HSC Physics Marathon 2013-2015 Archive (1 Viewer)

[Kaido]

re: HSC Physics Marathon Archive

Actually, I'll give it a go (considering this is under exam conditions, can't ask anything) :V

So Newton is known for his laws of gravity (in this scenario anyway), which describes the gravitational attraction between bodies (esp larger bodies e.g. planets). From the question, the Apollo mission crew utilised their knowledge (or perhaps issac newton, idk) of the 'gravity-assist' effect (aka slingshot) to manoeuvre their spacecraft towards Earth's satellite (the moon). As the spacecraft approaches the moon's gravitational field (where gravity actually plays a considerable effect in altering the spacecraft's trajectory), the moon's gravitational field attracts the spacecraft towards it - hence also from Newton's 3rd law (conservation of momentum), the spacecraft 'steals' some of the moon's angular momentum - converting it to increase its own velocity relative to the moon (the moon loses a negligible amount of energy). Since the moon also orbits Earth (and the Sun if you will), the spacecraft's velocity also increases relative to Earth - giving it a significant speed boost (V(f)=V(space craft initial) + 2V (Moon's velocity)) and hence enabling it to reproach the Earth after it has 'swung' around the moon (without expending much fuel).

Edit: Added conservation of momentum

 

[Rhinoz8142]

re: HSC Physics Marathon Archive

No clue what the question is asking.
And how does the spacecraft survive after getting hit?

'We just put Isaac Newton in the driver’s seat’ - is this a metaphor for something?

Just think about it. Try to figure out the key words. " fly around the back of the Moon and then fire the rocket engine to take the craft out of lunar orbit and put it into an Earth-bound trajectory.

At the completion of the rocket engine burn, mission leader Jim Lovell was heard to say, ‘We just put Isaac Newton in the driver’s seat’."

I know how you feel, I got stuck in this question but I started to think on what they actually meant by "putting Isaac Newton in the driver seat".







Just think about it.


Well you answered it...so well done !

 

[Kaido]

re: HSC Physics Marathon Archive

Was that exactly what the question was looking for?

 

[InteGrand]

re: HSC Physics Marathon Archive

Was that exactly what the question was looking for?

Impossible to say without looking at the marking criteria.

Here's the criteria for 4 out of 4 (not very helpful): "• Presents a logical, coherent argument to support Jim Lovell’s statement, for the period after the rocket burn including correct, relevant description of Newton’s laws" (source: http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2005exams/pdf_doc/physics_er_05.pdf )

 

[Kaido]

re: HSC Physics Marathon Archive

Oh yeah, forgot about conservation of momentum, that's a big one.

 

[PhysicsMaths]

re: HSC Physics Marathon Archive

Here's my attempt:
Lovell's statement refers to Newton's laws of motion which are responsible for their return back to Earth. Newton's first law of inertia states that an object will continue to move unless acted upon by an external force. As the spacecraft approached the moon, the moon's gravitational force pulled the spacecraft into an orbit, allowing it to gain velocity (relative to the sun) and also redirect their trajectory towards Earth. Newton's Third law of motion applies to the firing of the rocket, i.e. Frocket = -Fgasses, allowing the rocket to propel forwards. Newton also developed NLUG -> Fg = Gm1m2/d^2, hence by saying his statement, Lovell is referring to the role of gravity providing a net external force to the craft. This statement is valid as newton's laws are responsible for the safe return of Apollo 13 to Earth.

 

[Kaido]

re: HSC Physics Marathon Archive

^ Pro

 

[PhysicsMaths]

re: HSC Physics Marathon Archive

^ Pro

after considering the markers notes haha
I wonder in what way Newton's 2nd law can be applied?

 

[Kaido]

re: HSC Physics Marathon Archive

Lol, apparently the marking criteria didn't want to anything to do with slingshot.

Edit: After some consideration, Newton's law of gravity actually doesn't specifically describe the behaviour of gravity and hence the effect of gravity-assist.

So I guess we have to stick to Newton's laws of motion

 

[Kaido]

re: HSC Physics Marathon Archive

after considering the markers notes haha
I wonder in what way Newton's 2nd law can be applied?

