hyp
opp
?
adj
47

• The Old Arab Carried A
• Heavy Sack Of Hay
• Tan Opp/Adj Cos Adj/Hyp
• SinOpp/Hyp

48
hyp
opp
?
adj
49

• The squaw on the hippopotamus is equal
• to the sum of the squaws on the other
• two hides

50
N
3 km North
E
4 km East
Remember The vectors above are not tip to tail.
You must join them tip to tail
51
N
R ?
3 km North
?
E
4 km East
Bearing of 053.10
52
6N
6N North, 8N East - what is the resultant force
R ?
We ADD vectors HEAD to TAIL tip to toe
8N
R
?
53

• 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.

54
Which of these are units of speed?
metres
gallons

• miles per hour

seconds
minutes
amperes
miles
kilometres per second
miles per minute
watts
metres per second
Newtons
55
Speeds in.

• In Physics we normally use units
• m/s for velocity.

56
Average speed (m/s)
Snail
High speed train
Sound
270 m/s
13.4 m/s
0.006 m/s
UK town
Fast jet
747 jumbo jet
29790 m/s
10.3 m/s
97 m/s
Air molecule
Earth in orbit
Falcon
60 m/s
648 m/s
7500 m/s
Olympic sprinter
Earth satellite
UK motorway
500 m/s
300000000 m/s
340 m/s
Walking speed
Light speed
Concorde
1.7 m/s
31 m/s
833 m/s
57
Average speed ( m/s )
Light speed 300000000 m/s
Earth in orbit 29790 m/s
Earth satellite 7500 m/s
Concorde 648 m/s
Air molecule 500 m/s
Fast jet 833 m/s
747 jumbo jet 270 m/s
Sound 340 m/s
Falcon 97 m/s
High speed train 60 m/s
UK motorway 31 m/s
UK town 13.4 m/s
Walking speed 1.7 m/s
Olympic sprinter 10.3 m/s
Snail 0.006 m/s
58
What is speed?

• When we talk about speed we mean
• the distance covered by an object in a
• given time.

59
What is speed?

• If Hamish (the dog) runs 10 metres in 2
• seconds, what is his speed?

60
What is speed?

• His speed is 5 metres per second.
• So speed is

61
What is speed?

• If you forget the formula think of cars
  travelling at 30 kilometres per hour

62

• 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.

63
distance
time
speed
64
Speed Calculations

• A cyclist travels 100 m in
• 12 s. What is her speed?

65

• Step 1 write down what you know.

d 100 m t 12 s s ?
66

• 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 s ?
d s x t
67

• Step 3 substitute in your values.

d 100 m t 12 s s ?
d s x t 100 s x 12
68

• Step 4 rearrange

d s x t 100 s x 12 s
d 200 m t 40 s v ?
100
12
69

• Step 5 calculate

d s x t 100 s x 12 s 8.33
d 100 m t 12 s v ?
100
12
70

• Step 6 units!!!!

d s x t 100 s x 12 s 8.33
m/s
d 100 m t 12 s s ?
100
12
71

• 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.

72
Instantaneous and average speed

• Are instantaneous and average speed the same?

73
Instantaneous or average?

• A cars speed between Arbroath and
• Dundee
• Average

74
Instantaneous or average?

• The speed read from a cars speedometer
• Instantaneous

75
Instantaneous or average?

• A tennis balls speed as it crosses the net
• Instantaneous

76
Instantaneous or average?

• A racing cars speed over a lap of the track
• Average

77
Instantaneous or average?

• A parachutists speed as he/she lands
• Instantaneous

78

• 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.

79
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 Position of light gate from bottom of slope Position of light gate from bottom of slope Position of light gate from bottom of slope Position of light gate from bottom of slope
Acceleration (m/s2) 1st attempt 2nd attempt 3rd attempt Position 1 m Position 2 m Position 3 m Position 4 m
Acceleration (m/s2) 1st attempt 2nd attempt 3rd attempt
Average acceleration (m/s2)
80
What is acceleration?

• Acceleration is the change in velocity of an
  object per second (in one second).
• Is acceleration a vector or scalar quantity?

81
Acceleration

• What is the definition of acceleration?
• Is it a vector or a scalar?

