Download 2.2 Some Common Speeds

Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
VCE Physics
Unit 3
Topic 1
Motion in 1 & 2 Dimensions
Page 1
Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
INTRODUCTION.
Unit Outline
To achieve this outcome the student should demonstrate the knowledge and skills to:

apply Newton’s laws of motion to situations involving two or more forces acting along a straight line and in two
dimensions;

analyse the uniform circular motion of an object moving in a horizontal plane (FNET = mv2/R) such as a vehicle moving
around a circular road; a vehicle moving around a banked track; an object on the end of a string.

Apply Newton’s 2nd Law to circular motion in a vertical plane; consider forces at the highest and lowest positions only;

investigate and analyse the motion of projectiles near the Earth’s surface including a qualitative description of the effects
of air resistance;
apply laws of energy and momentum conservation in isolated systems;

analyse impulse (momentum transfer) in an isolated system, for collisions between objects moving along a straight line
(FΔt = mΔt);
•
apply the concept of work done by a constant force
work done = constant force x distance moved in the direction of the force
work done = area under force distance graph
•
analyse relative velocity of objects along a straight line and in two dimensions;
•
analyse transformations of energy between: kinetic energy; strain potential energy; gravitational potential energy; and
energy dissipated to the environment considered as a combination of heat, sound and deformation of material;
kinetic energy i.e. ½ mv2; elastic and inelastic collisions in terms of conservation of kinetic energy
strain potential energy i.e. area under force-distance graph including ideal springs obeying Hooke’s
Law ½ kx2
gravitational potential energy i.e. mgΔh or from area under force distance graph and area under field
distance
graph multiplied by mass
•
apply gravitational field and gravitational force concepts g = GM/r2 and F = GM1M2/r2
•
apply the concepts of weight (W = mg), apparent weight (reaction force, N) , weightlessness (W = 0) and apparent
weightlessness (N = 0)
•
model satellite motion (artificial, moon, planet) as uniform circular orbital motion (a = v 2/r = 4π2r/T2)
•
identify and apply safe and responsible practices when working with moving objects and equipment in investigations of
motion.
___________________________________
Chapter 1.
1.0
Units.
In Physics the Systeme Internationale d’Unites or SI (often incorrectly called the
METRIC SYSTEM) of units is used.
The system has two important characteristics;
 Different units for the same physical quantity are related by factors of 10.(eg. mm; cm;
km)
 Most of the units are constructed out of a few basic units, in fact just _____, as listed
below
These are Length, Mass, Time, Electric Current, Temperature, Luminous Intensity
and Amount of Substance.
All other units are derived from combinations of these basic units.
At this stage the important units are:
 Position (distance and/or displacement) is always measured in Metres (m).
 Time is measured in Seconds (s).
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
 Speed and/or Velocity is measured in metres per second (m/s) or more correctly
(ms-1).
 Acceleration is measured in metres per second per second (m/s2) or more correctly
(ms-2).
1.1
Position.
In order to specify the position of any object we first need to define an _____________,
or starting point, from which measurements can be taken.
For example on a number line the point ____ is taken to be the origin and all
measurements are related to that point. Thus a position +30 is 30 units to the __________
of point 0, while a position of -15 is 15 units to the ________ of point 0.
-30
-25
-20
-15
The Number Line
0
-10
-5
5
10
-15 units
1.2
15
20
25
30
+30 units
Vector and Scalar Quantities.
In order to further investigate this section of the course two new quantities need to be
introduced:
 A Scalar Quantity is completely defined by a ________ and a _________ eg.
temperature (17o), Age (16 y), mass (1.5 kg).
 A Vector Quantity is completely defined by a _______________, a ___________ and
a _________________ eg. Displacement 25 km West,
Force 14 N downward. A
direction may also be defined by using (+) to mean to the right and (-) to mean to the
left.
Vectors are usually represented by an arrow. The ___________ of the arrow is a measure
of the magnitude or size of the vector quantity and the _________________ of the arrow
represents the direction of the vector quantity.
N
A Vector of magnitude 15
units directed to the left
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1.3
VCE PHYSICS
TOPIC: Motion
Vector Addition.
When vectors need to be added, the process involves the drawing the first vector, adding
the tail of the second vector to the head of the first and then drawing a line from the tail of
the first to the head of the second. This line is the __________________ of the addition of
the two vectors. Its magnitude and direction can be determined either by trigonometry or
direct measurement from a scale diagram.
Magnitude =
N
Direction:
1.4
Vector Subtraction.
When vectors need to be subtracted, the negative vector has its _______________
reversed and then the two vectors are added as above.
8.0 ms-1 East
8.0 ms-1 South
Magnitude =
Direction:
1.5 Vector Components.
A vector can be broken up into a number of components (usually, but not always, two
components), this process is used to find two components which when added together
produce the original vector.
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VCE PHYSICS
TOPIC: Motion
40 ms-1
V VERTICAL
150
VHORIZONTAL
VHORIZONTAL =
V VERTICAL =
_____________________________________________________________
Questions
Adam is testing a trampoline. The diagrams show Adam at successive stages of
his downward motion.
Figure C shows Adam at a time when he is travelling DOWNWARDS and
SLOWING DOWN.
A
B
C
D
Q1: What is the direction of Adam’s acceleration at the time shown in Figure C ?
Explain your answer.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Chapter 2
2.0
Distance versus Displacement
Distance is a ____________ Quantity having a unit and a magnitude. The S.I. unit for
Distance is the ___________ (m)
Distance is best thought of as: “How far you have travelled in your journey”.
Displacement is a ____________quantity, having a unit, a magnitude and direction.
Displacement is best defined as how far you are from your starting point.
In a two dimensional system displacement must be defined using a coordinate system.
Distance and Displacement may or may not be numerically __________, depending
on the nature of the journey.
2.1
Speed versus Velocity
Speed is defined as the ________Rate of Change of ____________.Speed is a
______________ Quantity.
Mathematically: Speed = Distance/Time. The S.I. unit for Speed is metres/sec (ms-1)
Velocity is defined as the Time Rate Of Change of _____________________.
Velocity is a ___________ quantity. Thus:
v = d/t
v = Velocity (ms-1)
d = Change in Displacement (m)
t = Change in Time (s).
INSTANTANEOUS vs AVERAGE VELOCITY
The term velocity can be misleading unless a specific label is attached.
The label indicates whether the velocity is an _______________ value calculated over a
long period of time OR an Instantaneous value calculated at any _______________ of
time.
A simple example illustrates:
A journey of 40 km across the suburbs takes 1 hour;
VAV =
=
kmh-1
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
BUT VINST could be anything from _____ kmh-1 (stopped at traffic lights) to VINST = _______
kmh-1 (travelling along the freeway).
IN ALL CALCULATIONS AND EQUATIONS USED IN THE COURSE, ASSUME
_____________________ VALUES ARE REQUIRED UNLESS OTHERWISE STATED.
2.2
Some Common Speeds
Event
1. Grass Growing
2. Walking Pace
3. Marathon Runner
4. 100 m Sprinter
5. Suburban Speed Limit
6. Freeway Speed Limit
7. Boeing 737 Cruising
8. Speed of Light
2.3
Speed (ms-1)
5.0 x 10-8
1-2
5
10
16.7
30.6
246
2.99 x 108
Speed (km/h)
1.8 x 10-7
4-8
18
36
60
110
886
1.1 x 109
Acceleration.
