Ian Wilkinson
HSC Physics Module 9.2 Summary
1. The Earth has a
gravitational field
that exerts a force
on objects both on
it and around it
Define weight as the force
on an object due to a
gravitational field
Analyse information using
the expression
to determine the weight
force for a body on Earth
and for the same body on
other planets
Gather secondary
information to predict the
value of acceleration due to
gravity on other planets
All masses have a gravitational field associated with them, which is
an area in which other masses experience an attractive force
towards the original mass. This is similar to the concept of an electric
field around a point charge.
Weight is the force on a mass due to the gravitational field of
another mass. As it is a force, it is measured in Newtons (N). This is
different to mass, which is a measure of the quantity of matter in a
body, and is measured in kilograms (kg).
According to Newton’s Second Law:
As g is the acceleration due to gravity of a mass, weight force can be
determined by the following equation:
where:
 F = Force [N]
 m = Mass [kg]
 g = Acceleration due to gravity [ms-2]
The acceleration due to gravity on other planets (g) can be derived
by considering the formula for the gravitational force between two
objects, which will be discussed in 9.2.3
By substituting
which leads to
Explain that a change in
gravitational potential
energy is related to work
done
Where:
 g = Acceleration due to gravity [ms-2]
 G = Universal gravitational constant = 6.67x10-11Nm2kg-2
 M = Mass of the planet [kg]
 d = distance between the centres of masses
NOTE: d is the distance between the centres of masses, and thus is
measured from the centre of planets, NOT from the surface. HSC
questions will often give the height above the centre in the given
data, but the radius of the planet must be added in order to use the
above formula.
Gravitational potential energy, or Ep, is a measure of the potential
energy of a mass due to presence of a gravitational field. Recall that
work done is the change in energy of a mass. Thus if there is a
change in the Ep of a mass, work has been done on that mass. If the
Ep of a mass is increased, the work has come from an external object
Ian Wilkinson
Define gravitational
potential energy as the work
done to move an object
from a very large distance
away to a point in a
gravitational field
applying force to the mass, such as lifting a pencil upwards off a
table. When Ep is decreased, the work is done by the gravitational
field upon the mass, and Ep is most commonly converted to kinetic
energy.
The gravitational potential energy (Ep) can be calculated using the
formula for work done:
by substituting
The following equation can be derived
There is a problem with this equation, as it is assumes that g is
constant. This is not true however, as g is proportional to the inverse
square of the distance between centres of masses.
By substituting
And by recognising that potential energy is measured from centres
of masses, not from the surface of Earth (i.e. h=d=r)
Which leads to
There is however a problem with the above formula. The formula for
acceleration due to gravity was derived from Newton’s Law of
Universal Gravitation. In that formula, force has a value of zero at an
infinite distance from Earth. Thus it follows that the zero reference
point for Ep must be at an infinite distance also, where a mass
experiences no weight force. But as previously established, moving
an object towards a mass leads to a decrease in Ep. If an infinite
distance is taken as the zero point, moving an object towards a mass
must result in Ep taking a value less than zero, that is, a negative
value. Thus the formula for Ep is:
Where





Ep = Gravitational potential energy
G = Universal gravitational constant
m1 = Mass of object 1
m2 = Mass of object 2
r = distance between centres of masses
As can be seen in this diagram, Ep
increases towards zero as it moves away
from a body. Due to the Law of
Conservation of Energy, the kinetic
energy and Ep add to zero, as per the
diagram.
Ian Wilkinson
The formula can also be derived by considering that work done is
the integral of the force equation in respect to distance. Therefore,
by integrating Newton’s Law of Universal Gravitation, with limits
from infinity to r:
Perform an investigation
and gather information to
determine a value for
acceleration due to gravity
using pendulum motion or
computer-assisted
technology and identify
reason for possible
variations from the value
9.8ms-2





Refer to practical 9.2.1d)
METHOD
A retort stand with boss head and clamp was set up, and a
string attached to a 200g mass was clamped tightly. The
length of string was measured, held 10° to the vertical, and
released. The time for ten oscillation periods was recorded,
and then divided by 10. The method was repeated for
various lengths of string from 0.2m to 1.0m.
DRAW DIAGRAM IF POSSIBLE
For SAFETY, use small masses and small swings (i.e. small
angles) to minimise equipment damage and possible injury.
RESULTS
The following formula was used:

From the results, T2 (period squared) was plotted against l
(length), and the gradient was found. The value of g was
calculated using the gradient and the above formula, which
lead to the following equation.

The value obtained was 9.7m-2
ACCURACY
The value obtained was close to the accepted value of
9.8ms-2. Possible reasons for variation include:
o Inaccuracy of measuring the length of pendulum
o Unreliability of using a stopwatch to measure period
length => susceptible to human error
o Minor factors that influence g e.g. altitude where
measured
RELIABILITY
The experiment was repeated by measuring the time for 10
periods, and an average was taken => also minimised human
error of stopwatch
No outliers were present in data
All points were close to the line of best fit => precision




Ian Wilkinson






A gradient was measured => provides more reliable results
VALIDITY
By measuring the gradient, systematic error (y-intercept)
was eliminated
All other variables (e.g. location of experiment) were
controlled
A small angle of oscillation was used to minimise the
dampening of oscillation
The accuracy was limited by the reasons stated above
The accuracy and validity could be improved by using data
loggers and sensors to measure period, and by using
computer technologies to graph the result
Ian Wilkinson
2. Many factors have
to be taken into
account to achieve
a successful rocket
launch, maintain
safe orbit and
return to Earth
Describe the trajectory of
an object undergoing
projectile motion within the
Earth’s gravitational field in
terms of horizontal and
vertical components
Solve problems and analyse
information to calculate the
actual velocity of a
projectile from its
horizontal and vertical
components using:
Describe Galileo’s analysis
of projectile motion
Projectile motion is the motion of an object where gravity is the only
force on the object. This includes anything thrown, dropped, or
launched into the air and left to continue unpowered flight. So a
rocket is not a projectile, as it is powered by thrust force.
Recall that a vector can be resolved into its relevant dimensions. For
projectile motion, the relevant dimensions are the horizontal and
vertical component of an object’s velocity. After the projectile has
been launched, there is no horizontal force (ignoring air resistance),
and the only force in the vertical component is gravity. As a result, a
projectile accelerates towards the ground at a rate equal to the
acceleration due to gravity (g). The laws of motion can be applied to
the horizontal and vertical components independently.