Acceleration is the rate of change of velocity
per unit time OR change in velocity per unit time.
Vector since velocity is a vector.
82
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
83
Calculating acceleration

• We need to know
• the change in velocity so
• initial velocity (u)
• final velocity (v)
• and
• time (t)

84
(No Transcript)
85
change in velocity
in one second
86
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

87
Units of acceleration
final velocity initial velocity
a
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.
88
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.

89
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

90
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.

91
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

92
Acceleration Calculations

• What do I know?
• Initial velocity u 0 m/s
• Final velocity v 18 m/s
• time t 4 s
• Formula?

93
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!!

94
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?

95
Rearranging the acceleration equation
v-u a
t
96
Rearranging the acceleration equation
97

• 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

98
Acceleration using two light gates

• http//www.crocodile-clips.com/absorb/AP5/sample/m
  edia/010102AccnApp.swf
• The length of the mask is 5 cm. Calculate
• the acceleration.
• Remember calculate u (initial velocity) and
• v (final velocity) and use

99
Acceleration using a double mask

• http//www.crocodile-clips.com/absorb/AP5/sample/m
  edia/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

100

• 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.

101
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.

102
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
103
Vectors and Direction

• When dealing with vector quantities we
• must have both magnitude and
• direction.
• 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.

104
Velocity-Time Graphs
Describe the motion of this object.
Constant velocity does not change with time
0
0
105
Velocity-Time Graphs
Describe the motion of this object.
Increasing with time constant acceleration
0
0
106
Velocity-Time Graphs
Describe the motion of this object.
Decreases with time constant deceleration
0
0
107
Velocity-Time Graphs
Describe the motion of this object.
0
0
108
Speed-Time Graphs
Calculate the distance covered by the object in
the first 10 s of its journey.
The area under the graph tells us the
distance travelled.
0
0
109
Speed-Time Graphs
Calculate the distance covered by the object in
the first 10 s of its journey.
The area under the graph tells us the
distance travelled.
0
0
110

• 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 Earths
  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

111
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.

112
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

113
Units of Force?

• Force (F) is
• measured in
• newtons (N).

114
Measuring Forces

• A Newton (or
• spring) balance can
• be used to measure
• forces.

115
Mass and Weight

• We often use the words mass and weight
• as though they mean the same
• but do they?

116
Mass and Weight

• An objects 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.

117
Mass and Weight

• An objects weight is
• the force exerted by gravity on a mass.
• Since it is a force, weight must be
• measured in
• newtons.

118
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.

119
Results
Mass Weight in N
100g
200g
300g
400g
500g
1kg
2kg
5kg
120
Relationship between mass and weight

• From this we can see a relationship
• between mass and weight
• 100g 0.1 kg -gt 1 N
• 1kg -gt 10 N
• To convert kg -gt N multiply by 10
• To convert N -gt kg divide by 10

121
Gravitational Field Strength (g)

• Gravitational field strength on Earth is
• 10 N / kg

122
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
123
What is gravitational field strength?

• and the pull of gravity on a 2 kg mass is

20 N
124
Definition

• A planets gravitational
• field strength is the
• pull of gravity on
• a 1 kg mass.

125
Gravity in the universe

• Is gravitational field strength always the
• same?
• No! It varies on different planets.
• http//www.exploratorium.edu/ronh/weight/index.htm
  l

126
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.

127

• Mass on Earth 60 kg
• Weight on Earth 600 N
• Gravitational field strength
• Weight on Mercury 226.8 N g
• Weight on Venus 544.2 N g
• Weight on the Moon 99.6 N g
• Weight on Mars 226.2 N g
• Weight on Jupiter 1418.4 N g
• Weight on Saturn 549.6 N g

128
Units for g

• We found g by dividing weight in newtons
• by mass in kilograms.
• What are the units for g?

10 N / kg
129

• Which of the planets has the greatest
• gravitational field strength?
• Why do you think this is the case?

130
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

m x g W
mass
Gravitational field strength g
weight
131
Weight, mass and gravity
Why is weight measured in newtons?

• W mg

Gravitational field strength measured in N / kg
Mass measured in kg
Weight measured in newtons
132

• 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.

133
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.

134
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.

135
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

136
Increasing Friction

• On the approach to traffic lights and
• roundabouts, different road surfaces are
• used to increase friction compared with
• normal roads.

