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KICKSTART PHYSICS SPACE
1. SPEED AND ESCAPE VELOCITY
2. PROJECTILE MOTION
3. ACCELERATION AND G-FORCES
4. ‘C’ AND RELATIVITY
5. EINSTEIN
Kickstart would like to acknowledge and pay respect to the traditional owners of the land – the Gadigal people of the Eora Nation. It is upon their ancestral lands that the University of Sydney is built. As we share our knowledge, teaching, learning, and research practices within this University may we also pay respect to the knowledge embedded forever within the Aboriginal Custodianship of Country.
For more information head to http://sydney.edu.au/science/outreach/high-school/kickstart/index.shtml
The University of Sydney School of Physics Space
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Get to Know the Inner Space Risk Analysis Conduct a risk analysis by filling out the following table. List 3 risks to do with this investigation in the 2nd year lab. Also, list 3 risks in an industry where physics is used.
− What are the consequences of those risks? Use the risk matrix below to make your judgment. − What precautions would you take to stop those risks from coming about? − What steps would you take to mitigate those risks?
Risk Consequence Precaution/Mitigation
Kickstart
Electricity Radiation Equipment Water LN2
Electrocution (High) Radiation Sickness (High) Tripping and Injury (Medium) Slipping and Injury (Medium) Frostbite (High)
Safety Switch Low Dose/Shielding Don’t Touch No Food/Drink in Lab Personal Protective Equipment
Physics Industry
Industry – Finance/Tech, Games, Solar Power, Medical Physics, Radiology Research – University, Academia Public Service – CSIRO, DSTO, NMI, Questacon, Government, Teachers
See above, jobs might require more specific considerations
See above, jobs will require more specific considerations
What sort of careers do you think you could get if you studied this topic at the University of Sydney?
The University of Sydney School of Physics Space
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Speed & Escape Velocity There are a number of different types of orbits in orbital systems. Model each of the following orbits with the gravity trampoline, and identify what object might have that orbit.
Type of Orbit How to Model the Orbit Examples of Objects with the Orbit
Highly Eccentric Orbit Give the object a push, but not strong enough to dislodge it from making a
complete orbit Halley’s Comet
Hyperbolic Orbit Give the object a strong push to prevent it from continuing orbit Asteroid
Orbital Decay Start the orbit with a slight push so that it decays towards the centre International Space Station, LEO
After modeling Low Earth and Geostationary Orbits on the gravity trampoline, compare the two by listing their similarities and differences.
Similarities Differences
- Earth orbits - Used for communications - -
- Remote sensing - Sees different parts of the Earth - Different orbital speeds - Different purposes
We can use energy and force to determine the velocity of objects as they leave the planet and into orbit.
Escape Velocity
The kinetic energy of an object with mass m is given by:
𝐸! =12𝑚𝑣!
The gravitational potential energy of an object with mass m in the gravitational field of an object with mass M is given by:
𝐸! = −𝐺𝑚𝑀𝑟
Derive a formula for the escape velocity:
𝐸!! + 𝐸!! = 𝐸!! + 𝐸!! ⟹ since final kinetic and potential energies are 0
∴ 12𝑚𝑣! −
𝐺𝑚𝑀𝑟
= 0
12𝑚𝑣! =
𝐺𝑚𝑀𝑟
⟹ 𝑣! =2𝐺𝑀𝑟
∴ 𝑣 = !2𝐺𝑀𝑟
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Orbital Velocity
What do these formulae say about the concepts of escape and orbital velocity?
Kepler’s Laws Kepler’s three laws of planetary motion describe the motion of orbiting bodies. They are:
1. The orbit of every planet is an ellipse with the Sun at one of the two foci.
2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time:
3. 𝑇! ∝ 𝑅! Use the gravity trampoline to help demonstrate each of Kepler’s three laws of planetary motion. How would you derive Kepler’s 3rd Law from the orbital velocity of an object in orbit?
The equation for the force acting on an object with mass m and velocity v in a circular path of radius r is given by: (the centripetal force)
𝐹 =𝑚𝑣!
𝑟
The equation for the gravitational force between two objects with masses m1 and m2 is given by:
𝐹 =𝐺𝑚!𝑚!
𝑟!
Derive a formula for the orbital velocity: Since gravitational and centripetal force are pointed in the same direction, they are equal:
𝑚𝑣!