Through mathematical analysis, the predicted trajectory of an ideal
projectile is a parabolic shape.
Remember to only substitute in values after an equation has been
rearranged, and to also substitute the relevant units and dimensions
for data values. Always check the units and dimensions as a check
that your working is correct. Define the origin as the most
mathematically convenient location.
Projectile motion questions often involve finding the following data:
 Velocity of an object at any point in time (most commonly
initial and final) => use trigonometry to find horizontal and
vertical components.
 Range (horizontal distance travelled by a projectile)
 Maximum height (vertical velocity equals zero)
 Height at any time (vertical displacement)
 Time taken to reach ground
Galileo postulated that all masses, regardless of their size, fall at the
same rate (i.e. acceleration due to gravity is independent of mass).
Ian Wilkinson
This is only true if air resistance is ignored, and so Galileo had
difficulty demonstrating his postulate. He eventually tested and
measured his postulate by not dropping objects, but by rolling balls of
different masses down highly-polished inclines. The lower
acceleration of the balls made it easier to measure, and he was able
to use trigonometry to calculate the acceleration due to gravity on
Earth. He also showed that the flight time of an object projected from
the same height horizontally would be independent of its initial
horizontal velocity.
Explain the concept of
escape velocity in terms of
the:
 gravitational
constant
 mass and radius of
the planet
Galileo’s analysis of projectiles also introduced the idea of inertial
frames of reference and relativity. By considering cannonballs
dropped from moving ships, he observed that whilst from the ship’s
frame the ball drops vertically, to an observer the ball drops in a
parabolic shape. He concluded that velocity can be resolved into
horizontal and vertical components, and that a projectile moves due
to acceleration in the vertical component and inertia in the horizontal
component. He used this idea to prove the heliocentric model of the
universe, as it explained why objects weren’t left behind as the Earth
moved. This advance in scientific thinking challenged the Aristotelian
idea of impetus, and changed the direction of scientific thinking,
leading to Newton to develop his laws of motion and theories on
gravitation.
Escape velocity is the initial velocity required by a projectile to rise
vertically and just escape the gravitational field of a planet. An object
at escape velocity would rise up, slow down, but would not return.
Escape velocity can be calculated by considering the conservation of
energy, and comparing initial energy to final energy. If a projectile is
launched at escape velocity, its kinetic energy at an infinite distance
would be zero.
Where:
U = Total energy of projectile
Ian Wilkinson
Uk = Kinetic energy of projectile
UG = Gravitational potential energy of projectile.
By conservation of momentum:
Therefore
Rearranging we get:
Outline Newton’s concept
of escape velocity
Where:
v = escape velocity (ms-1)
G = 6.67x10-11kg-1m3s-2 = Universal gravitational constant
M = Mass of planet
r = radius of planet
As can be seen, escape velocity depends on the gravitational
constant, and the mass and radius of the planet. It is independent of
any physical features of the projectile. If a projectile travels at a speed
greater than escape velocity, it will also escape, and have some
kinetic energy when it is at an infinite distance.
Note that this equation should be derived in an exam.
Also, note that escape velocity is a theoretical idea, and that it would
be practically impossible to achieve from Earth’s surface. This is
because Earth’s atmosphere would cause the projectile to heat up
and potentially vaporise the projectile, and that the extreme g-forces
created as the projectile is accelerated would crush anything inside
the projectile. Escape velocity can be demonstrated by the slingshot
effect, which is discussed later.
Newton postulated that it is possible to launch a projectile fast
enough so that it could escape Earth’s gravitational field. He
considered a thought experiment of launching a projectile
horizontally from a very tall mountain. If the projectile is launched at
low horizontal velocities, it will fall to the ground in a parabolic path.
As the initial horizontal velocity it increased, the projectile will reach
further points on Earth’s surface. If it is launched at a fast enough
horizontal velocity, the object will travel around the Earth, because as
the object falls, the Earth’s surface curves away from the projectile.
The object would follow a circular orbit.
Ian Wilkinson
If the projectile is launched at faster velocities, it would follow an
elliptical orbit around the Earth. If it is launched at a fast enough
velocity, the projectile would follow a parabolic orbit and escape
Earth’s gravitational field (hyperbolic orbit at higher velocities). This is
Newton’s concept of escape velocity.
Identify why the term ‘g
forces’ is used to explain
the forces acting on an
astronaut during launch
Therefore, Newton’s reasoning is that there is an initial velocity at
which a projectile can be fired so that it will follow a bound orbit
around Earth and not hit the ground. Furthermore, if a projectile
exceeds a certain velocity (escape velocity), the projectile will follow
an unbound orbit and escape Earth’s gravitational field.
The g-force is the ratio of a person’s apparent weight at a given time
to their true weight. Apparent weight is the sensation of weight that a
person feels, and is equal to the sum of contact forces resisting a
person’s true weight. Another way of classifying g-forces is that it is a
measure of acceleration forces, with Earth’s gravitational acceleration
as the unit. A person at rest on Earth’s surface experiences a g-force
of 1.
The apparent weight experience by an astronaut is mg + ma, where as
shown in the diagram below.
Ian Wilkinson
Therefore, g-force in the vertical direction is given by:
Discuss the effect of the
Earth’s orbital motion and
its rotational motion on the
launch of a rocket
It is much easier however to remember the definition of g-force as
the ratio of apparent weight to true weight, as the above formula
does not work for horizontal and circular acceleration.
G-forces are used to explain the forces acting on an astronaut during
launch as it provides a more accurate and relevant representation of
the stress experienced by an astronaut. Astronauts have different
masses, so the forces acting on each astronaut is different. But as gforces are a ratio, g-force is independent of mass, and thus allows for
easier comparison of forces.
Earth’s rotation around its axis provides an initial velocity for a rocket
being launched into space, as the rocket has the same initial velocity,
thereby providing additional velocity during take-off. Similarly, Earth’s
orbital motion around the Sun provides more relative velocity. The
Earth’s rotates at 1700kmh-1 around the equator, and orbits at 107
000kmh-1 around the Sun. Thus exploiting the orbital and rotational
motion of the Earth allows rockets to be launched at a higher velocity
relative to an external frame.
To maximise the additional velocity from Earth’s rotational motion,
launch sites are chosen as close to the equator as possible (e.g.
Florida, French Guinea), and are launched east, as Earth rotates east.
Launches are also taken at the right time of day and right time of year
to maximise the initial velocity of the rocket.
