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Drouin Secondary College
VCE Physics
Topic: Movement
VCE PHYSICS
UNIT 2
MOVEMENT
Topic Notes
Page 1
Drouin Secondary College
VCE Physics
Topic: Movement
VCE Physics
Unit 2
Topic 1
Movement
Unit Outline
To achieve this outcome the student should use scientific methods, data, theories and knowledge to:
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Describe non-uniform and uniform motion along a straight line graphically;
Analyze motion along a straight line graphically, numerically and algebraically;
Describe how changes in movement are caused by the actions of forces;
Model forces as external actions through the centre of mass point of each body;
Explain movement in terms of the Newtonian model and some of its assumptions,
including Newton’s 3 laws of motion, forces act on point particles, and the ideal,
frictionless world.
Compare the accounts of the action of forces by Aristotle, Galileo and Newton.
Apply the vector model of forces including vector addition, vector subtraction and
components to readily observable forces including weight, friction and reaction forces;
Model mathematically work as force multiplied by distance for a constant force and as
area under the force versus distance graph.
Interpret energy transfers and transformations using an energy conservation model
applied to ideas of work, energy and power, including transfers between
– kinetic energy and gravitational potential energy close to the Earth’s surface;
– potential energy and kinetic energy in springs;
Chapter 1
Introduction
1.0
An Ideal World
To make life easier for Physics students situations or events which require
mathematical analysis are often described as occuring in an ideal,
frictionless world.
In the ideal world the laws of motion apply exactly, eg. objects which are
moving will continue to move with the same speed unless or until
something occurs to change this.
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Drouin Secondary College
VCE Physics
Topic: Movement
In the ideal world an object under the influence of Earth’s gravity will
accelerate at 9.8 ms-2 throughout its journey never reaching terminal
velocity.
In the ideal world energy transformations are always 100% efficient, so that
the potential energy of a pendulum at the top of its swing is all converted to
Kinetic Energy (motion) energy at the bottom.
In the ideal world perpetual motion machines are commonplace.
1.1
The S.I. System
In 1960, the “General Conference of Weights and Measures” , a Paris based
international organisation, agreed that one set of units would be adopted
world wide for the measurement of _______________ quantities.
This system is called the Systeme Internationale d’Units, or more simply the
____ _____ System.
The system is used and recognised worldwide and defines ___ fundamental
units.
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Drouin Secondary College
VCE Physics
Physical Quantity
Topic: Movement
S.I. Unit
metre
Mass
Time
Luminous Intensity
Symbol
m
kg
second
ampere
A
kelvin
candela
K
cd
Amount of Substance
mol
All other units are derived from these 7 fundamentals.
A derived unit is the force unit, the ______________, which is found from
mass x length x 1/(time)2
Thus the Newton has dimensions kg x m x s-2
1.2
S.I. Definitions
Length; metre [m]
It is the _______________ light travels, in a ___________, in 1/299,792,458th
of a second.
Mass; kilogram [kg]
It is the mass of a platinum-iridium cylinder kept at Sevres in France. It is
now the only basic unit still defined in terms of a _______________ object.
Time; second [s]
It is the length of time taken for 9,192,631,770 periods of vibration of the
________________ atom to occur.
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Drouin Secondary College
VCE Physics
Topic: Movement
Current; ampere [A]
It is that current which produces a _____________ of 2 x 10-7 N between two
parallel wires which are ______ metre apart in a vacuum.
Temperature; kelvin [K]
It is 1/273.16th of the thermodynamic temperature of the ___________ point
of water.
Amount of Substance; mole [mol]
It is the amount of substance that contains as many elementary units as
there are atoms in 0.012 kg of 12C
Luminous Intensity; candela [cd]
It is the intensity of a source of light of a specified frequency, which gives a
specified amount of power in a given direction.
_________________________________________________________________
QUESTIONS
1. Which of the following quantities have fundamental units and which have derived ?
Quantity (Unit)
Fundamental
Derived
Power (Watts)
Distance (metre)
Time (second)
Force (Newton)
Energy (Joule)
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Drouin Secondary College
VCE Physics
Topic: Movement
Mass (kilogram)
Electrical Resistance (ohms)
Temperature (kelvin)
Electric Current (amperes)
2. From which of the fundamental units do the following derive their units ?
Quantity (Unit)
e.g Force (Newton)
Fundamental Units
Mass (kg), length (m), time (s)
Acceleration (ms-2)
Momentum (kgms-1)
Impulse (Newton.second)
Velocity (ms-1)
Work (Joule)
Note: W = F.d
3. Show that 1 ms-1 = 3.6 kmh-1
1.3
Position
In order to specify the position of an object we first need to define an
______________ or starting point from which measurements can be taken.
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Drouin Secondary College
VCE Physics
Topic: Movement
For example, on the number line, the point _________ is taken as the origin
and all measurements are related to that point.
-40 -35 -30 -25 -20 -15 -10 -5
0
5
10
15 20 25 30 35 40
Numbers to the ____________ of zero are labelled positive
Numbers to the ____________ of zero are labelled negative
A number 40 is 40 units to the right of 0
A number -25 is 25 units to the left of 0
_________________________________________________________________
QUESTIONS
4. What needs to be defined before the position of any object can be specified ?
5 (a) What distance has been covered when an object moves from position +150 m to
position + 275 m ?
