9.2 Space (HSC Physics)
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Transcript of 9.2 Space (HSC Physics)
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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 to a gravitational field
Weight is a force acted on a mass due to a gravitational field Unlike mass, weight is not a constant, rather it changes due to the strength of the gravitational
field The formula is given as:
W is the weight measured in newtons (N) m is the mass measured in kilograms (kg) g is the acceleration due to gravity measured in metres per second per second ( )
Explain that a change in gravitational potential energy is related to work done
Gravitational Potential Energy (GPE) is the energy of the mass due to its position within a gravitational field
When work is done to an object in a gravitational field, the energy stored is converted into kinetic energy
When the object is moved away from its gravitational field, the energy stored within the object is GPE
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
Gravitational Potential Energy (GPE) is the work done to move an object from an infinite distance to some point in the gravitational field
As the object moves away from Earth, potential energy increases, as gravity pulls the object back to Earth, the potential energy converts into kinetic energy
Gravitational Potential Energy is zero at infinity, therefore, potential energy is negative
G is the gravitational constant ( ) is the mass of the planet measured in kilograms (kg)
is the mass of the object measured in kilograms (kg) is the distance separating the masses measured in metres (m)
Perform an investigation and gather information to determine a value for acceleration due to gravity
using a pendulum motion and identify reason for possible variations from the value
Aim: To determine the acceleration due to gravity on Earth, using the motion of the pendulum Equipment:
Retort Stand
Bosshead and clamp
Stopwatch
1 metre of string
50g pendulum bob
Metre Ruler Method: 1. Setup the equipment where the string is connected to the retort stand via the bosshead and clamp and the
mass is connected to one end of the string 2. Calculate the length from one end to the mass and record 3. Set the pendulum to a certain angle and, using a stopwatch, time how long it takes to complete 10 cycles 4. Repeat step 2/3, 5 times, shortening the string by 5cm each time
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Gather secondary information to predict the value of acceleration due to gravity on other planets
A gravitational field is a ‘region of influence’ where a mass experiences a force due to the presence of another mass (usually a larger mass)
Acceleration due to gravity is given by the following equation
Results:
Results are tabulated
Graphing against l, says that as length increases, the period of oscillation will increase as well
The period of the pendulum is calculated using √
and by readjusting the equation, g can be found
Discussion: Reasons for various values of g include:
Experimental errors such as equipment and human reaction
The value of acceleration due to gravity is commonly accepted as , however it can vary due to various factors: The Earth’s lithosphere varies in structure, density and thickness. This can influence the value of g Earth is not a perfect sphere thus the Earth’s globe is flatter at the poles, meaning the distance of the
surface from the centre is shorter which increases the value of g At the equator, the spinning effect due to Earth’s rotational motion, is the greatest, which lowers the
value of g The value of g reduces at increasing altitude above the Earth’s surface
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2. Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable 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 Any object moving through the air is undergoing projectile motion. The trajectory of the
projectile is always in a shape of a parabola Projectile motion is analysed in terms of two separate components – horizontal and vertical The horizontal component is always constant while the vertical component is undergoing
acceleration The velocity of a projectile at any point is the vector sum of horizontal and vertical velocity at
that point Describe Galileo’s analysis of projectile motion
Galileo concluded that: All projectile moved in a parabolic motion All projectiles dropped at the same height will land at the same time, regardless of their mass Horizontal and vertical components are always separate
Explain the concept of escape velocity in terms of the:
Gravitational Constant: Velocity depends on the gravitational constant but is independent of the mass trying to
escape Mass and Radius of the Planet
According to this equation: √
As mass increases, the escape velocity will also increase. Mass is proportional to velocity As radius increases, the escape velocity will decrease. Radius is inverse proportional to
velocity Outline Newton’s concept of escape velocity
Newton proposed that: An object could be put into orbit when launch horizontally on a cliff.