These set periods are called launch windows, and vary depending on
the mission. Launching a rocket during a launch window saves fuel
Ian Wilkinson
Analyse the changing
acceleration of a rocket
during launch in terms of
the:
 Law of
Conservation of
Momentum
 forces experienced
by astronauts
(therefore less environmental harm), and maximises possible
payloads for a rocket.
A rocket is propelled by the expulsion of combusted gas particles in
the opposite direction to the rocket’s motion. By Newton’s Third Law,
the force of the gas particles being expelled from the rocket is equal
to the force of the gas particles on the rocket, and so the rocket
accelerates in space.
Momentum
The propulsion of a rocket can also be analysed by applying the
conservation of momentum to the rocket system. Before a rocket
launches, its momentum relative to Earth is zero, as it has no velocity.
Therefore at any point in the flight, the net change in momentum for
a given time period must equal zero by the Law of Conservation of
Momentum.
The change in momentum of the rocket is equal and opposite to the
change in momentum of the gas particles being expelled from the
rocket. Note that the oxygen supply also has to be stored in the
rocket, as there is no oxygen in outer space.
Forces experienced by astronaut
By applying Newton’s Third Law to a rocket, we can also see that the
force of the gas particles being expelled is equal and opposite to the
force of the rocket.
Before launch, and astronaut experiences a force of 1g, as the rocket
is resting on the ground. During launch, a rocket experiences both
thrust and weight force, so the rocket accelerates according to
Newton’s Second Law.
Where:
T = Thrust force [N]
m = mass of rocket system [kg]
Before take-off, the mass of the fuel constitutes around 90% of the
initial mass. As the fuel combusts and is expelled from the rocket, the
mass of the rocket significantly decreases. Additionally, as a rocket’s
altitude increases, the acceleration due to gravity decreases. If thrust
force is constant, we can see from the above equation that the
acceleration of the rocket increases until the rocket exhausts of fuel.
Ian Wilkinson
Rockets that are launched into space are generally multi-stage
rockets, i.e. the rocket has multiple fuel supplies and engines that
operate in stages. Each stage is sequentially shutdown to avoid
excessive peaks in g-force that could impact astronauts. After each
stage shuts off, there is a brief moment of 0g (weightlessness), as no
force is supplied. The next stage then initiates, and proceeds much
like the previous stage.
G-forces above 4 are potentially unsafe, as it could lead to blackouts
for positive g-forces (blood drains from head, causing
unconsciousness), or red-outs for negative g-forces (blood rushes to
head, causing excessive bleeding and brain damage). Astronauts also
experience loss of peripheral and colour vision. If an astronaut is lying
upwards perpendicular to the g-force on a body-contoured couch, up
to 20 g may be tolerated, as blood flow to the head is less affected.
The sequential shutdown of multiple engines also reduces the effect
of an excessive change in g-force on an astronaut.
Ian Wilkinson
Analyse the forces involved
in uniform circular motion
for a range of objects,
including satellites orbiting
the Earth
Uniform circular motion is the motion of an object travelling in a
circle with constant linear orbital speed. The velocity of an object at
any instant whilst in uniform circular motion is tangential to orbital
path. As object’s velocity is changing direction whilst in circular
motion, there must be an acceleration, and hence a force. The force is
called centripetal force, and is directed perpendicularly to the object’s
velocity, and directed towards the centre.
Note that centripetal force is not a true force, but the force required
for an object to move in circular motion. In the above diagram, the
required centripetal force is provided by the tension in the rope
attached to the rock.
The equation for centripetal force is
Solve problems and analyse
A satellite orbiting Earth in uniform circular motion also experiences a
centripetal force, supplied by the gravitational force of the Earth on
the satellite. Earth’s gravitational force acts perpendicular to the
satellite’s velocity, causing the satellite to undergo centripetal
acceleration, and move in circular motion. The gravitational force on
a satellite moving in circular motion is constant however, and so for a
satellite, we need to consider the required orbital velocity for uniform
circular motion to occur. Orbital velocity can be calculated by
equating centripetal force with gravitational force (see below).
Remember that r is the distance between centres of masses. If the
Ian Wilkinson
information to calculate the
centripetal force acting on a
satellite undergoing
uniform circular motion
about the Earth using:
data given has the height of the orbit above Earth’s surface, you need
to add the radius of Earth for the equation to be correct.
Also note that for a satellite, centripetal force is provided
gravitational force, so centripetal force in this case can also be
calculated by using Newton’s Law of Universal Gravitation.
Compare qualitatively low
Earth and geo-stationary
orbits
A low Earth orbit is an orbit higher than 250km, and lower than
1000km. Above 250km a satellite is much less affected by
atmospheric drag. Below 1000km a satellite is below the Van Allen
radiation belts, which pose risk to live space travellers and electronic
equipment due to the high radiation of the belts.
A geo-stationary orbit is at an altitude over the equator so that the
period of the orbit exactly matches the period of Earth’s rotation. This
allows the satellite to appear to be over a fixed point on Earth’s
surface, and the receiving dish is points at a fixed point in the sky. The
radius of a geostationary orbit is 42 168km (altitude 35 800km), which
can be calculated using Kepler’s Third Law, and taking Earth’s rotation
period as 23h, 56m, 4s (one sidereal day). The orbital velocity is
approximately 11, 000kmh-1.
Below is a comparison of the two orbits.
Low Earth orbit
Geostationary orbit
250km-1000km altitude
35 800km altitude above
equator
~90mins period
Period same as Earth’s rotation
Cheaper to launch
More expensive to launch
Stronger signal with little delay Weaker signal with longer delay
Subject to drag and orbital
Do not experience orbital decay
decay
Closer, wider view of Earth’s
Limited view of Earth’s surface
surface
Satellite can be placed in any
Satellite can only be in one
orbit desired
specific orbital path
Uses include geotopographic
Communication satellites,
studies, studying weather
weather monitoring, and
patterns, military spying, and
information relay
civilian surveillance
Orbital velocity is the instantaneous velocity of an object in circular
motion along its path. This velocity needs to be maintained in order
for the satellite to stay in its path. Orbital velocity can be calculate by
considering velocity as displacement over time:
Define the term orbital
velocity and the
quantitative and qualitative
relationship between
orbital velocity, the
gravitational constant, mass
of the central body, mass of
the satellite and the radius
of the orbit using Kepler’s
Law of Periods
Where:
v = orbital velocity [ms-1]
r = radius of orbit from centre of central mass [m]
T = period of orbit [s]
Kepler’s Law of Periods is the following:
Ian Wilkinson
Where:
r = radius of orbit from centre of central mass [m]
T = period of orbit [s]
M = mass of central mass
Rearranging the expression for orbital velocity to make T the subject,
and then substituting into Kepler’s Law of Periods, we get the
following:
Rearranging:
Solve problems and analyse
information using:
Account for the orbital
decay for satellites in low
Earth orbit
Where:
v = orbital velocity [ms-1]
G = 6.67x10-11kg-1m3s-2 = universal gravitational constant
M = mass of central body
r = distance between centre of masses [kg]
The above expression can also be derived by equating centripetal
force with gravitational force.