(b) What distance has been covered when an object moves from position + 10 m to
position -133.5 m ?
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Drouin Secondary College
VCE Physics
Topic: Movement
Chapter 2
2.0
Scalars and Vectors
Before proceeding further we need to define two new quantities:
SCALAR QUANTITIES
These are completely defined by
• A _____________ and
• A Unit
Examples of scalars are: Temperature 170 0C, Mass 1.5 kg
VECTOR QUANTITIES
These are completely defined by
• A Number
• A Unit and
• A ___________
Examples of vectors are: Displacement 25 km West, Force 14 Newtons
South
Vectors are usually represented by an ____________, with the length of the
arrow indicating the size of the quantity and the direction of the arrow the
direction of the quantity.
Draw in the vector which represents a Force of 4 N, acting North West
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Drouin Secondary College
VCE Physics
Topic: Movement
_________________________________________________________________
QUESTIONS
6. Which of the following quantities are scalars and which vectors ?
Quantity
Unit
Distance
metre
Momentum
kgms-1 East
Kinetic Energy
joule
Acceleration
ms-2 N45oE
Gravitational Field
Strength
Displacement
Nkg-1 downwards
Age
years
Velocity
ms-1 West
Temperature
o
2.1
Scalar
Vector
metre sideways
C
Vector Addition & Subtraction
Vectors can be at any _______________ to one another and still be added.
This can be done in two ways:
Draw accurate, scale vectors on graph paper and measure the size
and direction of the result of the addition, called the “resultant vector”
Draw sketch vectors and use trig and algebraic methods to calculate
the size and direction of the resultant.
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Drouin Secondary College
VCE Physics
Topic: Movement
ADDITION
SUBTRACTION
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2.2
VCE Physics
Topic: Movement
Vector Components
A single vector can be broken up into two or more parts called
___________________.
This process is useful when, for example, trying to find the vertical and
horizontal parts of a force which is accelerating a mass through the Earth’s
atmosphere.
FH and FV are the COMPONENTS of the force F.
F = 5 x 106 N
FV
30o
FH
The Horizontal component of the force (FH) can be found using trig
methods:
FH = F cos 30o
= (5 x 106) ( 0.866)
= 4.3 x 106 N
Similarly for the Vertical component (FV),
FV = F sin 30o
= (5 x106)(0.5)
= 2.5 x 106 N
_________________________________________________________________
QUESTIONS
7. What is the resultant force when 2 forces (6.0 N west and 4.0 N south) act on an
object at the same time ?
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Drouin Secondary College
VCE Physics
Topic: Movement
8. Calculate the change in velocity of an object initially travelling at 8.5 ms-1 East whose
final velocity was 8.5 ms-1 West. (remember Change in Velocity = Final Velocity – Initial
Velocity)
9. An boy fires a stone from slingshot. The stone leaves with a velocity of 27 ms-1 at an
angle 320 above the horizontal. Calculate the vertical and horizontal components of the
stone’s velocity.
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Drouin Secondary College
VCE Physics
Topic: Movement
10. Calculate the acceleration of a car whose velocity changes from 16 ms-1 west to 21 ms-1
north in 1.5 seconds (acceleration = change in velocity/change in time)
Chapter 3 - Kinematics
3.0
Distance & Displacement
Distance is a _____________quantity. It has a Unit (metres) but no Direction.
Distance is best defined as “How far you have travelled in your journey”
Displacement is a _____________ quantity
Having both a Unit (metres) and a Direction.
Displacement is best defined as “How far from your starting point you are at
the end of your journey”
The difference between these two quantities is easily illustrated with a
simple example. You are sent on a message from home to tell the butcher
his meat is off.
2 km
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Drouin Secondary College
VCE Physics
Topic: Movement
At the end of the journey, Distance travelled = _________ = _______ km
while Displacement = ____________ = _____ km
3.2
Speed & Velocity
These two terms are used interchangeably in the community but strictly
speaking they are different:
Speed is the time rate of change of distance, i.e.,
Speed = Distance /Time
Speed is a ____________QUANTITY, having a unit (ms-1), but no direction.
Thus a speed would be: 100 kmh-1 or, 27 ms-1
Velocity is the time rate of change of displacement, i.e.,
Velocity = Displacement / Time
Velocity is a _____________ QUANTITY, having a unit (ms-1) AND a direction.
Thus a velocity would be:
100 kmh-1 South or - 27 ms-1
3.3
Acceleration
Acceleration is defined as the time rate of change of velocity, i.e.,
Acceleration = Velocity/Time
Acceleration is a ____________ QUANTITY having both a unit (ms-2) and a
direction.
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Drouin Secondary College
VCE Physics
Topic: Movement
There is no scalar measurement of acceleration, so acceleration MUST
always be quoted with a direction.
Typically, Acceleration means an _________________ in velocity over time,
while Deceleration means a __________________ in velocity over time.
When v and a are in the same direction, the car _____________________ and
its velocity will increase over time.
When v and a are in the opposite direction, the car __________________ and
its velocity will decrease over time.
3.4
Instantaneous & Average Velocity
The term velocity can be misleading, depending upon whether you are
concerned with an Instantaneous or an _________________ value.
The best way to illustrate the difference between the two is with an example.
You take a car journey out of a city to your gran’s place in a country town 90
km away. The journey takes you a total of 2 hours.