Given enough speed, the curvature of the projectile’s trajectory would match the curvature of the Earth, thus the object will go into orbit
On Earth, the escape velocity is 11.2km/s Identify why the term ‘g forces’ is used to explain the forces acting on an astronaut during launch
A body is not affected by velocity, but by acceleration The ‘g force’ on an object is a term used to describe the force experienced due to acceleration
expressed as the object’s apparent and true weight
People on orbit is weightless, this is because their apparent weight (g + a) is zero. A person can only tolerate up to 3 to 5g’s of force, above this will cause organ displacement and blackout
When the astronaut is lying down, they can tolerate up to 10g’s of force. They have oxygen supply and contour seats to reduce the effect of high g-forces
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Discuss the effect of the Earth’s orbital motion and its rotational motion on the launch of a rocket When a rocket is launched, it is launched towards the east as this is the Earth’s orbital rotation. Rocket are launched this way, so that they can take advantage of the Earth’s rotation and gain an
additional velocity of 1700km/h, which is achieved at the equator. Similarly, the launch can also take advantage of the Earth’s revolution around the sun by
launching the rocket at a specific time of the year where the direction of the Earth’s rotational direction correspond to the desired direction
This will add 107000km/h to the rocket’s velocity
Analyse the changing acceleration of a rocket during launch in terms of the: Law of Conservation of Momentum
As fuel is consumed, the mass of the rocket will decrease However, thrust (force from the engine) remains the same, the acceleration is begin to
increase, propelling the rocket upwards Momentum is conserved, as the momentum of the exhaust gas downwards is equal but
opposite impulse on the rocket going upwards This is the thrust which provides an increasing acceleration
Forces experienced by astronauts The astronaut’s body is exerting a downward force on the floor, and the floor will exert a
reaction force
The equation of the acceleration of the rocket is given by:
As acceleration is increasing, g-force will also increase at take-off. Analyse the forces involved in uniform circular motion for a range of objects, including satellites
orbiting the Earth An object moving in a circular motion will have constant speed, but it will undergo acceleration
that is directed towards the centre of the circle
By equating Newton’s second law and centripetal acceleration will gives:
Circular motion is the result from centripetal force. The centripetal force on the satellites is provided by the gravitational field of the Earth
Compare qualitatively Low Earth and Geo-stationary Orbits
Low Earth Orbits: These are satellites with an altitude of less than 1500km, but greater than 100km (to avoid
atmospheric drag). It is commonly used for fast communication and for satellite imagery. These are in polar orbits, so they span the Earth as it rotates
Geo-stationary Orbits These are satellites with a period of 24hrs, so their altitude is around 35800km and is
positioned above the equator. Therefore, geo-stationary satellites are useful as weather satellites
Define the term orbital velocity and 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 Orbital velocity is the velocity needed for a body to orbit around in one period Orbital velocity is found by equating centripetal force and gravitational force
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√
Then by equating the equation with average velocity
√
This equation is known as the Kepler’s Law of Periods. From this equation, orbital velocity depends on the radius and the period of the orbit but is independent on mass.
Account for the orbital decay of satellites in Low Earth Orbit
Satellites in low earth orbits are subjected to frictional forces. This results in a loss of energy, hence the satellite will drop down to a lower altitude
This is known as orbital decay. This process will speed up with time, and eventually will spiral down to Earth’s atmosphere, where it is burnt away
Discuss issues associated with safe re-entry into the Earth’s atmosphere and landing on the Earth’s
surface When spacecraft attempt for a safe re-entry into the Earth’s atmosphere, several issues must be
taken into account: Heating:
As the spacecraft re-enters, it will decelerate via friction, the kinetic and potential energy is converted into heat energy.
This is minimise through the existence of heat-resistance capsules G-Forces:
Re-entry requires large deceleration, therefore large g-forces. This will cause harm to the lives in the spacecraft.
G-forces should be limited to 3 to 8g’s. In order to achieve this, the spacecraft makes s-bend so that it descent longer.
Ionisation Blackout:
Heat around the space craft can cause particles to ionise as they collide with the spacecraft, therefore blocking the communication signal. This lasts around 16 mins.