Qualitatively, we can see that the square of the orbital velocity is
directly proportional to the mass of the central body, and inversely
proportional to the radius of the orbit. The constant of
proportionality is the universal gravitational constant. Note that
orbital velocity is independent of the mass of the satellite.
Remember that r is the distance between centres of masses. If the
data given has the height of the orbit above Earth’s surface, you need
to add the radius of Earth for the equation to be correct.
Satellites in low Earth orbit have a maximum altitude of 1000km, and
at this altitude are subject to interaction with the atmosphere,
despite the extremely low density of the atmosphere at this altitude.
As the satellite interacts with the atmosphere, the air particles exert a
frictional force in the opposite direction to the satellite’s velocity, and
a small lift force.
The atmospheric drag reduces the satellite’s velocity. Some of the
Ian Wilkinson
kinetic energy of the satellite is lost to heat energy due to friction as
the satellite slows down, and so the energy of the satellite reduces.
By considering the equation for centripetal acceleration
Discuss issues associated
with safe re-entry into the
Earth’s atmosphere and
landing on the Earth’s
surface
we can see that as velocity decreases, so does the radius of the
satellite’s orbit. As the satellite descends, its velocity actually
increases, as it is accelerating towards Earth. Its total energy is less
however, as its gravitational potential energy has decreased.
In addition, the atmosphere is denser at lower altitudes. Thus the
atmospheric drag on the satellite increases, and it decays at a faster
rate. This continues until ~200km, where the heat generated by
friction becomes great, and the satellite disintegrates.
When a spacecraft returns to Earth surface, the astronaut face many
dangerous issues. These issues include heat, g-forces, ionisation
blackout, and landing on Earth’s surface.
Heat
As a spacecraft is travelling through Earth’s atmosphere, it has a
velocity of around 30, 000kmh-1. The spacecraft has a high quantity of
kinetic energy, and much of this energy is converted to heat energy
during re-entry as a result of atmospheric friction. The heat can cause
the spacecraft to reach extreme temperatures, which could cause the
spacecraft to disintegrate.
The heat can be tolerated by designing the spacecraft to have a blunt
shape, as this dissipates some of the heat into the air. The space
shuttle also presents its underbelly at 40° to Earth’s atmosphere for
similar reasons. Spacecraft also have heat shields, such as ablative
material, which sacrificially burns to carry away heat. On the space
shuttle, insulating tiles made of glass fibre, though 90% of the
composition is air. This gives them excellent thermal insulation
properties, though they must be waterproofed between flights as the
tiles are porous. More simply, the temperatures the space shuttle
endures can be reduced by taking longer to re-enter, which lengthens
the time that kinetic energy is converted to heat. This is achieved by
the space shuttle through a series of sharp s-banking turns.
G-forces
The deceleration of a spacecraft during re-entry can cause g-forces of
up to 20g, which is extremely dangerous for humans. The tolerance of
humans to high g-forces can be reduced by having a transverse
application of the g-forces (i.e. lying perpendicular to deceleration).
This means the blood does not drain from the head. Additionally, the
astronaut should be lying face-up, as an “eyeballs-in” application of g
loads is easier to tolerate. Supporting the body also increases
tolerance, so astronauts lie in contoured couches specifically designed
for each astronaut.
Ian Wilkinson
Identify that there is an
optimum angle for safe reentry for a manned
spacecraft into the Earth’s
atmosphere and the
consequences of failing to
achieve this angle
Identify data sources,
gather, analyse and present
information on the
contribution of one of the
following to the
development of space
exploration: Tsiolkovsky,
Oberth, Goddard, EsnaultPelterie, O’Neill or von
Braun
Ionisation blackout
The extreme heat generated by a spacecraft during re-entry causes
atoms in the air around the spacecraft to become ionised. Radio
signals cannot penetrate this layer of ionised particles, and so radio
communication is not possible. This can cause an issue if urgent radio
contact is necessary during re-entry. This problem can be minimised
by carefully planning the re-entry so that the astronauts are selfsufficient.
Reaching the surface
After passing through the atmosphere, the issue of landing on Earth’s
surface still needs to be addressed. Early Russian cosmonauts would
decelerate, then jump out of the spacecraft and land with a
parachute. American astronauts deployed parachutes for the
spacecraft, and landed in the ocean. The spacecraft lands on a runway
by decelerating through a series of sharp S-turns with the nose at 40°,
and then land on a runway.
A spacecraft starts re-entry by orbiting the Earth in a low Earth orbit.
The astronauts will then retrofire of their rockets (i.e. position the
rockets in front of the spacecraft), causing the spacecraft to lose
energy, slow down, and descend. As the spacecraft enters Earth’s
atmosphere, both lift and drag act on the spacecraft. If the spacecraft
enters the atmosphere at an angle too steep, the g-forces and heat
experienced by the spacecraft could destroy the spacecraft. If the
angle is too shallow, the lift force will be too great, and the spacecraft
may skip off the atmosphere instead of penetrating it, and not have
enough fuel to re-attempt re-entry. Thus an optimum angle for safe
re-entry of manned spacecraft exists, and is between 5.2°-7.2°.
Wernher von Braun => some of his achievements are below.
 Developed high thrust engines using liquid fuel
 Responsible for the development of V2 guided missiles in
Germany
 Proved gyroscopes could help stabilise rockets
 After WWII, von Braun’s team continued research on the V2
rocket assembly, and test rocket for high altitude research
 He led the development of Redstone Rocket, which was used
for ‘first’ nuclear missile test
 He helped develop to put America’s first satellite, Explorer I,
into space in 1958
 Led the development of the Saturn rocket, culminating in the
Saturn V rocket, which propelled Apollo-11 to the moon in
1969.
Ian Wilkinson

Perform a first-hand
investigation and analyse
data to calculate initial and
final velocity, maximum
height reached, range and
time of flight of a projectile
for a range of situations by
using simulations, data
loggers and computer
analysis
Director of NASA’s Marshall space flight centre, which was
instrumental in the space race.