The __________________
___________________ for this journey,
vAV = Total Displacement = 90 = 45 kmh-1
Total Time
2
However, your instantaneous velocity measured at a particular time during
the journey would have varied between 0 kmh-1 when _____________ at
traffic lights, to, say 120 kmh-1 when speeding along the freeway.
Average and Instantaneous velocities are rarely the same.
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Drouin Secondary College
VCE Physics
Topic: Movement
Unless otherwise stated, all the problems you do in this section of the
course require you to use Instantaneous Velocities.
_________________________________________________________________
QUESTIONS
11. A runner completes a 400 m race (once around the track) in 21 seconds what is
(a) her distance travelled (in km), (b) her displacement (in km), (c) her speed (in ms-1)
and (d) her velocity (in ms-1) ?
12. A roller coaster, at the end of its journey, changes it’s velocity from 36 ms-1 to 0 ms-1 in
2.5 sec. Calculate the roller coaster’s acceleration.
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Drouin Secondary College
VCE Physics
Topic: Movement
Chapter 4 Motion by Graphs
4.0
Graphical Relationships
It is often useful and convenient to represent information about things like
position, velocity, acceleration etc., using graphs.
Graphs “_______ ______ ____ _____________”.
You need to develop the skills and abilities to “read the story”.
There are two basic types of graphs used in Physics:
(a) __________Graphs – give a “broad brush” picture of the general
relationship between the two quantities graphed.
(b) _________________ Graphs – give the exact mathematical
relationship between the two quantities graphed and may be used to
calculate or deduce numerical values.
4.1
Sketch Graphs
Sketch graphs have labelled axes but no numerical values, they give a
general broad brush relation between the quantities.
_________________________________________________________________
Dist
QUESTIONS
13.
The Story:
Time
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Drouin Secondary College
VCE Physics
Topic: Movement
Disp
The Story:
Time
Velocity
The Story:
Time
Displ
The Story:
Time
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Drouin Secondary College
4.2
VCE Physics
Topic: Movement
Exact Graphical Relationships
The graphs you are required to interpret mathematically are those where
distance or displacement, speed or velocity or acceleration are plotted
against time.
The information available from these graphs are summarised in the table
given below.
Graph Type
Read from Graph
Slope
Area
Learn this table off by heart.
Put it on any cheat sheet you are allowed to use.
_________________________________________________________________
QUESTIONS
14. Given below is the Distance vs Time graph for a cyclist riding along a straight path.
Distance (m)
A
B
C
D
20
10
Time (s)
0
10
20
30
40
50
60
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Drouin Secondary College
VCE Physics
Topic: Movement
(a) In which section (A,B,C or D) is the cyclist stationary ?
(b) In which section is the cyclist travelling at her slowest (but not zero) speed ?
(c) What is her speed in part (b) above ?
(d) What distance did she cover in the first 40 seconds of her journey ?
(e) In which section(s) of the graph is her speed the greatest ?
(f) What is her displacement from her starting point at t = 50 sec ?
15. Shown below is the Velocity vs Time graph for a motorist travelling along a straight
section of road.
Velocity (ms-1)
10
8
6
4
Time(s)
2
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
-2
-4
-6
-8
-10
(a) What is the motorist's displacement after 4.0 sec ?
(b) What is the motorists acceleration during this 4.0 sec period ?
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Drouin Secondary College
VCE Physics
Topic: Movement
(c) What distance has the motorist covered in the 20.0 sec of his journey ?
(d) What is the motorist's displacement at t = 20.0 sec
(e) What happens to the motorists velocity at t = 20.0 sec? Is this realistic ?
(f) Sketch an acceleration vs time graph for this journey.
16. An object is fired vertically upward on a DISTANT PLANET. Shown below is the Velocity
vs Time
graph for the object. The time commences the instant the object leaves the launcher
(a) What is the acceleration of the object ?
(b) What is the maximum height attained by the object ?
(c) How long does the object take to stop ?
(d) How far above the ground is the object at time t = 10.0 sec ?
Velocity (ms
-1
)
30
0
2
4
6
8
10
12
Time (s)
-30
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Drouin Secondary College
VCE Physics
Topic: Movement
Chapter 5
5.0
The Equations of Motion
The Equations of Motion are a set of equations linking displacement,
velocity, acceleration and time.
They allow calculations of these quantities without the need for graphical
representations.
The 3 main equations are:
v = u + at
v2 = u2 + 2as
s = ut + ½at2
Where, u = initial velocity (ms-1) v = final velocity (ms-1)
a = acceleration (ms-2) s = displacement (m) t = time (s)
THESE EQUATION CAN ONLY BE USED IF THE ACCELERATION IS
______________________
When using the equations, always ________ out the information given and
note what you need to find, then choose the most appropriate equation.
In some cases you also need to define a _____________direction, up or
down for vertical motion, left or right for horizontal motion questions
5.1
Motion Under Gravity
Objects (close to the surface) falling through the Earth’s ________________
field are subject to a constant acceleration of 9.8 ms-2.
Since the acceleration is constant this motion can be analysed by the
________________ of motion.
The acceleration in this case is ________________ directed downward.
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Drouin Secondary College
VCE Physics
Topic: Movement
Objects thrown or fired directly upwards would thus have their velocity and
______________________ in opposite directions.
The calculations using the equations of motion always ignore the effects of
friction and air resistance
You need to go through the same process of listing information and
deciding on a positive direction.