Acceleration is defined as the time rate of change of ______________.
Acceleration is a _______________ quantity. Thus:
a = v/t
-2
a = Acceleration (ms )
v = Change in Velocity (ms-1)
t = Change in Time (s)
Since acceleration is defined in terms of velocity, a body travelling at constant speed but
with a constantly changing _____________ is defined as having an acceleration. So a
cyclist travelling around a corner at constant speed is, in fact, _____________________ !
(More of this later).
For an accelerating vehicle the velocity and acceleration are in the _________
direction.
For a decelerating vehicle the velocity and acceleration are in ______________
directions.
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2.4
VCE PHYSICS
TOPIC: Motion
Graphical Relationships.
Much of the information delivered in this Physics course is presented graphically.
Generally, graphs “____________________” and you need to develop the ability to “read”
the story the graph is telling.
There are two basic families of graphs you should be familiar with:
(a) _____________ Graphs, paint a broad brush, general picture of the relationship
between the quantities graphed.
(b) _______________ Graphs from which exact relationships may be deduced and/or
exact values may be calculated.
Sketch graphs of this and other types are very useful and powerful tools and pop up in all
areas of this subject. You need to develop the skills to interpret them correctly.
Don’t forget to label the axes
Story:
Story:
Story:
Story:
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
________________________________________________________________
Questions
In a road test, a car was uniformally accelerated from rest over a distance of 400
m in 19 sec. The driver then applied the brakes, stopping in 5.1 sec with
constant deceleration.
The graphs A to F below should be used to answer the questions below. The
horizontal axis represents time and the vertical axis could be velocity or
distance.
A
B
C
D
E
F
Q2: Which of the graphs, A to F, represents the velocity time graph for the entire
journey ?
Q3: Which of the graphs, A to F, best represents the distance time graph of the
car for the entire journey ?
2.5
Exact Graphical Relationships.
In the interpretation of relationships and the determination of exact values obtainable from
graphs the following table contains all the theoretical knowledge you need to obtain any
piece of data.
Graph Type
Distance or
Displacement
versus
Time
Speed or Velocity
versus
Time
Acceleration
versus
Time
Read Directly from
Graph
______________
_____________
Speed
or
Velocity
Acceleration
Obtain from Slope
of Graph
Speed
or
_____________
_____________
No Useful
Information
Obtain from Area
under Graph
No Useful
Information
______________
or
Displacement
______________
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2.6
VCE PHYSICS
TOPIC: Motion
Equations of Motion.
The equations of motion are a series of equations linking velocity, acceleration,
displacement and time which allow calculations of these quantities without the need for a
graphical representation.
The equations can only be used if the ___________________ is constant.
They are summarised below.
v = u + at
v² = u² + 2ax
x = ut + ½at²
u = Initial Velocity (ms-1)
v = Final Velocity (ms-1)
a = Acceleration (ms-2)
x = Displacement (m)
t = Time (s)
Whenever using these equations always list out the information given and what is
required, then choose an appropriate equation. Some problems may require a two step
calculation.
It is sometimes necessary to define a positive direction, right or left in horizontal motion
problems, up or down, in vertical motion problems.
Questions
In a road test, a car was uniformally accelerated from rest over a distance of 400
m in 19 sec. The driver then applied the brakes, stopping in 5.1 sec with
constant deceleration.
Q4: Calculate the acceleration of the car for the first 400 m.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Q5: Calculate the average speed for the entire journey, covering both the
accelerating and braking sections.
CHAPTER 3.
3.0
Newtonian Motion.
Sir Isaac Newton (1642 - 1727) was unique for a number of reasons, but mostly because
he developed a set of laws describing the ________ of objects in the universe.
Prior to Newton, scientists believed that a set of laws existed which explained motion on
Earth and these laws had to be ______________ to describe motions in all other parts of
the universe.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Newton was the first scientist to realise that all motion anywhere in the universe could be
described by a single set of laws which then had to be modified for use in the
______________ riddled confines of the Earth.
3.1
Newton’s Laws
FIRST LAW
A body will remain at _________or in a state of uniform motion unless acted upon
by a net external ________. Often called the Law Of Inertia, (Inertia is the reluctance
of a body to change its state of motion).
SECOND LAW
The __________________ of a body is directly proportional to the net force applied
and inversely proportional to its __________ ie. a = F/m or as more often written F
= ma.
THIRD LAW
For every ____________ there is an equal and opposite _______________.
__________________________________________________________________________________________
Questions
A seaplane of mass 2200 kg takes off from a smooth lake as shown. It starts
from rest, and is driven by a CONSTANT force generated by the propeller. After
travelling a distance of 500 m, the seaplane is travelling at a constant speed,
and then it lifts off after travelling a further 100 m.
The total force opposing the motion of the seaplane is not constant. The graph
shows the TOTAL FORCE OPPOSING THE MOTION of the seaplane as a
function of the distance travelled.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Total Opposing
Force (N)
Opposing
10000
8000
6000
4000
2000
100 200 300 400 500 600 Distance
Q6: What is the magnitude of the net force acting on the seaplane after it has
travelled a distance of 500 m from the start ?
Q7: What is the magnitude of the seaplane’s acceleration at the 200 m mark ?
Q8: Estimate the work done by the seaplane against the opposing forces in
travelling for a distance of 500 m.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
In Figure 2, a car of mass 1000 kg is being towed on a level road by a van of
mass 2000 kg. There is a constant retarding force, due to air resistance and
friction, of 500 N on the van, and 300 N on the car. The vehicles are travelling at
a constant speed.
Figure 2
Q9: What is the magnitude of the force driving the van?
Q10: What is the value of the tension, T, in the towbar?
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
The figure shows a cyclist with the bicycle wheels in CONTACT with the road
surface. The cyclist is about to start accelerating forward.
a
FTR
FRT
Q11: Explain, with the aid of a clear force diagram, how the rotation of the
wheels result in the cyclist accelerating forwards.
3.2
Newton’s Laws Restrictions & Consequences
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VCE PHYSICS
TOPIC: Motion
RESTRICTIONS
The laws only apply at speeds much, much less than the speed of ___________.
The laws apply equally in ALL inertial frames of reference.
FRAME OF REFERENCE ?
A frame of reference is best described as “your point of _________________.”
An inertial frame of reference is one that is either _____________ or moving with constant
_________________.
A non inertial frame of reference is _____________________.
CONSEQUENCES
As far as Newton’s 1st law is concerned “rest” and “uniform motion” are the _________
state. You cannot perform any test which can show whether you are stationary or moving
at constant velocity.
The action and reaction law requires there to be ______ bodies interacting, the ACTION
force acting on one body and the REACTION acting on the other. Deciding when an Action
/ Reaction situation exists can be done by answering the question: Does the second
(reaction) force _________________ immediately the first (action) force disappears ?