 He proposed the idea of manned space station and Mars
mission
 Developed the concept of orbital warfare and the Space
Shuttle
 Promoted public interest in space exploration, as the
technical director of 38 Disney films
Sources of data include the NASA history page and New Scientist
article.
http://www.newscientist.com/blogs/culturelab/2009/11/hypocriticalor-apolitical-von-braun-deconstructed.html
http://history.nasa.gov/sputnik/braun.html
 Refer to practical 9.2.2o)
METHOD
 The following website was used:
http://zebu.uoregon.edu/nsf/cannon.html
 The angle of initial velocity was set to 30°. The initial velocity
of the projectile was varied, and the resulting maximum
height, range, and time of flight were recorded in a table. This
was repeated for angles of 45° and 60°.
RESULTS
 Refer to the results in the practical, though the results can
easily be calculated if needed by using the kinematics
equations
 TRENDS: An increased initial velocity resulted in a greater
range, time of flight, and maximum height reached
ACCURACY/RELIABLITY/VALIDITY
 The experiment was conducted as a computer simulation, so
was very accurate/reliable/valid, as it modelled the physical
application of the kinematics equations.
Ian Wilkinson
3. The Solar System is
held together by
gravity
Describe a gravitational field
in the region surrounding a
massive object in terms of
its effects on other masses
in it
Define Newton’s Law of
Universal Gravitation:
Recall that a field is a region in which a force is experienced, and
that gravity is the force of attraction between masses. The
gravitational field of a mass is the space surrounding it in which
other masses experience a force of attraction due to gravitational
force.
Gravitational fields a vector fields; i.e. the field lines contain both a
magnitude and a direction. The direction of the gravitational field is
towards the centre of the respective masses, as gravity is a force of
attraction. Whilst the field lines may look parallel close to the
surface of a mass, they are in fact radial, and the spaces between
field lines decrease the further away from a mass.
The gravitational field of an object theoretically extends to infinity,
but as gravitational force is relatively very weak, it is only
macroscopically observable for large masses for a finite distance.
The field strength is the force per unit mass, and hence is equal to
the acceleration of a mass due to gravity, or g.
The gravitational force of attraction between masses is proportional
to the following values:
 The mass in the centre of the field (directly) [m1 or M]
 The mass which is experiencing the force due to the
presence of the other mass (directly) [m2 or m]
 The inverse square of the distances between the two objects
[d]
Thus Newton’s Law of Universal Gravitation is the following:
Where:
 F is measured in Newtons [N]
 m1 and m2 are measured in kilograms (kg)
 d is measured in metres [m]
 G is the gravitational constant (6.67x10-11 m3kg-1s-2)
As can be seen from the above expression, it is symmetrical about
m1 and m2, which means they are interchangeable values. Hence
Newton’s Law of Universal Gravitation is in fact an action-reaction
pair which obeys Newton’s Third Law. The force of the first mass on
Ian Wilkinson
Present information and use
available evidence to discuss
the factors affecting the
strength of the gravitational
force
Solve problems and analyse
information using:
Discuss the importance of
Newton’s Law of Universal
Gravitation in understanding
and calculating the motion
of satellites
a second mass is equal in magnitude to the force of the second mass
on the first mass, but opposite in direction.
Also note the relatively small value of G, which is why gravity is
considered relatively a very weak force.
From the Law of Universal Gravitation
the strength of the gravitational force is dependent on the following.
 The mass of the two objects
 The distance between the masses.
In terms of Earth’s surface, the following can thus affect the strength
of the gravitational force:
 The altitude, as gravitational force decreases with an
increased distance
 Latitude => Earth is not a sphere, so gravity is strongest at
the poles
 Type of material below the surface, which alters the
strength of gravitational force. For example, gravity is
slightly stronger over land than over water.
Remember to always make sure units and dimensions are balance.
Also note that d is the distance between centres of mass, so radius
of Earth must be added if the height above Earth’s surface is given.
Newton’s Law of Universal Gravitation has allowed us to have a
more mathematical basis for understanding the motion of satellites.
This is because gravity is the basis for the motion of satellites, in
conjunction with other laws of motion. Hence the mathematical
expression for gravitational force has allowed us to accurately
calculate and predict the motion of satellites not only around Earth,
but in the universe.
Newton’s Law of Universal Gravitation has allowed us to calculate
the orbital velocities required for specific satellite paths by the
following derivation.
First equate Newton’s Law of Universal Gravitation and centripetal
force, which are equal for circular motion.
and
Giving
The constant in Kepler’s Law of Periods can also be obtained by
equating orbital velocity with
Ian Wilkinson
Identify that a slingshot
effect can be provided by
planets for space probes
which is just the velocity of an object around the circumference of a
circle. Newton’s Law of Universal Gravitation can also be used to
derive the formula for gravitational potential energy, which was
derived earlier.
All of these expressions are very important in understanding and
calculating the motion of satellites. Applications of this
understanding include being able to send artificial satellites into
specific orbital paths, and calculate the slingshot effect.
The slingshot effect, also known as a gravity-assist manoeuvre or
swing-by, occurs when a spacecraft is directed towards a planet at a
high speed. The spacecraft enters the planet’s gravitational field,
and then is ‘flung’ out at a higher speed, without expending much
fuel.
To further understand the slingshot effect, recall that orbits around
object can be circular or elliptical. These are just two shapes an orbit
can trace out; parabolic and hyperbolic orbits are also possible. As
can be inferred, the orbits of masses trace out conic sections. At
orbital velocity, the eccentricity of the orbit is zero, and hence a
mass has a circular orbit. As its velocity increases, it traces out
elliptical orbits with increasing eccentricity, until it reaches escape
velocity, where the eccentricity is one, and the orbit is parabolic.
Further increasing the velocity of the mass results in a path of
greater eccentricity, and hence hyperbolic orbits occur. Circular and
elliptical orbits are considered closed or stable orbits, whilst
parabolic and hyperbolic orbits are unbound orbits. The kind of orbit
in fact relies on the sign of the mechanical energy of the orbiting
mass, but velocity provides a simplified explanation for the shapes of
orbits.
During a slingshot manoeuvre, a spacecraft passes close to a planet,
and enters a hyperbolic orbit due to the gravitational field. The
spacecraft accelerates due to gravity as it enters the field, and
decelerates as it departs the planet. This results in the spacecraft’s
exit speed relative to the planet being theoretically equal to its
entrance speed, but the direction of its velocity is different.
From an external frame of reference however, such as the Sun, the
speed of the spacecraft has changed. This is because the planet itself
is moving at a velocity due to its orbit, and this relative velocity is
added to the spacecraft’s velocity. If the spacecraft passes behind
the planet, its velocity increases, and if it passes in front its velocity
Ian Wilkinson
decreases.
