HSC Physics Question Thread

[Happy Physics Land]

You have opened Pandora's Box 

Okay, so in classical physics we learn about Newton's 2nd Law, which can be used (in various forms) to predict the behaviour of a system over time. Classically, this is absolutely accurate. In quantum mechanics, we cannot predict the outcome of an event until it happens, we can only calculate the probabilities of certain events occurring. This links to the whole idea of Schrodingers Cat.

Picture a cat inside a box (we can't see inside), and next to it is a contraption with a radioactive isotope, a detector, and a flask of poison. Two things in this 'system' can occur. The particle can decay, and if this happens, the resultant gamma radiation will trigger the detector, release the poison, and kill the cat. If the particle does not decay, nothing happens and the cat stays alive.

Certain interpretations of quantum mechanics (Copenhagen Interpretations) would suggest that, since we cannot know whether the cat is alive or dead until we check, the cat is simultaneously alive and dead. This is known as a quantum superposition. Only when we open the box, does this superposition collapse into a reality where the cat is alive (yay!) or dead (wahh...). Really, the cat here is just enabling us to extend an atomic state (whether a particle decays or not) to a macroscopic, real living thing.

So, how do we predict the probability of the cat dying or living, or more generally, how do we predict the outcomes of a system? This is where the Schrodinger Equation comes in. This is a partial differential equation which describes how the quantum state of a system evolves over time. The equation looks like this, the subject of the equation being the weird symbol Psi appearing on both sides of the equation (the rest are an essay in itself)



The subject is the wave equation. Now, the probability of certain quantum states is proportional to the square of this wave function. To solve for the wave equation, therefore, is to have complete understanding of a system and the probability of any event occurring. In some interpretations of quantum physics, the wave function can be used to predict the evolution of HUGE systems, perhaps even the entire universe. Solving the Schrodinger Equation for a particle is hard enough though, for a universe is simply impossible 

The Schrodinger Equation has many implications:

- Depending on measurements, the states of a system are quantised, and thus, energy is quantised in all forms (not just for electromagnetic quanta). This is verified already, for example, electron energies in atoms are proven to be quantised.
- Under the Copenhagen interpretation of quantum mechanics, particles do not have set positions, and thus, the result when we measure is drawn from a probability distribution (wave function gives us this). Flowing on from this, we cannot know the precise position of a particle, unless we completely abandon any attempt to measure its momentum. The product of error in momentum and error in position of a particle must be larger than Planck's constant divided by 2 pi, this is Heisenberg's Uncertainty Principle. 
- There are, in certain systems, small probabilities of classical physics being completely broken. This is called Quantum Tunnelling. For example, there is always a slight probability that a particle will pass through a classically insurmountable barrier (the microscopic and basic equivalent of me appearing next to you, from where I am, with no lead up, right as you finish this sentence).

This is a very quick run through of a SUPER fascinating topic, you should definitely do some extra research if you can! And study Physics at uni, it is awesome 

Your pandora's box just caused a supernova in my brain ... every sentence I read felt like a quantum plucking out my hair. I think I will just rewrite the greek mythology here.

Board of Studies sent Pandora down to earth and gave her as a present to Epimetheus. BOSTES told Epimetheus that he should marry Pandora. Also, BOSTES sent Pandora with a little box, with a big lock on it and said not to ever open the box, and he gave the key to Epimetheus. But Pandora was very curious about what was in the box. One day Pandora stole the key and opened the box.

Oh! Under Newton's 2nd law, F-ma, every kind of trouble in the box that people had never known about before experienced a force and jumped out at 300N West! Special theory of relativity, Schrodinger's equation and the quantum theory all began to fly away like little bugs by overcoming the gravitational field and spread all over the place. Pandora was very sorry now that she had opened the box! She tried to catch them and put them back in the box but its too late! They all accelerated in another direction under the slingshot effect and landed in the brains of all NSW students!

But the very last thing to fly out of the box, as Pandora sat there crying, was not as ugly as the others. In fact it was beautiful. It was MATHS EXTENSION II, which Board of Studies sent to keep people going when all the nasty things got them down.

[jamonwindeyer]

Your pandora's box just caused a supernova in my brain ... every sentence I read felt like a quantum plucking out my hair. I think I will just rewrite the greek mythology here.

Board of Studies sent Pandora down to earth and gave her as a present to Epimetheus. BOSTES told Epimetheus that he should marry Pandora. Also, BOSTES sent Pandora with a little box, with a big lock on it and said not to ever open the box, and he gave the key to Epimetheus. But Pandora was very curious about what was in the box. One day Pandora stole the key and opened the box.

Oh! Under Newton's 2nd law, F-ma, every kind of trouble in the box that people had never known about before experienced a force and jumped out at 300N West! Special theory of relativity, Schrodinger's equation and the quantum theory all began to fly away like little bugs by overcoming the gravitational field and spread all over the place. Pandora was very sorry now that she had opened the box! She tried to catch them and put them back in the box but its too late! They all accelerated in another direction under the slingshot effect and landed in the brains of all NSW students!