_________________________________________________________________
QUESTIONS
17. A truck travels from rest for 10.0 sec with an acceleration of 3.0 ms-2. Calculate the
truck's final velocity and total distance travelled.
18. A ball rolling down an inclined plane from rest travels a distance of 20.0 m in 4.00
sec. Calculate its acceleration and its final speed
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Drouin Secondary College
VCE Physics
Topic: Movement
19. The speed of a freewheeling skateboard travelling on a level surface falls from 10.0 ms-1
to 5.00 ms-1 in moving a distance of 30.0 m. If the rate of slowdown is constant, how much
further will the skateboard travel before coming to rest ?
20. A bullet leaves the barrel of a gun aimed vertically upwards at 140 ms -1. How long will
it take to reach its maximum height ? (Ignore air resistance and use g = 10 ms-2) .
Chapter 6
Forced Change
6.0
What is a Force ?
"A force is an interaction between two material objects involving a ________
or a _________."
How is this different from the usual textbook definition of a Force simply
being a “push or a pull” ?
First, a force is an "_________________".
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Drouin Secondary College
VCE Physics
Topic: Movement
You can compare a force to another common interaction - a
conversation.
A conversation is an interaction between 2 people involving the exchange of
words (and ideas).
Some things to notice about a conversation (or any interaction) are:
To have a conversation, you need ________ people. One person can't have a
conversation
A conversation is something that happens between two people.
It is not an independently existing "thing" (object), in the sense that a chair
is an independently existing "thing".
_____________ are like conversations in that: To have a force, you have to
have 2 objects - one object pushes, the other gets pushed.
In the definition, "(material) objects" means that both objects have to be
made out of ______________ - atoms and molecules. They both have to be
"things", in the sense that a chair is a "thing".
A force is something that happens ________________2 objects. It is not an
independently existing "thing" (object) in the sense that a chair is an
independently existing "thing".
________________________________________________________________
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Drouin Secondary College
VCE Physics
Topic: Movement
QUESTIONS
21. A force is an interaction between 2 objects. Therefore a force can be likened to
A: Loving chocolate
B: Fear of flying
C: Hatred of cigarettes
D: Having an argument with your partner
22. Between which pair can a force NOT exist ?
A: A book and a table
B: A person and a ghost
C: A bicycle and a footpath
D: A bug and a windscreen
6.1
What Kinds of Forces Exist ?
For simplicity sake, all forces (interactions) between objects can be placed
into two broad categories:
·1. ______________ ____________ are types of forces in which the two
interacting objects are physically contacting each other. Examples of
contact forces include frictional forces, tensional forces, normal forces, air
resistance forces, and applied forces.
2. ____________
______________are forces in which the two interacting
objects are not in contact with each other, yet are able to exert a push or
pull despite a physical separation. Examples of field forces include
Gravitational Forces, Electrostatic Forces and Magnetic Forces
Force is a quantity which is measured using the derived metric unit known
as the ________________.
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Drouin Secondary College
VCE Physics
Topic: Movement
One Newton (N) is the amount of force required to give a 1- kg mass an
acceleration of 1 ms-2. So 1N = 1 kgms-2
Force is a __________________ quantity, you must describe both the
magnitude (size) and the direction.
_________________________________________________________________
QUESTIONS
23. Classify the following as examples of either Contact or Field forces in action (or
maybe both acting at the same time).
EXAMPLE
CONTACT
FORCE
FIELD
FORCE
(a) A punch in the nose
(b) A parachutist free falling
(c) Bouncing a ball on the ground
(d) A magnet attracting a nail
(e) Two positive charges repelling each other
(f) Friction when dragging a refrigerator across
the floor
(g) A shotput after leaving the thrower’s hand
6.2
What Do Forces Do ?
Forces affect motion. They can:
•
Begin motion
•
Change motion
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Drouin Secondary College
•
Stop motion
•
Have no effect
VCE Physics
Topic: Movement
BEGINNING MOTION:
A constant force (in the same direction as the motion) produces an ever
increasing __________________.
CHANGING MOTION:
A constant force (at right angles to the motion) produces an ever changing
_____________________ of velocity.
STOPPING MOTION:
A constant force (in the opposite direction to the motion) produces an ever
__________________________ velocity.
NO EFFECT:
A total applied force smaller than friction will not move the mass
6.3
Where Forces Act
Forces acting on objects must have a point of application, a place where the
force acts.
For Contact Forces the point of application is simply the point at which the
force initiator contacts the object.
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Drouin Secondary College
VCE Physics
Topic: Movement
For Field Forces, the only one applicable in movement being gravity, will act
through the centre of mass of the object
_________________________________________________________________
QUESTIONS
24. A body is at rest. Does this necessarily mean that it has no force acting on it ? Justify
your answer.
25. Calculate the net force acting on the object in each of the situations shown.
(a)
(b)
900 N
1200 N
N
(c)
250 N
250 N
75 N
95 N
(d)
150 N
450 N
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Drouin Secondary College
6.4
VCE Physics
Topic: Movement
Forces in 2 Dimensions
Forces can act in any direction and the total or ______________ force is the
vector sum of all the forces acting.
Tim, Tom and Tam, the triplets, are fighting over a teddy bear. Each exerts a
different force. What will be the net force on the bear ?