Thus the planet transfers energy to the spacecraft, and so the
manoeuvre can be considered an elastic collision, as both
momentum and kinetic energy are conserved. As the planet’s mass
is so large however, the change in its energy is very small.
The slingshot effect is normally achieved by the spacecraft
approaching the planet at an angle to its orbit. The craft enter the
orbit, swings around the planet, and exits at the same angle at which
it entered. The final velocity of the spacecraft is given by the
following equation, derived from the condition that the slingshot
effect is an elastic collision.
The resultant gain in speed occurs with little expenditure of fuel, so
is a useful manoeuvre for spacecraft travelling through space. The
maximum final speed occurs when the spacecraft approaches and
exits parallel to the planet’s orbit.
Ian Wilkinson
4. Current and
emerging
understanding
about time and
space has been
dependent upon
earlier models of
the transmission of
light
Outline the features of the
aether model for the
transmission of light
Describe and evaluate the
Michelson-Morley attempt
to measure the relative
velocity of the Earth through
the aether
Physicists in the 19th century observed light to act as a wave, and so
believed that it propagated through a medium, which they named
the aether. Scientists believed that the aether had the following
properties:
 It filled all space, as light travels everywhere
 It was transparent
 It had an extremely low density, hence was undetectable
 It was stationary
 It permeated all matter, and yet was permeable to material
objects
 It had great elasticity, otherwise energy would be lost during
the transmission of light over long distances
Theory behind the experiment
Physicists believed that the aether was stationary, and as such the
Earth was moving through the aether at 30kms-1. If this was true,
then a so-called aether ‘wind’ would be present on Earth. Under
Galilean relativity, which dominated physics at the time, this wind
would cause the speed of light to be different when measured from
Earth’s frame of reference. This is because light would be either
travelling with the wind, or against the wind, much like the
difference between rowing a boat upstream or downstream. Many
experiments tried and failed to detect the aether wind, but it was
determined that the mechanisms weren’t sensitive enough.
The Michelson-Morley Experiment
In 1887, the following experiment was set up by Michelson and
Morley in order to detect the aether wind:
Ian Wilkinson
Gather and process
information to interpret the
results of the MichelsonMorley experiment
Discuss the role of the
Michelson-Morley
experiments in making
determinations about
competing theories
Michelson and Morley had set up an interferometer that would
detect the interference pattern two light sources due to the aether
wind. A beam of light from the light source was split at the halfsilvered mirror (the beam splitter) in the centre of the apparatus.
The first beam travelled through the mirror, and was travelling
against the aether wind. The beam was then reflected by the mirror,
and was travelling with the aether wind, until it reached the halfsilvered mirror, and was reflected to the detector.
The second beam was initially reflected perpendicular to the aether
wind, and as such was travelling across the aether wind. This beam
was then reflected, and travelled through the half-silvered mirror to
the detector. Both of these beams had travelled the same distance
in the apparatus’ frame of reference, but under the aether model,
these two beams would have travelled at different velocities due to
the aether wind, with the perpendicular beam travelling faster than
the parallel beam. As such, it was expected that an interference
pattern would be detected, as the beams of light would be out of
phase with each other due to their different paths.
The experiment was conducted on a pool of mercury, which
dampened any external vibrations, and allowed the apparatus to be
rotated. If the apparatus was rotated, different interference
patterns should theoretically be detected under the aether model.
Result and evaluation
Despite Michelson and Morley conducted the experiment numerous
times, no shift in the interference pattern that could be attributed to
the aether wind was detected. They conducted the experiment at
different times of the year and at different locations, but they still
produced a null result.
The experiment was significant because it changed the direction of
scientific thinking on the model of light. Many scientists attempted
to explain the null result by changing the aether model, such as
introducing the aether ‘drag’. And whilst it did not disprove the
existence of the aether, it led more scientists to be more willing to
accept Einstein’s rejection of the aether model.
The result of the Michelson-Morley experiment was that no shift in
interference pattern was detected within error when the apparatus
was rotated through various angles, or the time of year it was taken.
Whilst the null result did not entirely disprove the aether model of
light, it did show that there was no evidence for the aether model of
light, and led to scientists to reconsider whether the aether model
was valid.
I obtained information on the Michelson-Morley experiment from
the Jacaranda Physics textbook, and from the University of Virginia
website.
The consequence of the null result from the Michelson-Morley
experiment was that it split scientific thinking on the nature of light
waves. Some scientists still maintained the aether model, and
believed that the model just needed improvement, as the aether
model was consistent with the successful wave model at the time.
Other scientists however believed that an alternative to the aether
model was needed, as there was little evidence to support the
Ian Wilkinson
Outline the nature of inertial
frames of reference
Discuss the principle of
relativity
Analyse and interpret some
of Einstein’s thought
experiments involving
mirrors and trains and
discuss the relationship
between thought and reality
predictions of the aether model.
Einstein had been proposing an alternate model of electromagnetic
radiation as a consequence of Maxwell’s equations and study into
EMR. When Einstein proposed his special theory of relativity, he not
only provided a competing theory to the aether model, he also
challenged the Newtonian mechanics concept of an absolute frame
of reference. Whilst scientists had initially been reluctant to accept
Einstein’s model of electromagnetic radiation, the null result from
the Michelson-Morley experiment aided scientists to become more
willing to accept Einstein’s theory.
A frame of reference is anything with respect to which we describe
motion and take measurements. Frames of reference can be classed
into two groups: inertial and non-inertial frames of reference. An
inertial frame of reference is one which is not accelerating, i.e. it is
at rest or moving with constant velocity. Newton’s laws apply in an
inertial frame of reference, but not in a non-inertial frame. In
addition, Einstein’s special theory of relativity only applies to the
special case of inertial reference frames; the general theory of
relativity applies to non-inertial frames.
Note that under special relativity, the Earth is a non-inertial
reference frame due to the presence of gravity and Earth’s rotation.
In calculations however, Earth is often approximated as an inertial
frame.
The principle of relativity states that the laws of physics must be in
the same form in all inertial frames of reference. This means that no
inertial reference frame is truer than another, i.e. there is no
absolute frame of reference. Hence if one event is observed from
two inertial frames, both their observations are correct within their
frame.
It also means that there is no experiment that can be conducted
inside an inertial frame to determine its state of motion (i.e. its
velocity). The only way to determine velocity is to compare it to
another frame of reference, and hence all motion is relative. For
example, if you are sitting on a non-accelerating train, it is
impossible to determine if you are moving or are stationary unless
you look out the window, from which you can determine the relative
motion of the train.