137
Decreasing Friction

• In some cases, we want to decrease
• friction. Some examples of this are
• Ice skating
• Skiing
• Aircraft design

138
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
• arent in contact because of a thin layer
• of oil between them.

139
Reducing Friction

• Friction can be reduced by
• Separating surfaces with air (e.g. a
• hovercraft).
• Making surfaces roll (e.g. by using ball
• bearings).

140
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.

141
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
142

• 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
• Newtons first law.

143
Force

• Force is a vector quantity. What do we
• mean by this?
• To describe it fully we must have size
• and direction.

144
Balanced Forces
F
F

• Balanced forces are EQUAL FORCES which act in
  OPPOSITE DIRECTIONS. They CANCEL EACH OTHER OUT.

145

• If balanced forces act on a STATIONARY OBJECT,
  it REMAINS STATIONARY.

If balanced forces act on a MOVING OBJECT, it
continues moving in the same direction with
CONSTANT VELOCITY.
146

• This is summarised by NEWTONS 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
- Newtons First Law
147

• To understand NEWTONS 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).
148

• 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?

149
Forces and Supported Bodies

• A stationary mass m
• hangs from a rope.
• What is the weight of
• the mass? In what
• direction does
• this act?
• W mg downwards

m
150
Forces and Supported Bodies

• The mass is stationary.
• Newtons law tells us
• that the forces must
• be
• balanced forces.
• The weight is
• counterbalanced by a
• force of the same size
• acting upwards due to
• the tension in the
• string.

m
151
Forces and Supported Bodies

• A book of mass m
• rests on a shelf.
• What is the weight of
• the book? In what
• direction does
• this act?
• W mg downwards

m
152
Forces and Supported Bodies

• The mass is stationary.
• Newtons law tells us
• that the forces must be
• balanced forces.
• The weight is
• counterbalanced by a
• force of the same size
• acting upwards due to
• the shelf.

m
153
What forces are acting on this stationary
hovering helicopter?
W mg
lift
W mg
154
Newtons First Law

• Newtons 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
- Newtons First Law
155
A moving car If a car moves with constant
velocity, then what forces are acting on it?
The ENGINE FORCE and the FRICTION FORCE
must be equal.
156

• Newtons 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 cars 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.
157
No seatbelt whats going to happen when the car
hits the wall? Explain this in terms of Newtons
1st law.
158
Whats going to happen when the motorbike hits
the wall? Explain this in terms of Newtons 1st
law.
159
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.
160

Forces in a Fluid
Terminal velocity Any free-falling object in a
fluid (liquid or gas) reaches a top speed, called
terminal velocity.
161
Terminal velocity The air resistance acting
on a moving object increases as it gets
faster. Terminal velocity is reached when the
air-resistance (acting upwards) has increased to
the same size as the persons weight (acting
downwards)
162
time 0s, velocity 0 m/s, friction 0 N
Friction Ff(air resistance) 0 N
a -10 m/s2
W weight
163
Ff
a lt -10 m/s2
v
W weight
164
Equal opposite forces Acceleration
zero Terminal velocity
Ff
a 0 m/s2
v
W weight
165
Velocity Time Graph
velocity (m/s)
Terminal velocity
0
0
time (s)
Virtual Int 2 Physics Mechanics Heat Forces
- Terminal Velocity
166
air resistance
Terminal velocity is reached when the air
resistance balances the weight.
weight
167
Terminal Velocity

• What effect does opening a parachute
• have on the 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.

Virtual Int 2 Physics Mechanics Heat Forces
- Terminal Velocity
168

• Key words Newtons 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

169

• The example of the parachutist accelerating
  until the forces are balanced helps us to
  understand NEWTONS 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
- Newtons First Law
170
Force, mass and acceleration
Acceleration (m/s2)

• F ma

Force (N)
mass (kg)
Virtual Int 2 Physics Mechanics Heat Forces
- Force, mass and acceleration
171
Force, mass and acceleration

• One newton (1N) is the force required to
• accelerate 1 kg at 1 m/s2

172
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
173

• 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.

174
Newtons 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)

175
Newtons Second Law

• Newtons 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.

176
Newtons 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

177
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.