Other than re-entry, landing on the Earth’s surface may cause a problem too. When the space craft is planning to land, it will release its parachutes to slow the spacecraft
down. The space craft can also land on water to minimise the impact
Identify that there is an optimum angle for safe re-entry for a manned spacecraft into the Earth’s
atmosphere and the consequences of failing to achieve this angle
Spacecraft has a re-entry window of 5.2 to 7.2. If it descent too shallow, the spacecraft will rebound off the atmosphere. This is due to
compression force beneath it If it descent too steeply, the spacecraft will burn up due to extensive heat built from g-forces
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Solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components using these equations Equations for horizontal components:
Equations for vertical components:
Solving Projectile: Assume no air resistance Time to maximum height is equal to time down from maximum height At maximum height, vertical velocity is zero Going down is negative
Steps for solving projectile: Draw a diagram Find components for velocity Write down known variables Find an equation to find unknown variable Round off answer
Identify data sources, gather, analyse and present information on the contribution of Goddard to the
development of space exploration Doctor Robert Hutchings Goddard (1882-1945) is considered as the father of modern rocketry In 1914, he received two US patents for the idea of fuel rocket and multistage rocket Afterwards, he made systematic studies and experiments about propulsion provided by various
gunpowder By 1926, he had constructed and tested the first rocket using liquid and was proven to be a
success When building the first liquid rocket, he has encountered many problems, these include:
Fuel valving for throttle, start and stop; fuel injecting, engine cooling and ignition Goddard has also developed a technique which is still used in modern rocketry, that is, having a
liquid oxygen to cool off the combustion chamber on its way from the fuel tank In 1929, he launched a rocket that carried a barometer, a camera and the first scientific payload Between 1930 to 1935, he launched rockets that attained speed of up to 885km/h
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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 A gravitational field is a field in which any masses within the field will experience a gravitational
force As the force of gravity will act on any object that has mass within Earth, it can be said that a
gravitational field is surrounding Planet Earth The gravitational field is acting towards the centre of Earth, therefore the force of gravity is
pulling all objects towards the centre of Earth As there is a gravitational field around Earth and Moon, directing towards the centre, there is a
null point where there is no gravity. This is done through the gravitational field line, the closer it is, the greater the force
Define Newton’s Law of Universal Gravitation:
Newton’s Law of Universal Gravitation states that every mass in the universe is attracted to every other mass in the universe by the force of gravitation
The force of gravitation is proportion to the product of the two masses and is inverse proportion to the square the distance between the two objects (from the centre)
Mathematically, the force is represented by this equation:
Discuss the importance of Newton’s Law of Universal Gravitation in understanding and calculating
the motion of satellites Satellite motion is only possible through centripetal force between the satellite and the planet
which it is orbiting around The orbit is only made possible by the gravitational force between the satellite and the planet’s
gravitation field Therefore the Newton’s Law of Universal Gravitation plays an extremely important role in
determining the force between Earth and the satellites Orbital velocity is calculated by equating gravitational force and centripetal force
Identify that a slingshot effect can be provided by planets for space probes
The slingshot effect is to provide spacecraft with momentum without burning fuel As the spacecraft gets closer to Earth, the Earth’s gravitational field will pull the spacecraft
towards itself, this will accelerate the spacecraft in relative to the planet, as a result, it will change direction
As the spacecraft leaves the gravitational field of that planet, the spacecraft’s velocity will decrease if it travels in front of the planet. Velocity will increase when it travels behind the planet
Present information and use available evidence to discuss the factors affecting the strength of the
gravitational force The force of the field length depends on the mass of the object, and the distance from it If there is more than one objects in an area, the gravitational field strength depends on the
relative strength of both objects The mass of the object being drawn towards the object producing a field, does not affect
gravitational field strength
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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
During the nineteenth century, light was believed to be of wave form and goes through a medium
However, such medium was not found, so one was hypothesised, and it was known as The Luminiferous Aether
Properties and features of the Aether model includes: Fill all the space and is stationary in space Being perfectly transparent Permeate all matters Has low density Have great elasticity in order to propagate the light waves
Describe and evaluate the Michelson-Morley attempt to measure the velocity of the Earth through
the aether The Michelson-Morley experiment was first tested in 1887 and its aim was to test the existence
of Aether Wind The apparatus was designed to have one light ray being split into two, one travelling across the
aether wind and back and one travelling against the aether wind and back, then measure the speed of the two light rays
This returned a null result as both light rays travelled with the same speed, this proved that no motion of Earth relative to the aether was detected
Discuss the role of the Michelson-Morley experiments in making determinations about competing
theories The Michelson-Morley experiment was set out to measure the speed of Earth through the
aether, but it returned null result This null result could only mean the possibility of no aether and that the speed of light in a
vacuum is independent of the speed of the source and observer Twenty years later, Einstein proposed the theory of special relativity, saying that an aether
model is not needed. Since then, scientists made a choice between the aether model(was never proved true) or the
relativity model(later proved true) Outline the nature of inertial frames of reference
The inertial frame of reference is a frame of reference that travels at constant velocity or at rest No one will know whether the inertial frame of reference is moving or not, unless compared with
an object outside the inertial frame of reference Discuss the principle of relativity