One of the problems with the aether model was that it violated the
principle of relativity. The speed of light within the frame would
depend on its absolute velocity under the aether model, and thus a
person would be able to determine the speed of the frame. This was
one of the dilemmas for Einstein, and one aspect of his special
theory of relativity.
When Einstein was forming his theories on light and relativity, many
of his postulates stemmed not from physical observations, but from
thought experiments. One of these thought experiments involves a
person travelling at the speed of light and looking at their reflection
in a mirror.
Ian Wilkinson
Describe the significance of
Einstein’s assumption of the
constancy of the speed of
light
Identify that if c is constant
then space and time
become relative
Einstein’s question was whether the person would be able to see
their own reflection. Under the aether model, light would travel at
the same speed as the train and would never reach the mirror;
hence the person would see no reflection. But this would violate the
principle of relativity, as then it would be possible to detect the
motion of the train within the inertial frame.
If the principle of relativity held, the person would be able to see
their reflection, and hence the light in the frame would be travelling
at the normal speed of light. But under Galilean relativity, an
observer at rest outside the train would see light travelling at twice
the speed of light.
Einstein believed that this would not occur, and instead both people
would see light travel at the speed of light (3x108ms-1). Thus he
postulated that the speed of light is constant in all frames of
reference.
This postulate was based on logical thought, as the technological
limitations of the time meant that Einstein had no way to physically
measure his postulates. His thought experiments however allowed
him to analyse and demonstrate his theory of relativity, even though
they could not be tested in reality. From these thought experiments,
Einstein was able to make deductions based on logic and fact to
develop new theories, many of which have been proven physically
correct since. Thus thought allows us to conduct hypothetical
experiments using logic to gain a deeper scientific understanding,
even if such experiments cannot be easily reproduced in reality.
One of the postulates of Einstein’s special theory of relativity is that
the speed of light c (3x108 ms-1) is constant in all frames. But by
considering the equation speed = distance/time, and applying it the
thought experiment above, under Newtonian physics the observer
would see light travel twice the distance in the same time, and
hence have a velocity at twice the normal speed of light.
For Einstein’s assumption of the constancy of the speed of light to
be true, the length and time measured by each person must be
different. Einstein thus deduced time and length are not absolute
values, but relative depending on the frame of reference. This also
supports the idea that there is no absolute frame of reference.
Under Newtonian mechanics, space and time were absolute, and
whilst motion was considered relative. But if we assume that the
speed of light is constant, space and time must also be relative
values too, leading to the concept of the space-time continuum. This
means that all events in the universe must not only be defined by
space, but also by time (i.e. in four dimensions). Such a definition
Ian Wilkinson
Discuss the concept that
length standards are defined
in terms of time in contrast
to the original metre
standard
Explain qualitatively and
quantitatively the
consequence of special
relativity in relation to:
 the relativity of
simultaneity
 the equivalence
between mass and
energy
 length contraction
 time dilation
 mass dilation
allows an event to be fully defined in a frame of reference, and
explains why both observers in Einstein’s thought experiment both
measure the speed of light as 3x108ms-1.
The metre was first defined in 1793 by the French government as
the one ten-millionth (10-7) of the distance between the equator and
the north pole, passing through Paris. Three platinum standards, and
several iron copies were created, and this was considered the
standard metre.
This current definition of the metre was adopted in 1983 as the
distance that light travels in 1/299 792 458 of a second (a second is
defined as 9 129 642 770 oscillations of a Cs-133 atom). The need for
this revision was because the initial definition of the metre was
defined under the Newtonian assumption that space and time were
absolute. But under special relativity, space and time are both
relative, and so the current length standard takes the constancy of
the speed of light into consideration.
The relativity of simultaneity
The relativity of time impacts on what we consider to be
simultaneous events. For two events to be simultaneous, they must
occur at the same time. But as time is relative, two events may be
seen to occur at the same time in one frame, but at different times
in a different relativistic frame, and hence meaning that simultaneity
is also relative.
One way to observe this concept is with another thought
experiment. Consider a train travelling near the speed of light with a
lamp in the centre of the carriage, and a front and back door.
The doors on the train are light-operated, so when the light from the
lamp reaches the closed doors, they will open.
In the frame of reference of the train, the distance to each door
from the lamp is equal. Thus when the lamp is turned on, the doors
will open at the same time, and will be a simultaneous event.
A different situation will occur for a stationary observer outside
however. Whilst the observer sees the light travelling at the same
speed (c), the distance it travels is different due to the relativistic
motion of the train. Hence the observer would see the two events of
the back and front door opening as distinct in time, and would not
Ian Wilkinson
be simultaneous. Both of these observations are correct, as space
and time are relative, and there is no absolute frame of reference.
The equivalence of mass and energy
Einstein proposed in his special theory of relativity that energy and
mass were equivalent, and that energy could be could be converted
to mass and vice versa. Einstein reached this conclusion by
considering the conservation of momentum on a relativistic scale, as
time dilation would result in momentum not being conserved unless
mass could be converted to energy. The energy-mass equivalence
can also be seen in nuclear fusion reactions in stars, where the mass
of the fuel (e.g. hydrogen) is converted to energy in the process of
fusion. Energy and mass are equivalent by a factor of the speed of
light (c) squared, leading to the equation:
Length contraction
As previously mentioned, space and time are relative quantities, and
depend on the relative velocities of different objects. For space,
length of an object contracts as measured from an external frame as
its relative velocity increases. Quantitatively:
where:
lv = the length of an object as measured from an external frame (will
always be less than proper length)
l0 = proper length = the length of an object as measured in its rest
frame (i.e. the frame of the object)
v = the relative velocity of the object to the external frame
c = 3x108ms-1 = speed of light in a vacuum
NOTE: Length only contracts in the direction of relative motion. The
length of an object perpendicular to motion does not contract.
Time dilation
If the length of an object contracts at relativistic speeds, the time
measured in an external frame must dilate (i.e. take longer) in an
external frame in order to maintain the constancy of the speed of
light. Hence as an object reaches higher speeds, the time measured
from an external dilates. Quantitatively:
where:
tv = time taken for an event to occur as measured from an external
frame
t0 = proper time = time taken for an event to occur as measured
from the rest frame of the object
v = the relative velocity of the object to the external frame
c = 3x108ms-1 = speed of light in a vacuum
Ian Wilkinson
Mass dilation
In addition to length contraction and time dilation, the mass of an
object dilates as it approaches relativistic speeds. Quantitatively:
where:
mv = the mass of an object as measured from an external frame
m0 = rest mass = the mass of an object as measured in its rest frame
v = relative velocity of the object to the external frame
c = 3x108ms-1 = speed of light in a vacuum.