If the answer is yes, you have an action reaction pair.
_______________________________________________________________
Questions
A train is travelling at a constant velocity on a level track. Lee is standing in the
train, facing the front, and throws a ball vertically up in the air, and observes its
motion.
Q12: Describe the motion of the ball as seen by Lee.
Sam, who is standing at a level crossing, sees Lee throw the ball into the air.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Q13: Describe and explain the motion of the ball as seen by Sam.
3.3
Forces In Two Dimensions.
A force is a ________ or a pull.
It can be a _____________ Force where direct contact is required for the effect of the
force to be felt eg. - a punch in the nose or a vehicle colliding with a tree, or it can be a ___________ Force where direct contact is not necessarily required for the effect of the
force to be felt eg. - the magnetic force or the force due to gravity.
Force is NOT one of the 7 fundamental units of the S.I. System and thus it is a
_____________ quantity.
The unit for Force is kgms-2. This was assigned the name the NEWTON (N), in honour of
Sir Isaac.
Forces can act in any direction and the TOTAL, NET or RESULTANT force is the
__________sum of all forces acting on a body.
The body will then ___________________ in the direction of the RESULTANT FORCE,
according to Newton 2.
________________________________________________________________________
Questions
A cyclist is towing a small trailer along a level bike track (Figure 1). The cyclist
and bike have a mass of 90 kg, and the trailer has a mass of 40 kg.
There are opposing constant forces of 190 N on the rider and bike, and 70 N on
the trailer. These opposing forces do not depend on the speed of the bike.
The bike and trailer are initially
travelling at a constant speed of 6.0
ms-1.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Q14. What driving force is being exerted on the road by the rear tyre of the
bicycle?
3.4
Momentum and Impulse.
Newton called momentum the "quality of motion", and it is a measure of a body’s
____________________ motion – its tendency to continue moving in a particular direction.
Roughly speaking, a body’s momentum indicates which way the body is heading and just
how difficult is was to get the body moving with its current velocity.
Momentum is the product of a body’s mass and velocity. Momentum is a
_____________ quantity. Thus:
p = mv
p = Momentum (kgms-1)
m = Mass (kg)
v = Velocity (ms-1)
The direction of the momentum is the same as the velocity’s direction.
Impulse is called the “_______________
________________” for the momentum. This
means that in order to change the momentum of a body you need to exert a
_______________ for some time in order to effect that momentum change.
Impulse is the product of force and the time during which that force acts. Impulse is a
_____________ quantity. Thus:
I = Ft
I = Impulse (Ns)
F = Force (N)
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
t = Time (s).
Momentum arises from Newton's second law (F = ma). Substituting for a = v/t, the law
becomes
F = mv/t
Rearranging we get:
Ft = mv
Or more often written as:
Ft = p
The product Ft is called the Impulse (I) of the force and mv represents the change in
momentum (p) of the body.
________________________________________________________________________
Questions
A small truck of mass 3.0 tonne collides with a stationary car of mass 1.0 tonne.
They remain locked together as they move off. The speed immediately after the
collision was known to be 7.0 ms-1 from the jammed reading on the car
speedometer. Robin, one of the police investigating the crash, uses
conservation of momentum to estimate the speed of the truck before the
collision.
Q15 : What value did Robin obtain?
The calculated value is questioned by the other investigator, Chris, who believes
that conservation of momentum only applies in elastic collisions.
Q16: Explain why Chris’s comment is wrong.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
A car of mass 1000 kg travelling on a smooth road at 5.0 ms–1 collides with a
truck that is stationary at a set of traffic lights. After the collision they are stuck
together and move off with a speed of 2.0 ms–1
Q17 : How much momentum did the car transfer to the truck?
Q18 : What is the mass of the truck?
Q19: If the collision took place over a period of 0.3 s, what was the average
force exerted by the car on the truck?
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
A railway truck (X) of mass 10 tonnes, moving at 6.0 ms-1, collides with a
stationary railway truck (Y), of mass 5.0 tonnes. After the collision they are
joined together and move off as one.
Q20: Calculate the final speed of the joined railway trucks after collision
Q21: Calculate the magnitude of the total impulse that truck Y exerts on truck X
3.5
Elastic And Inelastic Collisions.
All collisions (eg, cars with trees, cyclists with the footpath, neutrons with uranium atoms,
bowling balls with pins etc.) fall into one of 2 categories:
In _______________ collisions both momentum and kinetic energy are conserved
In ________________ collisions, momentum is conserved but kinetic energy is not
conserved.
The smaller of the two groups are the elastic collisions which generally only occur on the
atomic scale.
By far the largest group of collisions are the inelastic collisions where the lost kinetic
energy is converted to things like heat, sound, light.
Questions
Page 21
Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
A small truck of mass 3.0 tonne collides with a stationary car of mass 1.0 tonne.
They remain locked together as they move off. The speed immediately after the
collision was known to be 7.0 ms-1 from the jammed reading on the car
speedometer. Robin, one of the police investigating the crash, uses
conservation of momentum to estimate the speed of the truck before the
collision at 9.3 ms-1
Q22: Use a calculation to show whether the collision was elastic or inelastic.
A railway truck (X) of mass 10 tonnes, moving at 6.0 ms-1, collides with a
stationary railway truck (Y), of mass 5.0 tonnes. After the collision they are
joined together and move off as one at 4.0 ms-1.
Q23: Explain why this collision is an example of an inelastic collision. Calculate
specific numerical values to justify your answer.
3.6
Conservation of Momentum.
The concept of momentum is particularly useful in analysing collisions. This is because of
the law of conservation of momentum which states: In an isolated system, total
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VCE PHYSICS
TOPIC: Motion
momentum is _______________. Thus in a collision, the total momentum before equals
the total momentum after.
In collisions where momentum seems to have been lost, eg. a car hitting a tree and
coming to rest, the conservation law means that the apparently "lost" momentum has in
fact been transferred to the __________. Since the earth has such a large mass, the
resulting change in its ___________________ is negligible.
3.6
The Physics of Crumple Zones & Air Bags
A car crashes into a concrete barrier.
The change in ____________ suffered by the car (and passengers) is a ____________
quantity.
So, Impulse, (the product of F and t), is also _________.
However, individual values of F and t can vary as long as their _______________ is
always the same.
So if t is made longer, consequently F must be smaller.
Crumple Zones increase the time (t) of the collision.
So, F is reduced and the passengers are less likely to be injured.
The same logic can also be applied to Air Bags.
The air bag increases the ____________ it takes for the person to stop.
So the force they must absorb is ______________.
So they are less likely to be seriously injured.
A further benefit is this lesser force is distributed over a larger area.
Questions
In a car the driver’s head is moving horizontally at 8.0 ms -1 and collides with an
air bag as shown. The time taken for the driver’s head to come to a complete
stop is 1.6 x 10-1 s. This collision may be modelled as a simple horizontal
collision between the head of mass 7.0 kg and the air bag.
Q24: Calculate the magnitude of the average contact force that the air bag
exerts on the driver’s head during this collision.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Q25: Explain why the driver is less likely to suffer a head injury in a collision with
the air bag than if his head collided with the car dashboard, or other hard
surface.