A force diagram shows each boy’s contribution
FTOM = 25 N
FTIM = 26 N
FTAM = 18 N
Add the vectors head to tail.
The resultant force is the vector joining the starting point to the finishing
point.
The bear will then ________________ in the direction of the resultant force.
________________________________________________________________
QUESTIONS
26. Tim, Tom and Tam, the triplets, are fighting over a teddy bear. Each exerts a
different force. A force diagram shows each boy’s contribution. What will be the net
force on the bear ?
FTIM = 35 N
FTOM = 26 N
FTAM = 12 N
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Drouin Secondary College
6.5
VCE Physics
Topic: Movement
Weight
Weight is the outcome of a gravitational field acting on a _________
Weight is a ______________ and is measured in Newtons.
Its direction is along the line joining the centres of the two bodies which,
between them, generate the Gravitational Field.
Near the ____________ of the Earth, each kilogram of mass is attracted
toward the centre of the earth by a force of 9.8 N.
(Of course each kilogram of Earth is also attracted to the mass by the same
force, Newton 3)
So, the Gravitational Field Strength near the Earth’s surface = 9.8 Nkg-1
Weight and mass are NOT the same, but they are related through the
formula:
W = mg
W = Weight (N)
m = mass (kg)
g = Grav. Field
Strength (Nkg-1)
_________________________________________________________________
QUESTIONS
27. Fill in the blank spaces in the table based on a person whose mass on earth is 56 kg
Planet
Earth
Mass on
planet (kg)
56
Grav Field Strength
(Nkg-1)
9.81
Mercury
0.36
Venus
0.88
Weight on planet
(N)
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Drouin Secondary College
VCE Physics
Jupiter
26.04
Saturn
11.19
Uranus
10.49
6.6
Topic: Movement
Reaction Force
All objects on and near the Earth’s surface are subject to the gravitational
_______________.
Any object subject to a net or resultant force will ___________________ in
the direction of that force (Newton 2).
Why then do objects placed on a table on the Earth’s surface remain
__________________ ?
There must be a force equal in size and opposite in direction to cancel out
the gravitational force.
There is such a force. It is called the ________________ or NORMAL FORCE.
The Reaction Force only exists as a result of the action of the weight of the
vase acting on the table top and as such the reaction force does not exist as
an isolated force in its own right.
Because there is no net or resultant force on the vase, it remains stationary
on the table
Remove the table, the reaction force disappears and the vase accelerates
under the action of W, until it encounters the floor and probably smashes.
Note:
W and R are NOT an action reaction pair. Why?
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Drouin Secondary College
VCE Physics
Topic: Movement
Because when R disappears W does not.
Chapter 7
7.0
Centre of Mass
In order to deal with large objects it is useful to think of all the object’s
mass being ______________________ at one point, this point being the
Centre of Mass of the object.
For regularly shaped objects eg. squares or rectangles, cubes or spheres
the Centre of Mass of the object is in the geometric ______________ of the
object
For odd shaped objects such as a boomerang, the Centre of Mass may fall
outside the ________________ of the object.
The C of M is the point around which the object it will ____________ if a
torque or turning force is applied to the object.
7.1 Translation and Rotation
When a Force acts through the Centre of Mass (C of M) of an object or
structure, it causes ______________________ Motion, ie. The object moves
in the __________________ of the applied force according to Newton’s 2nd
Law. (see section 6.3)
When the force is applied to another part of the object or structure, a
_________________ or TWISTING FORCE or TURNING MOMENT is applied
and Rotational as well as Translational motion occurs
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Drouin Secondary College
VCE Physics
Topic: Movement
Chapter 8 - Newton’s Laws
8.0
Aristotle to Newton
Attempts to explain the “causes of motion” (a field of study called
_______________), were first recorded in the time of the ancient Greek
philosopher Aristotle (384 – 322 BC).
It was believed that ________________speed required a ___________ force.
This seemed logical as everyone could see that a horse needed to apply a
constant pull to haul a cart at constant speed.
However there were problems with the theories which could not, for
example, explain why falling objects tended to ___________ their speed in
the absence of any visible _____________ or why heavenly bodies behaved
differently than those on earth.
It was Galileo (1564 – 1642) who was the first to define the property of matter
we call ___________________, (matter’s tendency to resist changes in its
motion), with his law which said “when no force exists a body will stay at
rest or move with constant speed”.
Philosophers prior to Newton believed a set of laws covering __________ on
Earth could be developed, but they needed to be modified to explain the
motions of heavenly bodies.
Isaac Newton (1642 – 1727) was the first to realise there WAS a universal set
of laws which could describe the motion of ALL bodies, BUT these laws had
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Drouin Secondary College
VCE Physics
Topic: Movement
to be modified for use within the ____________ riddled confines of the Earth
and its atmosphere.
_________________________________________________________________
QUESTIONS
28. Match the statements with the scientists who made them
Scientist
Statement
Newton
Constant speed requires constant force
Aristotle
Defined the property of matter called inertia
Galileo
A universal set of laws applicable everywhere but must
be modified for use on earth
8.1
Newton’s Laws
Newton developed 3 laws which cover all aspects of motion (provided
objects travel at speeds are well below the speed of light).
Law 1 (The Law of ___________)
A body will remain at rest, or in a state of _____________ motion, unless
acted upon by a net external force.