Solve problems and analyse
information using:
Consider in the above equation as v tends to c (i.e. the object
approaches the speed of light). The bottom of the equation limits to
zero, and so the relativistic mass approaches infinity. Thus it is
impossible for an object with mass to reach the speed of light, as it
would require infinite energy to do so. As can be seen, some of the
energy that goes into accelerating an object to increase its kinetic
energy is in fact converted to mass.
Remember that length only contracts in the direction of motion.
Also, remember that the length of an object contracts at relativistic
speeds, whilst time and mass dilate. Take care to note what the rest
frame of an object is and what the external frame is.
Ian Wilkinson
Discuss the implications of
mass increase, time dilation
and length contraction for
space travel
Analyse information to
discuss the relationship
between theory and the
evidence supporting it, using
Einstein’s predictions based
on relativity that were made
One significant implication of special relativity is to relativistic space
travel. Whilst such space travel is not practically possible at the
moment, its implications mean that such space travel would be
subject to very different circumstances than have been currently
experienced.
Mass increase
As a spacecraft accelerates to relativistic speeds, much of the energy
supplied by the fuel converts to mass, increasing the mass of the
spacecraft. As the mass of the spacecraft increases, more force is
required to maintain a constant acceleration to reach relativistic
speeds, and thus more work needs to be done on the spacecraft.
Hence mass dilation means that it is also difficult to attain relativistic
speeds, since more energy is required to accelerate the spacecraft at
higher speeds. It would also be more costly to reach such speeds, as
more fuel would be required.
Another consequence of mass dilation is that the speed of light can
never be achieved, as the mass of an object tends to infinity. In
terms of the size of the universe, the speed of light is relatively
small, and thus reaching even the closest stars would take at a
minimum several years from Earth’s frame.
For example, the closest star to Earth is Proxima Centauri, which is
4.3 light years away. As an object cannot travel faster than the
speed of light, it would take at least 4.3 years in Earth’s frame to
reach the star, and then at least 4.3 years to return. To reach the
centre of the Milky Way, it would take 265 million years.
Time dilation
Time dilation causes time to be slower on board a spacecraft
travelling at relativistic speeds. Time dilation means that it would be
possible to achieve interstellar space travel within an astronaut’s
lifetime, despite the longer time taken in Earth’s frame.
For example, if a spacecraft where to travel to Alpha Centauri at
relativistic speeds, it would take less than 4.3 years in the
astronaut’s frame of reference.
Length contraction
Length contraction has the same implication on space travel as time
dilation. From the spacecraft’s frame, the distance they are covering
to the star is less as space is moving relative to the spacecraft, whilst
time appears to be normal. Thus the spacecraft appears to travel
less distance, and hence why it takes less time from the spacecraft’s
frame. This again shows that space and time are relative, as time
appears as normal on the spacecraft, even though it is slower in
Earth’s frame.
A successful scientific theory should be a successful explanation for a
scientific idea or concept that can be demonstrated in practice, and
be used to predict observations. A scientific theory should also be
consistent with other accepted scientific theories and laws. Whilst
most scientific theories are based on practical observations, it is not
necessary for a successful theory to have practical evidence if it is
Ian Wilkinson
many years before evidence
was available to support it
Perform an investigation to
help distinguish between
non-inertial and inertial
frames of reference
not possible to obtain it. As long as the theory is a logical
explanation for a scientific concept, and is consistent with other
accepted theories, it can be considered a valid scientific theory,
which can be confirmed later by evidence.
Einstein’s special theory of relativity is one example a theory made
without physical evidence. When Einstein proposed his theory in
1905, he did so without practical evidence, as there was no
technology at the time able to prove his theories. It was not until
several decades later that some of his theories were able to be
proven, and even modern technology is incapable of testing many
aspects of relativity. His theory has been successful however, as it
provided a logical explanation to relativity, and was consistent with
other theories at the time.
There is however scientific evidence of special relativity that was
discovered in the latter half of the 20th century, many years after
Einstein first proposed his theory. The evidence includes atomic
clock analysis and atmospheric mesons.
Atomic clocks
Atomic clocks that are accurate enough to measure time dilation at
relatively small speeds have only been developed in the past few
decades. The experiment involved calibrating two atomic clocks to
the same time, and then placing one onto a jet plane. The plane flew
around the world at high speed, whilst the other was stationary on
Earth. When the other atomic clock returned, it was found that the
one on the plane had run slightly slower, and hence time had dilated
due to its relative velocity.
Mesons
Another piece of evidence for time dilation is atmospheric mesons,
which are particles produced in the atmosphere by incoming cosmic
rays. In the laboratory, mesons only have a lifetime of 2.2μs, but
when they are travelling to Earth at 0.996c, it would take them 16μs
to reach Earth’s surface, where they have been detected. Thus in
their rest frame, mesons have a lifetime of 2.2μs, but their
relativistic speed causes time to dilate, and so is measured as 16μs,
and is thus evidence for time dilation.
As parts of Einstein’s theory of relativity have been proven many
years after they were first proposed, we can see that practical
evidence is not necessary for a successful scientific theory. Many
modern scientific theories do not have evidence in reality, but are
still accepted
 Refer to practical 3.2.4 l)
METHOD
 An accelerometer was attached to the back of a dynamics
trolley, and the position of the liquid in the accelerometer
was measured at rest. The accelerometer was then pulled at
various accelerations and at constant velocity, and the
resulting shape of the accelerometer was recorded.
 The following set up can also be used
Ian Wilkinson









DRAW DIAGRAM IF POSSIBLE
RESULTS
The accelerometer was flat at rest and at constant velocity
The liquid was sloped downwards, and more liquid was
towards the back of the accelerometer as it accelerated in
the positive direction
The liquid was sloped upwards, and more liquid was towards
the front of the accelerometer as it accelerated in the
negative direction
Refer to the practical report for the diagrams of the various
shapes of the accelerometer.
RELIABILITY/ACCURACY/VALIDITY
The experiment was repeated several times, and a general
image was obtained
The experiment was able to distinguish between inertial and
non-inertial frames, and hence tested the aim
The results corroborated with expected results
The accuracy/validity of the experiment could have been
improved by using sensors and data loggers to detect the
shape of the accelerometer.