CHAPTER 4
4.1
Centre Of Mass
In order to deal with large objects it is useful to think of all the mass of the object being
concentrated at one point, this point is called the centre of ___________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 oddly shaped objects e.g. a boomerang, the centre of mass may be outside the
perimeter of the object.
Centre of Mass
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VCE PHYSICS
TOPIC: Motion
The Centre of Mass of an object is the point around which the object will ________ when a
____________ or Turning Force is applied to the object.
4.1
Centre of Mass - Systems
For a system made up of two or more bodies, the position of the Centre of Mass may be
determined by the use of the formula:
XCM = (m1x1+ m2x2 + m3x3 + ...)/(m1 + m2+m3+ ...)
XCM = Position of Centre of Mass (m)
m1,m2 etc = Masses of individual objects (kg)
x1,x2 etc = Distance of individual masses from a chosen reference point (m).
5.0 m
1.0 m
1.0 m
30 kg
50 kg
A
A 30 kg block sits on a 50 kg beam . Where is the centre of mass of this system ?
Since the block and the beam are uniform each will have its centre of mass at its
geometric centre.
All measurements are taken from point A, ie. this is the reference point for this system.
XCM = [(50 x 2.5) + (30 x 3.5)] / [50 + 30]
= 2.875 m
Thus the centre of mass of this system is 2.875 m from A.
4.2
Weight.
The effect of a Gravitational Field on a Mass is called its _____________.
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VCE PHYSICS
TOPIC: Motion
Weight is a FORCE and therefore a ______________ quantity.
Mathematically:
W = mg
where W = Weight (N) m = mass (kg) g = Gravitational Field Strength (Nkg-1)
Weight acts through the Centre of Mass of the body and is directed along the line joining
the centres of the two bodies between which the Gravitational Field is generated.
On Earth, the Gravitational Field of Strength ________ Nkg -1 gives any mass under its
influence alone an acceleration of ________ ms-2
4.3
Reaction Force.
Any stationary body under the influence of the Earth's gravitational field must have an
equal and opposite force to that of gravity acting upon it. This force is called the
____________ Force. It only arises as the result of the action of another force and does
not exist as an isolated force in its own right.

R - Normal Reaction Force
Centre of Mass
Object, mass m
Table top
W = mg
NOTES:
1. The Weight force W acts from the Centre of Mass
downward toward the centre of the Earth.
2. The Normal Reaction Force acts from the boundary
between the object and the table. It acts up through
the Centre of Mass.
3. The Forces R and W should be co planer ie. they
should sit on top of one another. This is impossible
to show on the diagram, so they are slightly offset.
4. The Forces W and R are NOT an action - reaction
pair.
In the diagram above the two forces shown are NOT an action – reaction pair. This is
because they do not meet the fundamental requirement for such a pair – when one
disappears the other automatically disappears as well.
Look closely. If the R force disappears ie. you take the table away, the W force still exists.
thus these two are not an example of Newton 3. (although they are often used to illustrate
Force of TABLE on OBJECT
F
TO
These two forces are the action reaction
pair in this situation
Force of OBJECT on TABLE
F
OT
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Newton’s Third Law).
4.4
Bouncing Balls
When a moving ball arrives at a hard surface it is the Normal Reaction Force (R) which
provides the force needed to ________________ the ball to a stop and then accelerate
away from the surface.
R
R
a=g
a=g
a
v
a
v
W
v
v= 0
W
W
W
4.5
Friction
Friction is the most unusual of all forces in that is cannot __________ an object moving, it
can only slow down or ___________ an object once it is moving, or prevent it from starting
to move.
Slowing a moving object is the result of Dynamic Friction, while preventing an object from
starting to move is the result of __________ Friction.
It is usually the case that for the same pair of surfaces, static friction is greater than
dynamic friction. In other words the force need to start an object moving is greater than the
force needed to maintain its motion.
Generally the size of the frictional force between two surfaces depends upon:
(a) The __________________ of the surfaces (measured by the coefficient of friction ())
(b) the ________________ of the surfaces.
The Frictional Force is NOT dependent upon the ____________ of contact.
The size of the frictional force can be calculated from the equation:
FR = R
FR = Frictional force (N)
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TOPIC: Motion
 = Coefficient of Friction (no units)
R = Normal Reaction force (N) (numerically equal to Weight [mg]).
Note: the normal reaction force is always directed at right angles to the surface on which
Normal Reaction = R
Fr (Friction)
F (Pulling Force)
Weight = mg
the motion is occurring no matter the angle of that surface.
4.6
Friction Applications
Friction is NOT always a hindrance to living on Earth, often it is vital for movement over the
Earth’s surface.
Consider the following situation:
 A vehicle’s rear (driving) wheel is in contact with a __________ (having friction) road
surface.
 The frictional force between the tyre and the road is directed ___________, away
from the direction of motion. This force cannot provide the forward propulsion.
 It is the _____________ force (arising from Newton 3), of the road on the tyre,
Direction of Acceleration
It is the REACTION FORCE
which causes ACCELERATION
Force of
TYRE on ROAD
Action Force
Force of
ROAD on TYRE
Reaction Force
directed forwards, which is providing the force for forward motion
4.6
Various Force Situations
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Drouin Secondary College
VCE PHYSICS
Mass Stationary on Table
Block mass = m
R
Mass falling with Air Resistance
= C of M
W = mg
Lift – Accelerating Upwards
FR
a=0
+ve
TOPIC: Motion
a
+ve
R
+ve
W = mg
ΣF = ma
R – W = m(0)
So, R = W
a
W = mg
ΣF = ma
W – FR = ma
So, mg – FR = ma
ΣF = ma
R – W = ma
So, R = mg + ma
Mass is “heavier” by an amount = ma
Lift – Accelerating Downwards
+ve
Inclined Plane – No Friction
a
a
R
R
a
mg Sin θ
W = mg
Mass is “lighter” by an amount = ma
θ
θ
m2
┴ to plane: R = mg Cos θ
║to plane: mg Sin θ = ma
║to plane: mg Sin θ - FR = ma
Strings and Pulleys
+ve T
+ve
W
For m1 : T – FR = m1a
For m2 : W – T = m2a
Solve simultaneous
equation to obtain acc.
W = mg
┴ to plane: R = mg Cos θ
T
T
mg Cos θ
W = mg
Connected Bodies with Friction
a
FR
mg Cos θ
ΣF = ma
W – R = ma
So, R = mg - ma
m1
R
mg Sin θ
θ
θ
FR
Inclined Plane – With Friction
T
m1
W = m1g
For m1:
a T – m1g = m1a
m2
Pendulums
θ
For m2:
m2g – T = m2a
W = m2g
Solve simultaneous
equation to obtain acc.
Restoring Force
= mg Sinθ
T
T = mg Cosθ
mg Sinθ
W = mg
mg Cosθ
CHAPTER 5
5.0
Work.
In Physics, the term Work has a very strict meaning. When a force moves an object
through a distance, work has been done. Work is a ___________ quantity and is
calculated from the equation:
W = Fd
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TOPIC: Motion
W = Work (J [Joules])
F = Force (N)
d = Distance (m).