Law 2
The acceleration of a body is directly proportional to net force applied and
inversely proportional to its mass. Mathematically, a = F/m more
commonly written as F = ma
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Law 3 (___________ _____________ Law)
For every action there is an equal and opposite reaction.
Motion at or near the speed of ____________ is explained by Albert
Einstein’s Theory of Special Relativity.
8.2
Newton’s 1st Law
Newton’s 1st Law states:
A body will remain at __________, or in a state of uniform motion, unless
acted upon by a net external ____________.
Newton 1 deals with non accelerated motion.
It does not distinguish between the states of “rest” and “uniform motion”
(constant velocity).
As far as the law is concerned these are the same thing (state).
There is no experiment that can be performed in an isolated windowless
room which can show whether the room is stationary or moving at constant
velocity.
Most importantly:
Force is ________ needed to keep an object in motion
Is this how you understand the world works ?
8.3
Newton’s 2nd Law
Newton’s 2nd Law states:
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The ____________________ of an object as produced by a net force is
directly proportional to the magnitude of the net force FNET, in the same
direction as the net force, and inversely proportional to the mass of the
object.
Mathematically, a = FNET/m more commonly written as FNET = ma
Newton 2 deals with accelerated motion.
FNET is the ____________ SUM of all the forces acting on an object.
The acceleration and FNET are _____________ in the same direction.
Using the formula FNET = ma is only valid for situations where the mass
remains ______________
Newton actually expressed his 2nd law in terms of momentum.
Momentum (p) = mass x velocity.
8.4
Newton’s 3rd Law
Newton's 1st and 2nd Laws tell you what forces do.
Newton's 3rd Law tells you what forces are.
This statement is correct, but terse and confusing. You need to understand
that it means:
action...reaction" means that forces always occur in ________. Single,
isolated forces ___________ happen.
"action " and "reaction " are unfortunate names for a couple of reasons :
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1. Either force in an interaction can be the "action" force or the "reaction"
force.
2. People associate action/reaction with "first an action, then a reaction”
For example, first Suzie annoys Johnnie (action) then Johnny says
"Mommy! Suzie’s annoying me!" (reaction).
This is NOT an example what is going on here!
The action and reaction forces exist at the ___________ __________
"equal" means :
Both forces are equal in __________________. Both forces exist at exactly
the same __________.
They both start at exactly the same instant, and they both stop at exactly the
same instant.
They are equal in time.
"opposite" means that the two forces always act in opposite directions exactly 180o apart.
_________________________________________________________________
QUESTIONS
29. At what speeds are Newton’s Laws applicable ?
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Topic: Movement
30. Newton’s First Law:
A: Does not distinguish between accelerated motion and constant velocity motion
B: Does not distinguish between stationary objects and those moving with constant
acceleration
C: Does not distinguish between stationary objects and those moving with constant
velocity
D: None of the above
31. Newton’s Second Law:
A: Implies that for a given force, large masses will accelerate faster than small masses
B: Implies that for a given force, larger masses will accelerate slower than smaller masses
C: Implies that for a given force, the acceleration produced is independent of mass
D: Implies that for a given force, no acceleration is produced irrespective of the mass.
32. Newton’s Third Law:
A: Does not distinguish which force of a pair is the “action” force and which is the
“reaction” force.
B: Implies that both action and reaction forces begin and end at the same instant
C: Implies that forces always exist in pairs
D: All of the above.
33. Which of Newton’s Laws require that the vector sum of all the forces acting is needed
before a calculation of acceleration can be made ?
A: Newton’s 1st Law
B: Newton’s 2nd Law
C: Newton’s 3rd Law
D: Newtons 1st and 2nd Laws
34. A car of mass 1250 kg is travelling at a constant speed of 78 kmh-1 (21.7 ms-1). It
suffers a constant retarding force (from air resistance, friction etc) of 12,000 N
(a) What is the net force on the car when travelling at its constant speed of 78 kmh-1 ?
(b) What driving force is supplied by the car’s engine when travelling at 78 kmh-1 ?
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(c) If the car took 14.6 sec to reach 78 kmh-1 from rest , what was its acceleration
(assumed constant) ?
8.5
The Horse and Cart Problem
If the horse and cart exert ____________ and _________________ forces on
each other, how come the combination can move ?
An explanation hinges on a couple of simple points: (Lets assume no
friction)
1. An object _____________________ (or not) because of the forces that
push or pull on it. (Newton 2)
2. Only the forces that act on an object can ________________. Forces that
act on different objects don't cancel - after all, they affect the motion of
different objects!
Why does the cart accelerate?
Looking at the cart alone, just one force is exerted on it, (FHC) - the force that
the horse exerts on it.
The cart accelerates because the horse pulls on it!
The cart’s acceleration equals the net force on it divided by its mass
Why does the horse accelerate?
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Topic: Movement
There are ____ forces acting on the horse.
The cart pulls the horse backwards (FCH), and the road pushes the horse
forward (FRH).
The net force is the vector sum of these two forces.
The horse’s acceleration equals the net force on it divided by the its mass.
There are 2 pairs of Newton 3 forces in this situation:
FHC and FCH
FCH
FHC
FHR and FRH
FHR
FRH
H
If FNET on the horse is zero, what happens ?
The obvious answer is the horse and cart are at rest.