178
Forces are measured in?

• Newtons Second Law can be written as
• or more commonly

179
Forces are measured in?

• 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

180
Quick Quiz
Unbalanced force (N) Mass (kg) Acceleration (m/ s2)
10 2
20 2
20 4
2 5
10 10
5
10
5
10
1
181
Direction of force

• Consider the oil drop trail left by the car
• in motion.
• In which direction is the acceleration?
• In which direction is the unbalanced
• force?

To the right
To the right
182
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.
183
Newtons First and Second Laws

• Remember
• Forces do not cause motion
• Forces cause acceleration

184
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.

185
Using Newtons Second Law

• In the simplest case

Fun
m
186
Using Newtons Second Law
Direction of acceleration? Direction of
unbalanced force? Formula for calculating
acceleration?
F2
F1
m
187
Solving Problems

• Always draw a diagram showing all known
• quantities (forces magnitude and
• direction, resultant acceleration and
• direction, mass of object(s) )
• Remember that Funma can be applied to
• the whole system
• When working in the vertical direction
• always include the weight

188

• 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.

189
Acceleration due to Gravity
Definition A planets gravitational field
strength equals the force of gravity PER UNIT
MASS. Units? N/kg
To calculate an objects weight, use this
equation -
Virtual Int 2 Physics Projectiles
Acceleration due to gravity and gravitational
field strength
190
Acceleration due to Gravity

• Near a planets surface all objects experience
  the same gravitational acceleration.
• This acceleration is numerically equal to the
  planets gravitational field strength.

191
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?
192
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
  planets
• surface.
• What will happen to the weight of an object as it
  gets
• further from the surface? Explain your answer.
• It will decrease.

193

• The force of gravity near
• the Earths surface gives
• all objects the same
• acceleration.
• So why doesnt the
• feather reach the ground
• at the same time as the
• elephant?

194

• Why are the gaps
• between the balls
• increasing?

195

• An object is released from rest close to the
  Earths
• surface. Which formula can be used to find its
  velocity
• at a given time?
• v u at
• where v ? , u 0 , a
  , t
• What is its velocity
• At the time of release?
• After 1 second?
• After 2 seconds?
• After 3 seconds?
• After 4 seconds?

196
Projectiles

• Virtual Int 2 Physics Projectiles
• Projectile Motion

197
Forces acting on projectiles

• What would happen to a ball kicked off a
• cliff, in the absence of gravity?

198
Forces acting on projectiles

• There would be no vertical motion
• therefore the ball would continue at
• constant speed in a straight
• line (remember Newtons first law)

199
Objects projected horizontallyThink about

• What is the initial vertical speed of a
• projectile fired horizontally?
• How will the horizontal speed vary during
• the objects flight?

0 m/s
It will remain the same as the initial horizontal
speed.
200
Objects projected horizontallyThink about

• Describe the vertical motion of an object
• projected horizontally

It will accelerate downwards due to gravity.
201
Projectiles
Virtual Int 2 Physics Projectiles Comparing
Projectile Motion with Vertical Motion Virtual
Int 2 Physics Projectiles Graphs of
Projectile Motion
202
Objects projected horizontallyThink 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?

time of flight (s)
horizontal displacement (m)
sh vht
horizontal velocity (m/s)
203
Which ball will hit the ground first?
http//www.fearofphysics.com/XYIndep/xyindep_corre
ct.html
204
Summary
Horizontal motion Vertical motion
Forces Are there forces present? If so, in what direction are they acting? No Yes The force of gravity acts downward
Acceleration Is there acceleration? If so, in what direction? What is the value of the acceleration? No Yes Acceleration "g" downward at 10 m/s2
Velocity Constant or changing? Constant Changing by 10 m/s each second
205
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 isnt a test of memory so
  while you should learn your formulae, dont 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.

206
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.
• 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.

207
Example

• (b) Calculate the vertical speed of the flare
  after 4s
• final speed v ?
• initial vertical speed u 0 m/s Initial
  vertical speed is always 0 m/s!
• acceleration a 10 m/s2
• time t 4 s
• v u at
• v 0 10 x 4
• v 40 m/s

208
Example

• (c) Draw a graph to show how vertical speed
  varies with time.
• Initial vertical speed 0 m/s
• Final vertical speed 40 m/s

209
Example

• (d) Use this graph to calculate the height of the
  cliff.