No work is done if the force has not caused the object to ___________.
Provided the force remains constant the above formula may be used.
BUT, If the force ______________ during the course of doing the work, (as in
compressing a spring) the only way to calculate the size of the work done is to calculate
the area under the graph of F vs d.
Force
Area = Work Done
= 1/2 F x d
d
Distance
5.1 Work & Energy
In the Physics world, Work and __________ are intimately related.
Energy is very difficult to define. It is easy to say what energy can do but not so easy to
say what it is.
Thus energy is defined in terms of ______________.
An object is said to possess energy if it has the ability or capacity to do work.
Work is the “Transfer Mechanism” for Energy meaning that if some work has been done
on an object the amount of energy it possesses has been changed.
_________ DONE = ENERGY _____________________
__________________________________________________________________________________________
Questions
A model rocket of mass 0.20 kg is launched by means of a spring, as shown in
Figure 1. The spring is initially compressed by 20 cm, and the rocket leaves the
spring as it reaches its natural length. The force-compression characteristic of
the spring is shown in Figure 2.
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TOPIC: Motion
Q26 : How much energy is stored in the spring when it is compressed?
Q27: What is the speed of the rocket as it leaves the spring?
Q28: What is the maximum height, above the spring, reached by the rocket?
You should ignore air resistance on the way up since the rocket is very narrow.
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TOPIC: Motion
When the rocket reaches its maximum height, the parachute opens and the
system begins to fall. In the following questions you should still ignore the effects
of air resistance on the rocket, but of course it is critical to the force on the
parachute. This retarding force due to the parachute is shown as R in
Figure 3, and its variation as a function of time after the parachute opened is
shown in Figure 4.
Q29: What is the acceleration of the rocket at a time 5 s after the parachute
opens?
In a storeroom a small box of mass 30.0 kg is loaded onto a slide from the
second floor, and slides from rest to the ground floor below, as shown below.
The slide has a linear length of 6.0 m, and is designed to provide a constant
friction force of 50 N on the box. The box reaches the end of the slide with a
speed of 8.0 m s–1
Q30: What is the height, h, between the floors?
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5.2
VCE PHYSICS
TOPIC: Motion
Energy Types
Kinetic Energy
Kinetic energy is the energy possessed by a ________ body, sometimes called "the
energy of motion". Kinetic Energy is a ________ quantity. It is calculated from the
equation:
K.E. = ½mv²
K.E. = Kinetic Energy (J)
m = Mass (kg)
v = Velocity (ms-1)
Gravitational Potential Energy
Gravitational
Potential
Energy
is
the
energy
a
body
possesses
due
to
its
_______________ and thus is generally called the "energy of position". Potential Energy
is a Scalar quantity. It is calculated from the equation:
P.E. = mgh
P.E. = Potential Energy (J)
m = Mass (kg)
g = Gravitational Field Strength (Nkg-1)
h = Height (m)
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TOPIC: Motion
The value of the height (h) used in the equation depends upon the where the __________
for height is defined. This is usually, but not always, the surface of the earth. It is important
to know where this zero point is defined to be before using the formula.
Elastic Potential Energy
The energy stored in ___________ materials (eg. Springs & rubber bands)
Mathematically: Es = ½ kx2
where, Es = Elastic P. E. (J ) k = Spring Constant (N kg-1)
x = Extension or Compression (m)
Questions
The box in the previous question then slides along the frictionless floor, and is
momentarily stopped by a spring of stiffness 30 000 Nm–1
Q31: How far has the spring compressed when the box has come to rest?
5.3
Power.
Power is the time rate of doing __________ and since;
WORK DONE EQUALS ENERGY TRANSFERRED
power can also be defined as the time rate of energy transfer.
Power is a ___________ quantity. Thus:
P = W/t = E/t
P = Power ( W =Watts)
W = Work (J)
t = Time (s)
It is also useful to note that since W = F.d, and v = d/t then;
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VCE PHYSICS
TOPIC: Motion
P = F.d/t = F.v
This form of the power formula can be used to calculate power for a body moving at
constant _____________.
5.4
Conservation Of Energy.
The law of conservation of energy states:
Energy can be neither ____________ nor _______________, but only transformed
from one form to another. Most energy conversion processes result in the conversion of
useful, Ordered Energy (energy that can easily be used to do work) into relatively useless
Disordered Energy. This disordered energy is called Thermal Energy and is the energy
we associate with temperature. It is sometimes called Internal Energy or "low grade,
non recoverable" Heat.
The percentage ____________________ of energy transfers is calculated from:
%Eff = EOUT/EIN x 100/1
No energy transfer process can be 100% efficient in our friction ridden world.
If 100% efficiency could be attained __________ motion machines would then be possible.
5.5
Seeing Energy
With a little practice you can “__________ ” energy flow through a system just as an
accountant can “watch” money flow through an economy.
The most obvious form of energy is Kinetic Energy , the energy of _________. It is easy
to see when kinetic energy is transferred to or from an object. As KE leaves the object it
slows down: as in a car slowing down when you lift off the accelerator pedal. A water polo
ball speeds up when you do work on it during the action of throwing, you are transferring
___________ from your body into the ball, where the energy shows up in the __________
of the ball.
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TOPIC: Motion
Potential Energy is more difficult to “see”. It can take many different forms, as shown in
the table below. In each case nothing is moving; but because the objects still have a great
potential to do work, they possess Potential Energy.
Form of Potential Energy
1. Gravitational Potential Energy
2. Elastic Potential Energy
3. Electrostatic Potential Energy
4. Chemical Potential Energy
5. Nuclear Potential Energy
Example
A person standing at the top of a building
A wound clock spring
A cloud in a thunderstorm
A firecracker
Uranium
CHAPTER 6.
6.0
The Experience of Acceleration.
Nothing is more central to the laws of motion than the relationship between force and
_________________. Up to now we have looked at forces and noticed they can produce
accelerations (Newtons 2nd Law). Now we will reverse the process – looking at
accelerations and noticing that they require _____________. For you to accelerate,
something must push or pull on you. Just where and how that force is exerted on you
determines how you “_________” when you accelerate.
The “backward” force you feel as a car accelerates is caused by your body’s
________________, its tendency not to want to accelerate.
The car and your seat are accelerating forward, and since the seat back acts to keep you
from falling “through” its surface, it provides a forward support force which causes you to
accelerate forward. But the seat can’t exert a force uniformly throughout your body.
Instead, it pushes only on your back and your back then pushes on your bones, internal
organs and tissues to make them accelerate forward.
The experience of the accelerating car seat is very similar to the experience of “gravity”
when you stand still on the Earth’s surface. In this situation you feel “heavy” ie. you
experience your ____________.
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Drouin Secondary College
6.1
VCE PHYSICS
TOPIC: Motion
Fictitious Forces
When the car seat is causing you to accelerate forward, you also feel “_______”; your
body senses all the internal forces needed to accelerate its pieces forward, and you
interpret these sensations as “weight”. This time you experience the weight directed
toward the back of the car.