𝑟=𝐺𝑚𝑀𝑟!
𝑣! =𝐺𝑀𝑟
∴ 𝑣 = !𝐺𝑀𝑟
For either orbital velocity or escape velocity, we do not need to consider the mass of the object we are concerned with; it is not a variable!
velocity = distancetime
=2𝜋𝑟𝑇
Substituting into our orbital velocity equation, 2𝜋𝑟 𝑇
= !𝐺𝑀𝑟⟹
4𝜋!𝑟!
𝑇!=𝐺𝑀𝑟
Simplication and rearrangement gives us:𝑟!
𝑇!=𝐺𝑀4𝜋!
-‐ that is, Kepler's Third Law!
The University of Sydney School of Physics Space
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Projectile Motion
Monkey and the Hunter
Predict Observe Explain
Above: Students make predictions Miss
In projectile motion, gravity is acting on both of the object’s
vertical velocities, but not on it’s horizontal motion.
Below: Students make predictions Miss
In projectile motion, gravity is acting on both of the object’s
vertical velocities, but not on it’s horizontal motion.
At: Students make predictions Hit
In projectile motion, gravity is acting on both of the object’s
vertical velocities, but not on it’s horizontal motion.
This process of Predict, Observe, Explain, Apply was used by David Unaipon (1872-1967), known as “Australia’s Leonardo Da Vinci”. He was of the Ngarrindjeri people of South Australia and was an Aboriginal inventor and author who made significant contributions to science. David invented many devices, including a sheep shearer that is still in use today. He never received any recognition or monetary benefit from any of his innovative inventions.
The University of Sydney School of Physics Space
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Acceleration & G-Forces
Acceleration Describe how you moved for each of the graphs that you matched:
Where would you experience the highest and lowest g-force? Highest = where acceleration is greatest and acting against gravity, lowest = where acceleration is greatest and acting with gravity.
Position vs Time Velocity vs Time Acceleration vs Time
Features
Straight lines correspond to constant velocity; there can be positive and negative
directions.
Horizontal lines correspond to constant acceleration.
Positive and negative values for acceleration are
observed.
Characteristics Move forward and back. Move forward and back. Move forward and back.
The University of Sydney School of Physics Space
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‘C’ & Relativity
The Michelson-Morley Interferometer Observe the interference pattern as you change the path length for one of the light beams by carefully adjusting the position of the moveable mirror. What happens to the pattern? Sketch the interference pattern you see through the view piece:
The University of Sydney School of Physics Space
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A Slower Speed of Light Relativity is a very difficult thing to study. This is why we use models and visualisations. With the game “A Slower Speed of Light” you can qualitatively describe some effects of relativity. However, with all models, there are limitations and inaccuracies. Sometimes, the use of a model can actually have a negative effect on the intended purpose of the model. In the following table, list some limitations and inaccuracies to this model:
Advantages Limitations
Can visualise effects of speed of light travel Easy to understand demo of effects Can get some quantitative and qualitative data
Not the full story Much more complicated than presented Inaccuracies and misconceptions can arise from the model
The University of Sydney School of Physics Space
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Einstein An hour sitting with a pretty girl on a park bench passes like a minute, but a minute sitting on a hot stove seems like an hour. - Albert Einstein Using the equation for time dilation:
𝑡! =𝑡
1 − 𝑣!
𝑐!
fill in the table for the effect of time dilation in days and years with respect to the percentage of the speed of light.
Speed (% of c) Days Years
0 1 0.003
50 1.15 0.003
90 2.29 0.006
99.5 31.6 0.02
99.999999999 223606 612
What is the time dilation experienced by astronauts on the International Space Station from the reference frame of people on the surface of the Earth? The orbital speed of the ISS is 7.66 kms-1.
𝑡! =1
!1 − 7666.67!
𝑐!
= 1.01 days = 0.003 years
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Inertial Frames of Reference vs Non-Inertial Frames of Reference Inertial Frame of Reference: The frame of reference where the Newtownian concept of inertia holds. Non-Inertial Frame of Reference: The frame of reference where the Newtownian concept of inertia does not hold. How can we distinguish between the two? The easiest way to illustrate this difference is with rotating reference frames. Why is that? Use the graph paper to illustrate the difference between inertial and non-inertial reference frames:
Inertial Frame
Non-Inertial Frame