Actually, conservation of momentum is linked to the second law (in fact, all three laws could be described for any given motion). The Force of gases can be calculated to determine the acceleration of the rocket; then perhaps link it to the fact that as mass decreases (from fuel consumption), acceleration increases.

 

[Fizzy_Cyst]

re: HSC Physics Marathon Archive

You all are misinterpreting the Newton question!

It says for the period AFTER the rocket burn was completed. You should not mention ANYTHING about expulsion of gases as this would be DURING the rocket burn

 

[Kaido]

re: HSC Physics Marathon Archive

You all are misinterpreting the Newton question!

It says for the period AFTER the rocket burn was completed. You should not mention ANYTHING about expulsion of gases as this would be DURING the rocket burn

LOL, i never even understood what the question was in the first place

 

[Kaido]

re: HSC Physics Marathon Archive

One more attempt:

Considering that the spacecraft's fuel has completely exhausted, the statement "Newton in the driver's seat" would refer to the 'free return trajectory' a spacecraft experiences due to their inertial velocity as it approaches Earth. Recall Newton's 1st law that an 'object in motion remains in motion unless acted upon a net force'. Thus, since there is no net force (until it approaches Earth's noticeable gravitational field), the spacecraft is left to freely traverse in the direction of Earth. When the gravitational force acts on the spacecraft (as it comes close to Earth), it experiences a net force - altering its acceleration and hence velocity - though the required velocity and force to enter the Earth's atmosphere depends on the combined effects of Newton's second law (F=ma) and the spaceship's prior velocity. Thus the statement by (whatever his name is) holds true.

 

[Kaido]

re: HSC Physics Marathon Archive

Somehow, as i was writing the response, the statement became clear to me.
THANKS FIZZY FOR TELLING ME AFTER IVE WRITTEN A LOAD OF IRRELEVANT STUFF

 

[Fizzy_Cyst]

re: HSC Physics Marathon Archive

LOL, i never even understood what the question was in the first place

It's quite a difficult question! Essentially, it wants you to justify the statement made by Jim Lovell, in order to do this, you must explain how Newtons Laws apply to the motion of the craft after the rockets engines are extinguished.

 

[PhysicsMaths]

re: HSC Physics Marathon Archive

You all are misinterpreting the Newton question!

It says for the period AFTER the rocket burn was completed. You should not mention ANYTHING about expulsion of gases as this would be DURING the rocket burn

OK!
Newton's first law (inertia) states that an object will continue to move at constant velocity unless acted upon by an external force. Based on this, Apollo 13 should continue on its path towards earth even if no external force existed. Newton' developed NLUG -> Fg = Gm1m2/d^2, hence by saying this statement, Lovell is referring to the role of gravity in providing a net external force (re-direct trajectory + gain velocity) to the craft which allowed it to return back to Earth. Lovell's statement is valid as Newton's laws are responsible for the safe return of Apollo 13 to Earth.

 

[Kaido]

re: HSC Physics Marathon Archive

An observer on Earth watches two spaceships. According to their measurements, spaceship A is travelling away from Earth at 0.5c, and spaceship B is approaching Earth at 0.75 c. How fast is spaceship A moving according to the crew on spaceship B?

(2015ers only, trollface.jpg)

 

[funnytomato]

re: HSC Physics Marathon Archive

No clue what the question is asking.
And how does the spacecraft survive after getting hit?

'We just put Isaac Newton in the driver’s seat’ - is this a metaphor for something?

I am not sure whether it's Jim Lovell or Tom Hanks the one who said that.
I have this doubt because all the sites with that particular quote(or the ones I've seen) are referring to the movie.

But anyways, from what I understand, the spacecraft did not get hit by anything(like a meteor).

It had 3 components, the Service Module, the Command Module and the Lunar Module.
SM and CM together form the "main" body of the craft that will finish the entire journey and the astronauts will stay mostly in the CM.
The Lunar Module was only intended to be used for moon landing so it had limited power and other resources(like water and LiOH etc.).

What they meant by 'explosion' in the HSC paper was the explosion of the oxygen tank(hence the loss/reduction of fuel/power) in the main body.
Hence they had to abort the mission of landing and use the Lunar Module to get back on Earth. Without the LM, there is huge chance they wouldn't survive.