The gravity-like “force” that you experience as you accelerate is truly indistinguishable from
the force of gravity. No laboratory instrument can determine directly whether you are
experiencing gravity or simply accelerating.
However despite the convincing sensations, the backward heavy feeling in your gut as you
accelerate forward is not due to a ________ force. This experience of acceleration is
explained by the supposed action of a Fictitious Force.
This Fictitious Force always points in the direction _____________ to the
acceleration that causes it and its strength is proportional to the acceleration.
6.3
Apparent Weight
a1
a2
Fictitious Force
Fictitious Force
a2 > a1
Apparent Weight
Weight
Gentle acceleration - small fictitious force
Apparent weight mostly downward
6.2
Apparent Weight
Weight
Large acceleration - large fictitious force
Apparent weight more backwards and down
Circular Motion in Horizontal Circles.
When left alone, no object will travel in a _________. Newton’s First Law says that an
object experiencing no net force will move in a straight line at constant speed.
Thus, in order to make an object travel in a circle ie. constantly change the direction of its
velocity, a force must be constantly applied to it. This means the object is constantly
__________________.
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TOPIC: Motion
Many objects, however, do execute circular motion, wheels, moons, planets, and electric
motors all move is circles.
The laws covering circular motion are derived from the laws covering straight line motion.
The number of times an object spins around per second is called its Frequency.
An object travelling around a circle completes one full spin in a time interval called a
Period (T). Period and frequency (f) are the inverse of one another. Thus:
T = 1/f
T =Period (sec)
f = Frequency (Hz or sec-1)
Circumference = 2r
r
The distance covered in 1 period is the circumference of a circle (2R), thus the velocity of
an object moving in a circle is given by the general expression distance/time or:
v = 2R/T = 2Rf
v = Velocity (ms-1)
R = Radius (m)
T = Period (s)
f = Frequency (Hz)
Since the direction of the velocity at any point is the tangent to the circle at that point, the
direction of the velocity is constantly changing, thus an object travelling in a circular path is
subject to a constant acceleration. The size of this acceleration is given by:
a = v²/R
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VCE PHYSICS
TOPIC: Motion
r
v
r
v
Substituting for v = 2R/T, the acceleration equation becomes:
a = 4²R/T² = 4²Rf²
This acceleration acts toward the centre of the circle and is called the
__________________ Acceleration. The term arising from the centre seeking nature of
the acceleration.
6.5
Centripetal Force
The fact that an acceleration exists requires there to be a force, in the same direction,
which produces this acceleration. This force is called the ________________ Force and
arises from Newton's Second Law. Thus:
F = ma = mv²/R = m 4²R/T²
Centripetal Force is, itself, not a _________ FORCE in its own right, but is supplied
by other real, measurable forces.
In the case below, the girl requires a Centripetal Force to travel her circular path
The _______________ (T) of her muscular grip on the pivot pole of the ride provides the
Centripetal Force.
She, of course, will use the idea of a Fictitious Force, centrifugal force, to explain the
“outward” pull she feels while on the constantly accelerating ride.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Questions
Mark Webber and his Formula 1 racing car are taking a corner at the Australian
Grand Prix. A camera views the racing car head on at point X on the bend where
it is travelling at constant speed. At this point the radius of curvature is 36.0 m.
The total mass of the car and driver is 800 kg.
Camera's head on
view
of racing car at point
X
36.0 m
X
Camera
Q32: On the diagram showing the camera’s view of the racing car, draw an
arrow to represent the direction of the NET force acting on the racing car at this
instant.
Q33: Calculate the speed of the car.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Q34: Referring to the racing car from the previous slide, explain:
(a) Why the car needs a horizontal force to turn the corner.
(b) Where this force comes from.
The safe speed for a train taking a curve on level ground is determined by the
force that the rails can take before they move sideways relative to the ground.
From time to time trains derail because they take curves at speeds greater than
that recommended for safe travel.Figure 5 shows a train at position P taking a
curve on horizontal ground, at a constant speed, in the direction shown by the
arrow.
Q35: At point P shown on the figure, draw an
arrow that shows the direction of the force
exerted by the rails on the wheels of the train.
The radius of curvature of a track that is safe at
60 km/h is approximately 200 m.
Q36: What is the radius of curvature of a track
that would be safe at a speed of 120 km/h,
assuming that the track is constructed to the
same strength as for a 60 km/h curve?
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Q37: At point Q the driver applies the brakes to slow down the train on the
curve.
Which of the arrows (A to D) indicates the direction of the net force exerted on
the wheels by the rails?
6.6
Centrifugal Force
Centripetal Force & Acceleration
Fictitious Force
Girl's Path
Velocity
Despite its fictitious nature, centrifugal force creates a compelling sensation of gravity like
_________. The girl on the ride feels as though gravity is pulling her outward as well as
down and must hold the handle tight in order not to fall off.
Fictitious forces, such as Centrifugal Force, do _________ contribute to the net force
experienced by an object. Thus if the girl lets go she will fly off the ride in the direction of
the linear velocity NOT in the direction of the fictitious force.
A stationary object on Earth experiences a weight force of 1g. The fictitious centrifugal
force experienced by 5 kg of clothes during the spin cycle in a washing machine, travelling
in a 0.25 m radius circle at 20 ms-1 is about 163 g’s and they have an apparent weight of
815 kg.
6.7
Banked Corners
Race track and road designers tend to build their tracks or roads with “__________” on the
corners. This design feature is used to enhance the safety of the track or road allowing
users to round corners at higher speeds (and with a greater margin of safety) than they
could if the corner was not banked.
Any vehicle travelling around a corner with velocity v needs a centripetal force (F C) acting
toward the centre of the corner.
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VCE PHYSICS
TOPIC: Motion
FC
v
In the case of the flat, non banked, corner this centripetal force (F C) is supplied by the
__________ of the road against the tyres (FRT)
With the banked corner the centripetal force has an extra component - that being a
component of the car’s ________ force acting toward the centre of the corner.
This gives a _________ overall Centripetal Force (FC) larger than in the non banked case.
The larger FC allows the car either a greater margin for safety or a faster speed around a
banked corner compared to a flat corner of the same radius
6.8
Circular Motion – Vertical Circles
Objects travelling in vertical circles are subject to the acceleration due to gravity, thus their
speed will vary depending where in their motion observations are made.
Analysis of this type of motion is based on energy considerations and the fact that the
motion takes place in a uniform gravitational field.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
In theoretical situations, the TOTAL ENERGY REMAINS _________, but varies between
Kinetic and Potential, depending on where in the circle you choose to look.
PE = max
KE = min
KE
PE
KE = max
KE
Total Energy = KE + PE = a constant
PE
Body moving anticlockwise
PE = min
6.9
PROJECTILE MOTION.
Projectile motion is that motion which objects launched at some angle to the earth's
gravitational field, undergo. It is a combination of two ________________ motions;
(a) Horizontal motion which is constant ___________ motion.
(b) Vertical motion which is constant __________________ motion.
