Hello again everyone! Time for another HSC Physics Guide! This one is going to cover a few dot points, all concerning the physics of rocket launches. This means all those associated dot points, and I'll mix in gravity as well. Like the other guides, this guide will aim to summarise all the related content and address a few common exam style questions. Essentially, the guides will form something you can read to revise the whole course in a couple of hours. Covering this amount of content means that I can't go into as much detail as you may need. While I'll try to slow down to cover the hard stuff, you may have questions. In that case:
Remember to register for an account and ask any questions you have below! Let's begin. I'll cover gravity first!
Gravity is one of the four fundamental forces, caused by the mass of objects. Gravitational fields surround all masses, and are theoretically infinite in size. They decrease rapidly in strength with distance from the object (inverse square law), and are stronger for greater masses. Any mass in a gravitational field will experience an attractive force, according to Newton's Law of Universal Gravitation
.
Gravitational potential energy (GPE) is the energy possessed by an object due to its position in a gravitational field. In HSC Physics, we take the zero point for GPE (when the GPE of an object is zero) as when the distance from the origin from the field is infinite. As the object moves closer, it loses GPE, and so the value becomes negative. Thus, GPE is a negative quantity. See the diagram below if that is a little unclear. The formula for GPE is
.
Questions on gravity alone are unusual, but questions on GPE are quite common.
Example One: What is the gravitational potential energy of the moon with respect to the earth? The mass of the moon is
kilograms and the mass of the earth is
kilograms. The earth moon distance is
kilometres.
This is simply a formula question. Now, this question doesn't require it, but a lot of questions have an extra trick;
remember the distance is taken from the centre of the earth. Add the radius of the earth to your distance if necessary (EG- if the question says altitude). Other tricks, ensure you convert kilometres to metres, and check your data sheets for seemingly missing quantities. Regardless, we substitute:
Next, the physics of rocket launches. You should understand (in a little more detail than I give here) the following:
- The idea of escape velocity. Newton envisaged this as firing a cannonball increasingly quickly, thus causing it to travel further. Eventually, it would travel all the way around the earth, and then eventually beyond. This velocity is called escape velocity , and is defined as
- The idea of G forces, used to define the reaction forces on an astronaut in terms of the force felt due to gravity on the earth's surface
- How the earth's rotational and orbital motion can be used to increase the velocity of a rocket, and the associated benefits for fuel economy. We can launch rockets to the east to gain the earth's rotational velocity (picture a catapult). Similar reasoning applies to the earths orbit around the sun.
- The slingshot effect, whereby a rockets velocity is increased due to interaction with the gravitational field of a planet or other astronomical body. Picture that scene in Ferris Bueller's Day Off, where Ferris grabs on to the cars while he is skateboarding. He speeds up, because he is being 'dragged' along.
- The ideal re-entry angle (5-7 degrees), and the consequences of failing to meet this angle. Too shallow, and the rocket will bounce back into space, since excessive kinetic energy remains. Too steep, and the rocket will overheat and disintegrate. There are also other re-entry issues, including ionisation blackout and heat, and shedding the adequate amount of energy to land
Any of these concepts can be asked in a describe/explain question, or where applicable, a mathematical question. Be sure to know enough to explain what is going on for each concept. The most common question asked, which I'll answer below, concerns a final concept: An Analysis of a Rocket Launch.
Example Two: Analyse the changing acceleration of a rocket during launch in terms of the Law of Conservation of Momentum and the forces experienced by astronauts
This is a direct syllabus dot point, and if this was asked in an exam, it would be worth a bare minimum of 6 marks. Likely 8. You would answer similar to this:
- The law of conservation of momentum states that the momentum within a system (eg- a rocket) must remain constant.
- Since the rocket is initially stationary, this means the momentum of the rocket system (rocket + fuel) must remain equal to zero.
- As the rocket is launched, the fuel is accelerated downwards as thrust, and thus has momentum downwards. Therefore, the rocket has momentum upwards (and equal in magnitude)
-
- Assuming constant thrust, the momentum of the fuel remains constant. However, the mass of the rocket decreases as fuel is burnt, so the velocity of the rocket must increase (since momentum must remain constant). Thus, the rocket accelerates upwards
- The force to accelerate the rocket upwards is provided by the reaction to the thrust force. We assume this force is constant. However, according to
, as fuel is burnt and mass decreases, acceleration increases. - This means that, as acceleration increases, the astronauts experience increasingly large G-forces throughout the initial stages of launch
- Assuming multi stage rockets are used, these G forces briefly drop to zero as the stages are jettisoned (since acceleration is zero at this time). This is essential, as prolonged exposure to large G forces can be fatal
Obviously this is a quite demanding question, and would likely not be so broad in the exam. But it does pop up in some form
a lot , so be ready. You should also be ready for the stranger questions, usually concerning your practical investigations, and/or your research into a
chosen rocket scientist . That last point is in over half the papers from the last few years, they like to punish the people who forget it
The final area which requires understanding is orbits. An orbit occurs when the object is travelling at a certain speed; not fast enough to escape a gravitational field, but fast enough to not be sucked in to the centre. In this course, we consider orbits as uniform circular motion, with the centripetal force provided by the gravitational force. By equating these two formulae, we can obtain many quantities. The orbital velocity formula is one of these:
We can also equate centripetal and gravitational force, and with some clever substitutions, derive Kepler's Law of Periods:
Mathematical questions concerning Kepler's Law of Periods are common, such as the one below:
Example Three: A space probe is placed in an orbit at an altitude of 188 km above Earth. Given Earth has a radius of 6380 km, calculate the period of this orbit.
Kepler's law of periods makes this an easy question, but be careful with your value for
!
Also note the use of
SI UNITS . Rearrange to get an answer of 88.11 minutes for T (we take the positive value).
There are other concepts to do with orbit which can be asked in describe/explain style questions. Be sure you are familiar with:
- Comparing low earth and geostationary orbits. Low earth orbits have a higher velocity and shorter period that geostationary ones (the closer an object to the centre of a field, the faster it must travel to remain in orbit)
- Accounting for orbital decay for satellites. Simply, it is caused by ozone particles, which impart a frictional force which decelerates the satellite, causing it to fall from its orbital path.
There is much less here than above, but I
guarantee that Kepler's Law will show up, and one of these other concepts is likely to pop up as well, perhaps as a quick 2 mark question. Further, few questions in these sections would require any diagrams, so this makes things a little easier to prepare for (getting full marks for diagrams is tricky). However, be sure to draw them anyway if it helps your explanations, and the marker will love it.
That's about it for gravity and rocket launches! Hopefully this guide proves useful. Read over it, see if the summaries jog memories. If things are a bit iffy, do some practice questions, and of course, feel free to
register for an account and ask any questions you have in the comments. It is difficult to cover everything for Physics in a guide which doesn't become excessively long, so ask away! I'm happy to help.
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