The study of relativity begun during Galileo’s time: The Law of Mechanics are the same for a body at rest and a body moving with constant velocity
Soon, Newton proposed that: It is impossible to do any mechanical experiment within in inertial frame to show whether that frame is moving or at rest
Einstein made two assumption that formed the principle of relativity: The law of physics are the same for all inertial frame of reference The speed of light is constant
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Describe the significance of Einstein’s assumption of the constancy of the speed of light Einstein’s Theory of Special Relativity stated that the speed of light is constant and is
independent to anything else Einstein’s assumption of the speed of light explained the Michelson-Morley experiment, and has
proved that there is no such thing as an absolute frame of reference This has overturned the aether theory that stood for centuries Also Special Relativity has also proved that length and time are variables
Identify that if c is constant then space and time become relative
For c to be a constant, space and time must be relative This means that all variables (that is, length, mass and time) that was true must be changed in
order to allow c to be a constant Discuss the concept that length standards are defined in terms of time in contrast to the original
metre standard All measurement are relative to a frame of reference and is compared to a standard Before, 1 metre is defined as one ten millionth of the distance between the equator and the
North Pole along the meridian passing through Paris
1 metre is defined as light travelling at
of a second
According to Special Relativity, length is a relative as length will change when it travels at close to light speed, thus it was necessary for the definition of length to change
At that time, the speed of light was considered to be the only constant therefore, length was redefined in relative to light speed
Explain qualitatively and quantitatively the consequence of special relativity in relation to:
The Relativity of Simultaneity When one person in a frame of reference observed two events being simultaneous, another
person observing the same two events in a difference frame of reference may disagree This means, whether the two events are happening simultaneously depends on where you
are standing The Equivalence between Mass and Energy
When work is done on an object, energy becomes acceleration, as the object gets closer to the speed of light, some of the energy is converted into mass, therefore energy and mass are interchangeable, as mass can also be converted into energy
Length Contraction
It is said that as an object approaches light speed, the observer outside the frame of reference will see the object getting shorter as opposed the observer inside the frame of reference
√
Time Dilation It is said that as an object approaches light speed, the observer outside the frame of
reference will see time travelling slower, as opposed to the observer inside the frame of reference
√
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Mass Dilation It is said that as an object approaches light speed, the observer outside the frame of
reference will the mass of the object getting heavier, as opposed to the observer inside the frame of reference
√
Discuss the implications of mass increase, time dilation and length contraction for space travel
This has great implications on space travel, as it proves that time travel into the future is possible and that long distance can be theoretically travelled with little ageing of astronauts.
However, communication is made not possible with the spacecraft, as by the time the spacecraft returns to Earth, hundreds of years may have past
Mass dilation proved that getting the spacecraft to a certain speed is extremely difficult and expensive
Gather and Process information to interpret the results of the Michelson-Morley experiment
All model of the Michelson-Morley experiment will need to compare the speed of two identical object and one method is to race them
One of the object will move across the current, while the other will move against and along the current
When the comparison is done properly, the data collected will show that the object travelling across the current wins the race
The Michelson-Morley experiment is similar, but they are comparing to light rays. The aim was to detect the existence of the aether wind
However, it returned a null result, as the two light rays reached the starting point at the same time, so there were no clear results
Perform an investigation to help distinguish between non-inertial and inertial frame of reference
By using a marble and two trucks, we are able to distinguish whether it is a non-inertial or an inertial frame of reference
By placing a marble on top of truck 1, then push it, the marble will move, meaning it is a non-inertial frame of reference. This is because the truck is accelerating; therefore the object will experience a force. This does not obey Newton’s First law of motion
By placing a marble on top of truck 2, then push it, the marble will not move, meaning it is an inertial frame of reference. This is because the truck is travelling at constant speed (or at rest). This is obeying Newton’s First Law of Motion
Analyse and interpret some of Einstein’s thought experiments involving mirrors and trains and
discuss the relationship between thought and reality Einstein has used many thought experiment to support his theories due to technological
limitations of the time. One thought experiment performed by Einstein is that:
One person is holding a mirror in front of him, inside a train travelling at light speed. If he could see his reflection, then an observer outside the train would be seeing the train
travelling at twice the light speed, which is impossible If he could not see his reflection, he is able to conclude that the train is moving, which is
proven to be impossible Einstein concluded that the reflection can be seen but train is not travelling twice the light
speed, instead distance and time will change as speed = distance/time
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This though experiment was a major part of Einstein’s theory of relativity Analyse information to discuss the relationship between theory and evidence supporting it, using
Einstein’s prediction based on relativity that were made many years before evidence was available to support it Predictions was made after data was recorded, however during Einstein’s time, they do not have
the technology to prove his assumption on the theory of relativity Today, many evidence was made, these include:
Time dilation has been shown through atomic clock that was flowing around the world, that was lagged behind the stationary clock
Muons created in the upper hemisphere has longer lifespan when travelling to the surface at near light speed
Mass and time dilation can be seen in particle accelerators can be seen in atomic weapons and nuclear reactor