But the very last thing to fly out of the box, as Pandora sat there crying, was not as ugly as the others. In fact it was beautiful. It was MATHS EXTENSION II, which Board of Studies sent to keep people going when all the nasty things got them down.

Made my night  also realise the irony of saying that MX2 is your escape from 'nasty' things 

[Happy Physics Land]

Made my night  also realise the irony of saying that MX2 is your escape from 'nasty' things 

That situational irony was totally intentional

[jamonwindeyer]

That situational irony was totally intentional

You should use that post above as a Related Text for English 

[smiley2101]

Hey Smiley!

The answer to this multiple choice is going to be C. We can figure this out by process of elimination: gravity is actually the MAIN force acting on any spacecraft orbiting our planet, as it causes the orbit to occur in the first place (the shuttle is dragged down to earth, but is traveling so fast that it 'misses' the ground due to the curvature of the planet!), so the answer can't be A. The 'orbiting around the Sun' etc. thing doesn't even make any sense, and the whole 'inversely proportional' relationship thing would require some sort of mathematics that told you WHEN the astronaut would stay with the spacecraft, and when it would not. As the forces on the two objects are the same (namely, gravity), there is no reason that their ACCELERATION would be different!.

Remember, gravity has units that are meters per second, per second. There is no 'kilograms' or anything like that in the units, meaning that it operates INDEPENDENTLY of the mass of the object!

Jake

but the answer says it is D?

[Happy Physics Land]

but the answer says it is D?

I cant really see why the answer would be D but according to Newton's 2nd law F=ma, it is true that mass and acceleration would be inversely proportional. Since the gravitational force acting on both the spaceship and the person are constant (since both objects are in the same orbit), the person should be accelerating towards the centre at a higher value than the spaceship which has a much larger mass. I think l agree with with Jake's explanation except for that point.

[jakesilove]

I cant really see why the answer would be D but according to Newton's 2nd law F=ma, it is true that mass and acceleration would be inversely proportional. Since the gravitational force acting on both the spaceship and the person are constant (since both objects are in the same orbit), the person should be accelerating towards the centre at a higher value than the spaceship which has a much larger mass. I think l agree with with Jake's explanation except for that point.

https://www.youtube.com/watch?v=E43-CfukEgs

An object with a greater mass does not accelerate towards the earth more quickly. The terminal velocity may be different, but as you can see, a bowling ball and a feather falls at the same rate (and by extension, a person and a space ship!). Pretty cool, and pretty counter intuitive.

Jake

[RuiAce]

Your pandora's box just caused a supernova in my brain ... every sentence I read felt like a quantum plucking out my hair. I think I will just rewrite the greek mythology here.

Board of Studies sent Pandora down to earth and gave her as a present to Epimetheus. BOSTES told Epimetheus that he should marry Pandora. Also, BOSTES sent Pandora with a little box, with a big lock on it and said not to ever open the box, and he gave the key to Epimetheus. But Pandora was very curious about what was in the box. One day Pandora stole the key and opened the box.

Oh! Under Newton's 2nd law, F-ma, every kind of trouble in the box that people had never known about before experienced a force and jumped out at 300N West! Special theory of relativity, Schrodinger's equation and the quantum theory all began to fly away like little bugs by overcoming the gravitational field and spread all over the place. Pandora was very sorry now that she had opened the box! She tried to catch them and put them back in the box but its too late! They all accelerated in another direction under the slingshot effect and landed in the brains of all NSW students!

But the very last thing to fly out of the box, as Pandora sat there crying, was not as ugly as the others. In fact it was beautiful. It was MATHS EXTENSION II, which Board of Studies sent to keep people going when all the nasty things got them down.

Yeah nah mate Jamon's stuff made more sense

I cant really see why the answer would be D but according to Newton's 2nd law F=ma, it is true that mass and acceleration would be inversely proportional. Since the gravitational force acting on both the spaceship and the person are constant (since both objects are in the same orbit), the person should be accelerating towards the centre at a higher value than the spaceship which has a much larger mass. I think l agree with with Jake's explanation except for that point.

To back up Jake's comment.

F=ma implies that force varies according to mass. But not acceleration.

(Note that the concept of a terminal velocity comes straight out of elementary particle kinematics.)

[jamonwindeyer]

but the answer says it is D?

Just to qualify, the answer would be D.

Examine C. It says that the force due to gravity on each the astronaut and the spacecraft is equal. Now we know that gravitational force is equal to the centripetal force in an orbit, so we can equate the force due to gravity to centripetal force for both the astronaut (the top equation) and the spaceship (the bottom):




What we notice is that, for the astronaut and the spaceship to not drift apart, we require their velocities to be equal, and their radius of orbit to be equal. The gravitational force on both must be equal IF C is to be correct.