BUT, they could also be moving at ___________ _____________ ! Newton 1
_________________________________________________________________
QUESTIONS
35. Explain why, if a cart exerts an equal an opposite force on a horse as the horse exerts
on the cart, the combination is able to move forward.
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36. A car mass 1500 kg is towing a trailer of mass 750 kg. The car/trailer combination
accelerate at 3.4 ms-2. The trailer suffers a constant retarding force of 500 N, while the
car suffers a constant retarding force of 1000 N.
(a) Calculate the net force acting on the trailer.
(b) Calculate the driving force supplied by the car’s engine.
8.6
Momentum and Impulse
Newton described Momentum as the “___________ ____ ___________”, a
measure of the ease or difficulty of changing the motion of an object.
Momentum is a vector quantity having both magnitude and direction.
Mathematically,
p = mv
Where,
p = momentum (kgms-1)
m = mass (kg)
v = velocity (ms-1)
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VCE Physics
Topic: Movement
In order to change the momentum of an object a ___________________ for
that change is required.
This mechanism of change is called _________.
Mathematically,
Where,
I = Impulse (N.s)
F = Force (N)
t = Time (s)
I = Ft
The relationship between momentum and impulse can be derived from
Newton’s 2nd Law:
F = ma and a = v/t, so F = mv/t
Rearranging we get:
Ft = mv
ie. Impulse = Momentum
8.7
Conservation of Momentum
The concept of Momentum is particularly useful in analysing ____________.
This is because of the Law of Conservation of Momentum which states:
IN AN ISOLATED SYSTEM, TOTAL MOMENTUM IS ___________________.
The term “isolated system” means no _______________ forces are acting in
the situation under investigation.
In a crash situation, where the vehicle comes to a halt after, say, hitting a
tree, both its velocity and momentum fall to zero.
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The apparently “___________” momentum, has, in fact, been transferred via
the tree to the Earth.
Since the Earth has a huge mass (6 x 1024 kg). The change in its velocity is
so small as to be negligible.
In the crash mentioned, the momentum change is a _____________ quantity
so the _________________ (the product of F and t) is also a fixed quantity.
However the individual values of F and t can vary as long as the multiply to
give that fixed value.
If t, the time during which the crash occurs, can be ___________________,
then the force which needs to be absorbed by the car and its occupants is
reduced.
Modern vehicles use this concept in __________________ zones and air
bags as both are designed to extend the time and so reduce the force.
_________________________________________________________________
QUESTIONS
37. A car (and its occupants) is of total mass of 2250 kg and is travelling at 50 kmh-1 .
Approaching, head on, is a motorcycle (and rider) of total mass 350kg travelling at 180
kmh-1
(a) Which vehicle (car or bike) has the greater momentum ?
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VCE Physics
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(b) They collide head on and stick together. What velocity will the “wreck” have
immediately after collision ?
38. While talking on a mobile phone a truck driver loses concentration and runs off the
road and hits a tree. His speed goes from 20 ms-1 to 0 ms-1 in 0.7 sec. his truck has a mass
of 42 tonnes (1 tonne = 1000 kg)
(a) Calculate his change in momentum
(b) Calculate the Impulse during the collision
(c) Calculate the force he will experience during the collision
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39. Explain why, in a modern car equipped with seat belts and an air bag , he would
likely survive the collision whereas in the past, with no such safety devices, he would
most likely have been killed.
Chapter 9
Work, Energy & Power
9.0
Work
In Physics, the term _____________ is very strictly defined.
When a ___________moves an object through a _______________, work has
been done.
Mathematically:
W=Fxd
Where,
W = Work (Joules)
F = Force (N)
d = distance (m)
Work is a ___________________quantity, meaning it has a magnitude but no
direction.
If a force is applied and the object does not move, _________ WORK has
been done.
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If the force applied is constant, the work done can be calculated from the
formula, W = F x d
But, if the force _________________ during the course of doing the work, as
in compressing a spring, the work must be calculated from the area under
the force versus distance graph
Force
Distance
40. Calculate the work done on a refrigerator when a net force of 125 N acts over a
distance of 4.5 m
41. The graph shows the force required to compress a spring
(a) Calculate the work done in compressing the spring
by 3.0 cm.
Force (kN)
6000
45 0 0
3000
1 5 00
Distance (cm)
1.0
2 .0
3.0
4.0
(b) Calculate the further work required to compress the spring from 3.0 cm to 4.0 cm
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9.1
VCE Physics
Topic: Movement
Work and Energy
It is very easy to say what energy can do, but very difficult to define exactly
what energy is.
The concept of WORK was developed BY PHYSICISTS as a means of
quantifying and measuring _____________.
The relation between work and energy is summarised by one simple but
powerful statement:
__________ ___________ = ___________ _____________________
If work has been done on an object, the amount of energy it has MUST have
increased. By how much ? By exactly the amount of work done on the
object.
If an object has done some work, the amount of energy it has MUST have
decreased. By how much ? By exactly the amount of work done by the
object.
Questions
42. How much energy is stored in the spring in question 41 when it has been compressed
by 2.0 cm
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9.2
VCE Physics
Topic: Movement
Kinetic Energy
Kinetic Energy is the energy possessed by moving objects.
It is called the “Energy Of Motion”.
Kinetic Energy is a _____________ quantity.