Here ---> http://en.wikipedia.org/wiki/Circumlunar_trajectory ( yeah , I know wikipedia is not quite a reference) , it says:

This was used on Apollo 13, when an oxygen tank rupture necessitated return to Earth without firing the Service Module engine, although a number of course corrections using the Lunar Module descent engine were required to maintain this trajectory.[2]

Also http://www.nasa.gov/mission_pages/apollo/missions/apollo13.html#.VKfCeWSUc6E mentions:

One of the big questions was, "How to get back safely to Earth?" The LM navigation system wasn't designed to help in this situation. Before the explosion at 30 hours, 40 minutes, Apollo 13 had made the normal midcourse correction, which would take it out of a free-return-to-Earth trajectory and put it on a lunar landing course. Now the task was to get back on a free-return course. The ground computed a 35-second burn and fired it five hours after the explosion. As they approached the moon, another burn was computed; this time a long five-minute burn to speed up the return home. It took place two hours after rounding the far side of the moon.

The command module navigational platform alignment was transferred to the LM, but verifying alignment was difficult. Ordinarily the alignment procedure uses an onboard sextant device, called the Alignment Optical Telescope, or AOT, to find a suitable navigation star. Then with the help of an onboard computer, it verifies the guidance platform's alignment. However, due to the explosion, a swarm of debris from the ruptured service module made it impossible to sight real stars. An alternate procedure was developed to use the sun as an alignment star. Lovell rotated the spacecraft to the attitude Houston had requested and when he looked through the AOT, the sun was just where it was expected. The alignment with the sun proved to be less than 1/2 a degree off. The ground and crew then knew they could do the five-minute P.C. + 2 burn with assurance, cutting the total time of their voyage to about 142 hours

And this http://www.imdb.com/title/tt0112384/trivia?ref_=tt_trv_trv :

The movie makes no mention of a mid-course correction made while en route to the moon which took the spacecraft off of a free return trajectory. After the explosion, a second correction was successfully made to put the spacecraft back on a free return trajectory. Without this correction, the astronauts still would have swung around the moon, but would have missed the earth on the return leg. Although a free return trajectory was agreed upon in the movie, the engine burn to accomplish this was not portrayed. The astronauts also made a four-minute engine burn after swinging around the moon to gain additional speed and to enable them to splash down in the Pacific Ocean. There is a brief reference to this in the movie, but this maneuver was not portrayed

This is a rather interesting video for more info (I think Mr Lovell is looking sharp for a man in his 80s, also check out 31:20) ,

 

[funnytomato]

re: HSC Physics Marathon Archive

Here's my attempt:
Lovell's statement refers to Newton's laws of motion which are responsible for their return back to Earth. Newton's first law of inertia states that an object will continue to move unless acted upon by an external force. As the spacecraft approached the moon, the moon's gravitational force pulled the spacecraft into an orbit, allowing it to gain velocity (relative to the sun) and also redirect their trajectory towards Earth. Newton's Third law of motion applies to the firing of the rocket, i.e. Frocket = -Fgasses, allowing the rocket to propel forwards. Newton also developed NLUG -> Fg = Gm1m2/d^2, hence by saying his statement, Lovell is referring to the role of gravity providing a net external force to the craft. This statement is valid as newton's laws are responsible for the safe return of Apollo 13 to Earth.

Not sure whether Newton's 1st law is relevant.
But the version above seems rather ambiguous.

Then again, Newton's laws of motion are quite tricky.
Up until 2nd year uni, I still didn't quite understand Newton's 2nd Law.

 

[funnytomato]

re: HSC Physics Marathon Archive

Actually, conservation of momentum is linked to the second law (in fact, all three laws could be described for any given motion). The Force of gases can be calculated to determine the acceleration of the rocket; then perhaps link it to the fact that as mass decreases (from fuel consumption), acceleration increases.

you mean change in momentum ?

Impluse can be seen as (or causes) change in momentum:

http://en.wikipedia.org/wiki/Impulse_(physics)

In the case where F is constant, we have:

http://www.grc.nasa.gov/WWW/k-12/airplane/newton2.html


Coming back to the question, if the intended answer involves using the engine.
Then essentially what the above says is that the duration of burn will determine the change in velocity.(or the other way around when you're computing the time required for a certain delta V)