The horizontal motion has only one relevant equation:
v = d/t
The vertical motion, being constantly accelerated motion, is covered by the equations of
motion with the acceleration being that due to gravity, usually g = 10 ms -2. It is vital that a
positive direction is chosen and correctly assigned to the known and unknown values in
the equations:
v = u + at
v² = u² + 2ax
x = ut + ½at²
The only common factor between the two motions is the t, the time of flight.
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VCE PHYSICS
TOPIC: Motion
Questions
A
B
B
H
G
Direction of
Motion
A
C
D
H
G
C
D
X
F
E
Y
F
E
A car takes off from a ramp and the path of its centre of mass through the air is
shown below.First model the motion of the car assuming that air resistance is
small enough to neglect.
Q38: Which of the directions (A - H), best shows the VELOCITY of the car at X ?
Q39. Which of the directions (A - H), best shows the VELOCITY of the car at Y ?
Q40: Which of the directions (A - H), best shows the ACCELERATION of the car
at X ?
Now suppose that AIR RESISTANCE CANNOT BE NEGLECTED.
Q41: Which of the directions (A - H), best shows the ACCELERATION of the car
at X ?
A bushwalker is stranded while walking. Search and rescue officers drop
an emergency package from a helicopter to the bushwalker. They release
the package when the helicopter is a height (h) above the ground, and
directly above the bushwalker. The helicopter is moving with a velocity of
10 ms–1 at an angle of 30° to the horizontal, as shown in Figure 1. The
package lands on the ground 3.0 s after its release. Ignore air resistance in
your calculations.
Figure 1
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Q42: What is the value of h in Figure 1?
Q43: Assuming that the helicopter continues to fly with its initial velocity, where
is it when the package lands?
Which one of the statements below is most correct?
A. It is directly above the package.
B. It is directly above a point that is 15 m beyond the package.
C. It is directly above a point that is 26 m beyond the package.
D. It is directly above a point that is 30 m from the bushwalker.
Q44: Which of the graphs below best represents the speed of the package as a
function of time?
Page 46
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VCE PHYSICS
TOPIC: Motion
Fred is playing tennis on the deck of a moving ship.
He serves the ball so that it leaves the racket 3.0 m above the deck and travels
perpendicular to the direction of motion of the ship.
The ball leaves the racket at an angle of 8° to the horizontal.
At its maximum height it has a speed of 30.0 ms-1. You may ignore air
resistance in the following questions.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Q45: With what speed, relative to the deck, did the ball leave Fred’s racket?
Give your answer to three significant figures.
Q46: At its highest point, how far was the ball above the deck?
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VCE PHYSICS
TOPIC: Motion
The ship is travelling straight ahead at a velocity of 10 ms-1
Q47: When the ball is at its highest point at what speed is it moving relative to
the ocean?
Q48: at what angle is the ball travelling relative to the direction of the ship’s
travel?
6.10
Projection Angles
There are two basic types of projectile motion:
(a) Objects projected horizontally from a position some distance above the earth's surface.
V horiz
V horiz
V vert
V horiz
V vert
V vert
V horiz
V vert
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TOPIC: Motion
(b) Objects which are projected at an angle to the horizontal from the surface of the earth.
These objects have a path which can be divided into two equal parts, one to the point of
maximum height and the other from the point of maximum height back to earth. The two
parts are mirror images of one another.
V horiz
V vert = 0
V vert
V horiz
V horiz
V vert
INITIAL VELOCITIES FOR ANGLED PROJECTILES
Initial Horizontal Velocity = Horizontal component of Initial Velocity = VCos
Initial Vertical Velocity =Vertical component of Initial Velocity = V Sin
Initial Velocity (V)
V

V vert
= V Sin

V horiz
= VCos
6.11
Projectiles – Time, Height & Range
An object is fired from ground level with a velocity v at an angle θ to the horizontal
v
h
θ
Range (R)
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
1. Time to reach Maximum Height (h)
Upward is +ve.
u = v sin θ
use eqns of motion:
v=0
v = u + at
a = -g
0 = v sin θ – gt
s=?
t = v sin θ
t=?
g
2. Total Time of Flight
Total time = (time to reach h) x 2
= 2 v sin θ
g
3. Maximum Height
Upward is +ve
u = v sin θ
v=0
use eqns of motion
a = -g
v2 = u2 + 2as
s=h
0 = v2 sin2θ – 2gh
t = v sin θ
h = v2 sin2θ
g
2g
4. Range of Projectile
Horizontally vH = dH / t
vH = v cos θ
R = 2v sinθ x v cos θ
dH = R
g
t = 2v sinθ
2
= v x 2 sin θcos θ
g
g
= v2 sin 2θ
g
5. Maximum Range
occurs when sin 2θ = 1
2θ = 900
or θ = 450
6.12
Real Life Projectiles
The mathematical analysis of projectile motion ignores the effects of __________, in
particular air resistance.
The real world trajectory differs from the theoretical trajectory in three main ways.
(1) The actual range (horizontal distance) covered in the real world is less because of the
reduction of the horizontal component of velocity due to air resistance.
(2) The actual height achieved will be less, due to the effect of air resistance on the
upward vertical velocity.
(3) The object will fall more steeply than it rises, the path of the projectile is no longer
symmetrical around its highest point.
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VCE PHYSICS
TOPIC: Motion
CHAPTER 7
7.0
POTENTIAL ENERGY IN ELASTIC MATERIALS.
Elastic materials display ______________ behaviour. This means that when they are
deformed, stretched or compressed, they change their _____________ and when the
force used to deform them is removed they return to their original condition. Such
materials are able to store energy when deformed and release that energy when allowed
to return to original condition.
The mathematical relation between force and extension is called Hooke's Law which
states
F = -k∆x
F = Restoring Force (N)
k = Spring constant of material (Nm-1)
∆x = Compression or Extension (m)
The negative sign indicates that the restoring force F acts in the _________________
direction to the extension or compression ∆x
A plot of the Compressive (or Extensive) force vs extension will be a straight line with
Force
Slope = k (Spring Constant)
Area = Elastic Potential Energy
Extension
slope equal to the Spring Constant (k).
7.1 Potential Energy in Elastic Materials
Elastic materials store ___________ when they are deformed and release that energy
when they return to their original condition.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
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 and or
compression (m)
For materials which display “irregular” behaviour, the Potential Energy stored can only be
found from the area under the Force vs Extension (or Compression) graph.
“REGULAR” ELASTIC BEHAVIOUR
Force
“IRREGULAR” ELASTIC BEHAVIOUR
Slope = Spring
constant (k)
Force
F
F
Extension
Extension
x
x
Area = ½Fx = ½kx2
= Energy stored
up to extension x
CHAPTER 8
8.0
Law of Universal Gravitation
________________ is the most well known of all the Natural Forces.
We live with the effects of gravity every day and would lead completely different lives if
gravity was not present. It is gravity alone which gives us our sense of “up and down”.
Gravity is a ___________________ force, it acts at a distance.
It is ALWAYS an ___________________ force.
Gravity arises from the interaction of ____ masses.
The size of the gravitational force is directly proportional to the product of the two masses
and inversely proportional to the square of the distance between them.