However, that means EVERYTHING except the masses of the objects has to be equal. This then, for the equations above to be true, means the astronaut must have the same mass as the spaceship. Unless we have a ship made of balsa wood, or the astronaut has eaten too much pie in toothpaste form, this just doesn't make sense. Thus, C has to be incorrect.

D is therefore correct by the process of elimination. And indeed, if we examine the formula for acceleration, and then substitute in centripetal force formula:



This does show that the acceleration of the astronaut/spaceship is inversely proportional to its mass, and then when we substitute, we find that the acceleration of each body is dependent only on velocity and radius of orbit, which are equal by definition.

This last bit is a little roundabout in nature, I personally think that it is easier to answer this one by eliminating options A-C, which is usually the best way to avoid silly mistakes anyway  hope this helps!!

[Happy Physics Land]

https://www.youtube.com/watch?v=E43-CfukEgs

An object with a greater mass does not accelerate towards the earth more quickly. The terminal velocity may be different, but as you can see, a bowling ball and a feather falls at the same rate (and by extension, a person and a space ship!). Pretty cool, and pretty counter intuitive.

Jake

Right, so Galileo's experiment can equally be applied to space things as well. Yeah sorry I was ignorant that acceleration due to gravity should be of the same value because spaceship and the astronaut are at the same position away from earth

Just to qualify, the answer would be D.

Examine C. It says that the force due to gravity on each the astronaut and the spacecraft is equal. Now we know that gravitational force is equal to the centripetal force in an orbit, so we can equate the force due to gravity to centripetal force for both the astronaut (the top equation) and the spaceship (the bottom):




What we notice is that, for the astronaut and the spaceship to not drift apart, we require their velocities to be equal, and their radius of orbit to be equal. The gravitational force on both must be equal IF C is to be correct.

However, that means EVERYTHING except the masses of the objects has to be equal. This then, for the equations above to be true, means the astronaut must have the same mass as the spaceship. Unless we have a ship made of balsa wood, or the astronaut has eaten too much pie in toothpaste form, this just doesn't make sense. Thus, C has to be incorrect.

D is therefore correct by the process of elimination. And indeed, if we examine the formula for acceleration, and then substitute in centripetal force formula:



This does show that the acceleration of the astronaut/spaceship is inversely proportional to its mass, and then when we substitute, we find that the acceleration of each body is dependent only on velocity and radius of orbit, which are equal by definition.

This last bit is a little roundabout in nature, I personally think that it is easier to answer this one by eliminating options A-C, which is usually the best way to avoid silly mistakes anyway  hope this helps!!

I didnt think to jump straight into F_g = m_av²/r . I've always been trying to use the formula for orbital velocity which made me think its C

[Maz]

NOTE THAT THIS IS NOT AN HSC QUESTION ~Jake

hey
could u please help me with this question?
i attached it 

thankyou so much

[jakesilove]

hey
could u please help me with this question?
i attached it 

thankyou so much

Hey! To be completely honest, I have never done this kind of physics in depth. After a touch of research, I think I have got an answer out for a) Essentially, you need to sum up the three torques (the first two are obvious, but apparently the third is just the perpendicular distance from the chord to the pivot point, which I guess makes sense, times to tension force) and set it equal to zero. My answer is below.



Apologies for the sideways-ness.

As for the other two parts, I'll keep thinking. My intuition told me that, since the pivot isn't moving, the sum of all forces on it must equal to zero. I can't imagine that's the answer you're looking for, though, but I can't seem to move beyond that mentality.

I'll keep thinking. For HSC students who are skimming through the forum, note that this is not able to be assessed in the HSC!

Jake

[jakesilove]

hey
could u please help me with this question?
i attached it 

thankyou so much

Okay, I've found something that appears to answer your question. Now, these are formulas that I have found, and for a more detailed explanation (although, to be honest, not a very satisfactory one), take a look here. However, this appears to be what you need to do.



To be clear, I don't actually know much about 'classical' physics (that's next year for me!). Very likely, I'm just totally wrong.

Jake

[jamonwindeyer]

Right, so Galileo's experiment can equally be applied to space things as well. Yeah sorry I was ignorant that acceleration due to gravity should be of the same value because spaceship and the astronaut are at the same position away from earth

I didnt think to jump straight into F_g = m_av²/r . I've always been trying to use the formula for orbital velocity which made me think its C

I always had trouble with when to use what fact, many of my practice papers are scribbled with a few different attempts at getting the result I want aha! 

[JellyBeanz]

I always had trouble with when to use what fact, many of my practice papers are scribbled with a few different attempts at getting the result I want aha! 

Jamon, i'm interested in the solution of the question that mq123 posted, can you please have a look at Jake's solution and comment on it?
Thanks