Mathematically:
K.E. = ½mv2
9.3
Where:
K.E. = Kinetic Energy (Joule)
m = mass (kg)
v = speed (ms-1)
Gravitational Potential Energy
Gravitational Potential Energy, often just called Potential Energy, is the
energy possessed by an object due to its position.
It is called the “Energy of Position”
Potential Energy is a ______________ quantity.
Mathematically:
P.E. = mgh
Potential Energy needs a
Where:
P.E. = Potential Energy (Joules)
m = mass (kg)
g = Grav. Field Strength (Nkg-1)
h = height (m)
___________ point for the measurement of the height, h.
The zero point is usually, but not always, the ______________ of the Earth.
The zero point needs to be known for the calculation to have meaning.
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_______________________________________________________________
Questions
43. A cyclist is riding her bike along a flat road. She and her bike have a mass of 105 kg.
she is travelling at a constant speed of 15 ms-1.
(a) Calculate her Kinetic Energy
(b) She accidently rides over a 15 m cliff. What is her potential energy at the top of the
cliff ? (take g = 10 ms-2)
(c) If all the PE she had at the top of the cliff is converted to KE at the bottom,
calculate her vertical speed just before she hits the ground.
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9.4
VCE Physics
Topic: Movement
Hooke’s Law
Developed by English scientist Robert Hooke in 1676, the law states that the
________________ Force in an elastic material is directly proportional to its
_______________________.
Mathematically:
F = - kx
Where:
F = Restoring Force (N)
k = Spring Constant (Nm-1)
x = Extension (m)
The negative sign in the equation indicates that the restoring force and the
extension are in opposite directions.
The spring constant (k) is a measure of the nature or quality of the elastic
material. The higher its value the greater is the restoring force for a given
extension.
Questions
44. A spring of length 100 cm and spring constant 2.5 x 102 Nm-1 hangs vertically from a
retort stand. A total mass of 15.6 kg is hung from the spring. Calculate the extent of the
spring’s extension under this load. (Take g = 10 Nkg-1)
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9.5
VCE Physics
Topic: Movement
Energy Transfers
The Law of Conservation of Energy says:
ENERGY CANNOT BE CREATED OR DESTROYED BUT ONLY
TRANSFERRED FROM ONE FORM TO ANOTHER.
When doing problems concerning energy and energy transfers, it is
assumed that the transfers are ______________ efficient, meaning no
energy losses occur.
For instance, a roller coaster will have a large Gravitational Potential Energy
component at its ______________ point most of which will have been
converted to Kinetic Energy at its _____________ point and in calculations a
direct equality can be made between P.E. at the top and K.E at the bottom
In real life, these types of conversion processes are never 100% efficient.
Friction and the production of heat and sound mean significant losses
occur.
The efficiency of energy transfer processes can be calculated from:
% Eff = Energy Out x 100
Energy In
1
9.6
Elastic Potential Energy
Energy stored in _____________ is called elastic potential energy
• Elastic materials store energy when they are deformed and release that
energy when they return to their original condition.
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Topic: Movement
• The amount of energy stored can be found from the Elastic Potential
Energy Formula: ES = ½kx2
where
ES = Elastic P. E. (J )
k = Spring Constant (Nm-1)
x = extension or compression (m)
The stored energy can be used to
increase the _____________ energy of the “arrows” such as used in cross
bows
Questions
45. Calculate the amount of elastic potential energy stored in the extended spring in
question 44.
“REGULAR” ELASTIC BEHAVIOUR
Slope = ___________________
Force
F
Area = ½Fx = ½kx2
= ______ _ _ _________ __
Extension
x
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9.7
VCE Physics
Topic: Movement
Energy Transfers & Heat
In our _______________ riddled world, no energy transfer process is 100%
efficient.
The end result of the action of these frictional effects is the production of
what is called “________ grade, unrecoverable __________”
This means the heat energy cannot be harnessed to do any useful work,
such as boil water or run a pump.
Large sources of this kind of heat are the exhausts from fossil fuelled
transport such as cars, trucks and trains and from the electricity generation
industry.
9.8
Power
Power is the time rate of doing work, and since work and energy are
equivalent is also the time rate of energy transfer.
Mathematically:
P = W/t = E/t
Since
Where:
P = Power (W, Watts)
W = Work (J)
E = Energy (J)
t = time (s)
P = W/t and W = F.d, we can say
P = F.d/t but d/t = v so
P = F.v
So, the power for a body moving at constant velocity can be found in a one
step calculation.
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Questions
46. A train of mass 1.5 x 104 kg is travelling at a constant speed of 70 kmh-1. If the engine
is providing a driving force of 3.0 x 107 N , at what power is the engine operating ?
47. A roller coaster moves through its journey from
A to F. The coaster has no motor and is not powered
after it leaves point A. Its total mass is 650 kg
A
E
The heights above ground of each portion
C
D
of the track are given below.
F
B
Position Height above
Ground (m)
A
25.0
B
5.0
C
12.5
D
12.5
E
15.0
F
7.5
(a) Between which points is (i) the Kinetic Energy increasing, (ii) the Potential Energy
falling, (iii) the coaster accelerating
(b)At which point is the force exerted on the coaster by the track at its greatest ?
(c) Calculate the Gravitational Potential Energy at Point A. (take g = 10 ms-2)
(d)Assuming no frictional losses, calculate the Kinetic Energy at point F
(e) Calculate the speed of the coaster at point F
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