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Drouin Secondary College
VCE PHYSICS
Mathematically:
TOPIC: Motion
Fg = GM1M2
R2
where
Fg = Gravitational Force (N)
Constant = (6.67 x 10-11 Nm2kg-2)
G = Universal Gravitational
M1, M2 = masses (kg)
R = Separation of the masses (m)
EACH of the bodies experiences the ___________ FORCE even though they may have
vastly different masses.
________________________________________________________________
Questions
Newton was the first person to quantify the gravitational force between two
masses M and m, with their centres of mass separated by a distance R as
F= GMm
R2
where G is the universal gravitational constant, and has a value of 6.67 × 10-11 N
m2 kg-2.
For a mass m on the surface of Earth (mass M) this becomes F = gm, where g
= GM
R2
________________________________________________________________________
Questions
Q49: Which one of the expressions (A to D) does not describe the term g?
A. g is the gravitational field at the surface of Earth.
B. g is the force that a mass m feels at the surface of Earth.
C. g is the force experienced by a mass of 1 kg at the surface of Earth.
D. g is the acceleration of a free body at the surface of Earth.
The radius of the Earth’s orbit in its circular motion around the Sun is 1.5×1011 m
Q50: Indicate on the diagram, with an arrow, the
direction of the acceleration of Earth.
Page 54
Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Q51: Calculate the mass of the Sun. Take the value of the gravitational constant
G = 6.67 × 10–11 N m2 kg–2.
Nato III is a communication satellite that has a mass of 310 kg and orbits Earth
at a constant speed at a radius R = 4.22 x 107 m from the centre of Earth.
Q52: What is the speed of Nato III in its orbit ?
R
Nato III
Earth
Q53: Which ONE of the following statements (A - D) about Nato III is correct ?A:
The net force acting on Nato III is zero and therefore it does not accelerate.
B: The speed is constant and therefore the net force acting on Nato III is zero.
C: The is a net force acting on Nato III and therefore it is accelerating.
D: There is a net force acting on Nato III, but it has zero acceleration
8.1
Gravitational Attraction
What Gravitational Force do the Earth and the Moon experience because of their proximity
Earth
to one another ?
Moon
Mass of Earth
ME = 5.98 x 1024 kg
Mass of Moon
MM= 7.34 x 1022 kg
Page 55
Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Q54: What is the magnitude of the force exerted by Earth on a water molecule of
mass 3.0 × 10-26 kg at the surface of Earth?
Nato III is a communication satellite that has a mass of 310 kg and orbits Earth
at a constant speed at a radius R = 4.22 x 107 m from the centre of Earth.
Q55: Calculate the magnitude of the Earth’s gravitational field at the orbit radius,
R = 4.22 x 107 m, of Nato III. Give your answer to 3 sig figs. You MUST show
your working. G = 6.67 x 10-11 Nm2kg-2 Me = 5.98 x 1024 kg.
8.2 Circular Orbits under Gravity
On the large scale of planets, moons, stars and other bodies in the universe, their motions
are determined by the gravitational attractions between them.
If, for example, a moon travels in a circular orbit around its host planet, it must be subject
to a ___________________ Force.
This Centripetal Force must be supplied by some kind of interaction between the planet
and its moon.
This interaction is the GRAVITATIONAL ATTRACTION between the Planet and its Moon.
Page 56
Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Thus the Centripetal Force (FC) needed for circular motion is supplied by the Gravitational
attraction (Fg) between the planet and its moon.
8.3
Mathematics of Circular Orbits
The Centripetal Force (FC) the moon is subject to is given by:
FC = MMv2/R
Remember the velocity of an object travelling in a circle is:
v = 2R/T
 v2 = 4 2R2/T2
Substituting for v2 we get:
FC = MM 42R2/T2
This Centripetal Force is supplied by the Gravitational Force between the Planet and the
Moon:
FG = GMMMp/R2
 GMMMP/R2 = MM42R2/T2
Rearranging we get:
R3/T2 = GMP/42
The terms G, MP, and  are all constants so their ratio is constant.
 The ratio R3/T2 is also a constant
8.4
Kepler’s Law
Johannes Kepler (1570 - 1630) discovered the laws governing planetary motion which
describe the movement of the planets in our solar system.
In 1615 Kepler discovered that the ratio of the of the cube of the average sun - planet
distance (R3) to the square of its period (T2) was a constant for _______ planets in our
solar system, this became known as Kepler’s Third Law.
His other 2 laws establish planets’ speeds and the elliptical nature of planet orbits.
In the previous section we found the ratio R3/T2 was a constant,
(its value is roughly 3.0 x 1018 ).
Page 57
Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
The 3rd law:
R3/T2 = GMP/42 can be rewritten as:
3
R=
GMPT2
42
Notice that the radius of orbit of any satellite, while it does depend on the mass of the
planet around which it circulates, _______
depend its own mass.
This is true of any satellites whether man made of naturally occurring.
________________________________________________________________
Questions
A satellite in a circular orbit of radius 3.8 × 108 m around Earth has a period of
2.36 × 106 s.
Q56: Calculate the mass of Earth. You must show your working.
8.5
Satellites in Space
A satellite moving through space will often use the gravitational field of a planet, like
Jupiter or star like our Sun to help propel it through space.
At point A, the satellite comes under the influence of the gravitational field of the planet.
The field does Work ON the satellite, accelerating it toward the planet.
By the time it has reached B, the satellite has increased its Kinetic Energy, and hence its
Speed, sufficiently to pass around, rather than crash into, the planet.
The satellite flies past the planet leaving with greater speed, having “___________” some
of the energy stored in the planet’s field.
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Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
This is the normal way of sending satellites to the outer planets and even outside our solar
system.
8.6
Energy Transfers in Gravitational Fields
The Gravitational Field vs Distance graph for Jupiter showing positions A and B for the
satellite is shown.
g(Nkg-1)
RJ
B
A
Distance R (m)
Since Work Done = Energy Transferred, the area under the graph represents the work
done by the field on, and the change in energy possessed by, “1 kg of satellite mass” in
moving from A to B.
In exam questions, the area normally needs to be found by the “counting the squares”
method.
Area gives:
1. Work by the field on 1 kg of satellite moving from A to B.
2. The increase in Kinetic Energy possessed by 1 kg
of satellite in moving from A to B.
3. The loss in Potential Energy of 1 kg of
satellite moving from A to B
For the satellite with a mass >1 kg, total energy possessed = area x mass
Page 59
Drouin Secondary College
VCE PHYSICS
TOPIC: Motion
Questions
The Russian space station MIR (Russian meaning - peace) was in a circular
orbit around the Earth at a height where the Gravitational Field Strength is 8.7
Nkg-1
Q57: Calculate the magnitude of the gravitational force exerted by Earth on the
astronaut of mass 68 kg on MIR
When the astronaut wishes to rest he has to lie down and strap himself into bed.
Q58: What is the magnitude of the force that the bed exerts on the astronaut
before he begins to fasten the strap ?
Newspaper articles about astronauts in orbit sometimes speak about zero
gravity when describing weightlessness.
Q59: Explain why the astronaut in the orbiting MIR is not really weightless.
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