Displacement area under velocity-time graph ½
bh ½ x 4 x 40 80 m Height of cliff 80 m
210
Projectiles
Virtual Int 2 Physics Projectiles Example
Problem
Virtual Int 2 Physics Projectiles Newtons
Thought Experiment
211

• Key words Newtons third law, newton
• pairs
• By the end of this lesson you will be able
• to
• State Newtons 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.

212
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.
213
Newtons 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
214
Firing a gun

• Force of GUN on BULLET

Force of BULLET on GUN
215
Starting a sprint

• Force of RUNNER on BLOCKS

Force of BLOCKS on RUNNER
216
A falling apple

• Force of EARTH on APPLE

Force of APPLE on EARTH
217
A Rocket
Force of GAS on ROCKET

• Force of ROCKET on GAS

218

• 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.

219
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

220
Momentum

• The momentum of an object is the
• mass x velocity
• It is a vector quantity.
• It has units of kg m/s

221
Momentum Collisions
Virtual Int 2 Physics Mechanics and Heat
Momentum Collisions

• We will consider two types of collision
• Vehicles bounce apart
• after collision
• 2.Vehicles stick together
• after collision

222
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.

223
How can we find the answer?

• Using the Law of Conservation of Momentum!

224

• total momentum before collision
• total momentum after collision
• providing no external forces are acting.

225
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.

226
Collisions where vehicles bounce apart

• Before After

1 kg
2 kg
1 kg
2 kg
? m/s
1 m/s
0 m/s
3 m/s
momentum mass x velocity
momentum mass x velocity
Conservation of momentum tells us momentum
before momentum after
227
Collisions where vehicles bounce apart
1 kg
2 kg
? m/s
1 m/s
momentum mass x velocity
228
Collisions where vehicles bounce apart
1 kg
2 kg
? m/s
1 m/s
Check does this work?
Conservation of momentum tells us momentum
before momentum after
229
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.

230
Collisions where vehicles stick together

• Before After

1 kg
1 kg
1 kg
1 kg
0 m/s
momentum mass x velocity
2 m/s
? m/s
momentum mass x velocity
Conservation of momentum tells us momentum
before momentum after
231
Collisions where vehicles stick together
1 kg
1 kg
momentum mass x velocity
? m/s
232
Collisions where vehicles stick together
1 kg
1 kg
momentum mass x velocity
1 m/s
Check does this work?
Conservation of momentum tells us momentum
before momentum after
233

• 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.

234
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.

235
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.

236
Work done?

• Formula linking work done, force and
  displacement?
• 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.

237
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

238
Work done

• What do I know?
• F 30N
• d 15m
• Formula?

Virtual Int 2 Physics Mechanics Heat Work
Done Example Problem
239
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
time in seconds
Power in watts (joules per seconds)
240
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

241
Power

• What do I know?
• F 30N
• d 15m
• t 20s
• Formula?

242
Power

• What do I know?
• F 30N
• d 15m
• t 20s
• Ew 450J
• Formula?

243

• 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.

244
Gravitational Potential Energy

• is the potential energy
• gained by an object when
• we do work to lift it
• vertically in a gravitational
• field.

245
Gravitational Potential Energy

• The work done in lifting an
• object vertically

What force is required?
246
Gravitational Potential Energy
To lift the object we must overcome the weight
Wmg
247
Gravitational Potential Energy
Vertical distance we call this height h
248
Gravitational Potential Energy
Virtual Int 2 Physics Mechanics Heat
Potential Energy Example Problem
249
Kinetic Energy

• is the energy associated with a moving object.

250
Kinetic Energy

• depends on
• The mass of the object

251
Kinetic Energy

• depends on
• The velocity of the object

252
Kinetic Energy
Virtual Int 2 Physics Mechanics Heat
Kinetic Energy Example Problem
Virtual Int 2 Physics Mechanics Heat Power
Example Problem
253
(No Transcript)
254
Speed and Stopping Distance

• The distance required to stop a moving vehicle is
  a combination of two things
• Thinking distance
• Braking distance

255
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
256
Speed and Stopping Distance
This is the distance you travel between pressing
your brakes and the car coming to a stop.

• Braking distance

To stop a