# Thread: HSC Physics Marathon 2016

1. ## Re: HSC Physics Marathon 2016

NEXT QUESTION:
1. An ice skater coats around a uniform circular track at constant speed. Compare and contrast the motion of the skater with the motion of a satellite orbiting the Earth (3M)

2. Europa and Lo are the moons that orbit Jupiter, and Europa orbits (orbital radius) at a distance of 670,900 km from the centre of Jupiter. Calculate the distance between the centres of Lo and Saturn GIVEN that Europa takes exactly 4 times as along as Lo to orbit Saturn. Give your answers to 2 significant figures. (3M)

2. ## Re: HSC Physics Marathon 2016

not sure if this has been asked, too lazy to read through this but this is something to consider:

What is the difference between a geosynchronous and geostationary orbit? (not 100% sure if this is even in the syllabus)

3. ## Re: HSC Physics Marathon 2016

I don't think geosynchronous orbit is in the syllabus but I saw in one of the Independent Trials they asked about it, so it's good to know

4. ## Re: HSC Physics Marathon 2016

Originally Posted by mrpotatoed
not sure if this has been asked, too lazy to read through this but this is something to consider:

What is the difference between a geosynchronous and geostationary orbit? (not 100% sure if this is even in the syllabus)
Not needed. If it gets asked it has to be vaguely defined.

5. ## Re: HSC Physics Marathon 2016

Originally Posted by RachelGreen
NEXT QUESTION:
1. An ice skater coats around a uniform circular track at constant speed. Compare and contrast the motion of the skater with the motion of a satellite orbiting the Earth (3M)

2. Europa and Lo are the moons that orbit Jupiter, and Europa orbits (orbital radius) at a distance of 670,900 km from the centre of Jupiter. Calculate the distance between the centres of Lo and Saturn GIVEN that Europa takes exactly 4 times as along as Lo to orbit Saturn. Give your answers to 2 significant figures. (3M)
I like the first one.
EDIT: My bad I thought it was something else...

Change it to an ice skater doing a spin on her skates.

6. ## Re: HSC Physics Marathon 2016

Originally Posted by RachelGreen
NEXT QUESTION:
1. An ice skater coats around a uniform circular track at constant speed. Compare and contrast the motion of the skater with the motion of a satellite orbiting the Earth (3M)

2. Europa and Lo are the moons that orbit Jupiter, and Europa orbits (orbital radius) at a distance of 670,900 km from the centre of Jupiter. Calculate the distance between the centres of Lo and Saturn GIVEN that Europa takes exactly 4 times as along as Lo to orbit Saturn. Give your answers to 2 significant figures. (3M)
1. Both the ice skate and the satellite are undergoing a form of circular motion. This circular motion entails tangential momentum but also some form of a centripetal force causing a centripetal acceleration. This acceleration does not effect the magnitude of the object's velocity, but rather the direction. The forces providing this centripetal accelerations are different for the ice skater and the satellite. The ice skater's centripetal force is provided by contact forces between the skates and the ice while the centripetal force for the satellite is provided by gravity.

I'm a little bit confused by 2. It sounds like a Kepler's law of periods question, but I don't know how I could calculate it without the relative masses of Jupiter and Saturn. Also, in the question you've said that Li orbits Jupiter, than you said it orbits Saturn. What's going on?

7. ## Re: HSC Physics Marathon 2016

Originally Posted by Ambility
1. Both the ice skate and the satellite are undergoing a form of circular motion. This circular motion entails tangential momentum but also some form of a centripetal force causing a centripetal acceleration. This acceleration does not effect the magnitude of the object's velocity, but rather the direction. The forces providing this centripetal accelerations are different for the ice skater and the satellite. The ice skater's centripetal force is provided by contact forces between the skates and the ice while the centripetal force for the satellite is provided by gravity.

I'm a little bit confused by 2. It sounds like a Kepler's law of periods question, but I don't know how I could calculate it without the relative masses of Jupiter and Saturn. Also, in the question you've said that Li orbits Jupiter, than you said it orbits Saturn. What's going on?
Now explain (1) if an ice skater spins in a circle.

8. ## Re: HSC Physics Marathon 2016

Originally Posted by Drsoccerball
Now explain (1) if an ice skater spins in a circle.
Like on the same spot?

9. ## Re: HSC Physics Marathon 2016

Originally Posted by RachelGreen
NEXT QUESTION:
1. An ice skater coats around a uniform circular track at constant speed. Compare and contrast the motion of the skater with the motion of a satellite orbiting the Earth (3M)

2. Europa and Lo are the moons that orbit Jupiter, and Europa orbits (orbital radius) at a distance of 670,900 km from the centre of Jupiter. Calculate the distance between the centres of Lo and Saturn GIVEN that Europa takes exactly 4 times as along as Lo to orbit Saturn. Give your answers to 2 significant figures. (3M)
$The moon's name is actually \emph{Io} (starts with capital i), not Lo.$

10. ## Re: HSC Physics Marathon 2016

Originally Posted by Ambility
1. Both the ice skate and the satellite are undergoing a form of circular motion. This circular motion entails tangential momentum but also some form of a centripetal force causing a centripetal acceleration. This acceleration does not effect the magnitude of the object's velocity, but rather the direction. The forces providing this centripetal accelerations are different for the ice skater and the satellite. The ice skater's centripetal force is provided by contact forces between the skates and the ice while the centripetal force for the satellite is provided by gravity.

I'm a little bit confused by 2. It sounds like a Kepler's law of periods question, but I don't know how I could calculate it without the relative masses of Jupiter and Saturn. Also, in the question you've said that Li orbits Jupiter, than you said it orbits Saturn. What's going on?
The Saturn part is a typo, replace the Saturns with Jupiters (i.e. the moons orbit the same planet).

11. ## Re: HSC Physics Marathon 2016

Originally Posted by Ambility
Like on the same spot?
We would need to use the concept of conservation of angular momentum to explain the physics of an ice skater spinning on the same spot, and this concept is not in the high school syllabus.

12. ## Re: HSC Physics Marathon 2016

Originally Posted by InteGrand
We would need to use the concept of conservation of angular momentum to explain the physics of an ice skater spinning on the same spot, and this concept is not in the high school syllabus.
bruh go study for u exam

13. ## Re: HSC Physics Marathon 2016

Originally Posted by RachelGreen
2. Europa and Lo are the moons that orbit Jupiter, and Europa orbits (orbital radius) at a distance of 670,900 km from the centre of Jupiter. Calculate the distance between the centres of Lo and Saturn GIVEN that Europa takes exactly 4 times as along as Lo to orbit Saturn. Give your answers to 2 significant figures. (3M)
You mean Jupiter.

If the period of orbit for Io is T, then the period of orbit for Europa is 4T.
r_Europa^3/T_Europa^2 = r_Io^3/T_Io^2 as they both orbit Jupiter
(670 900 000)^3/(16T^2) = r_Io^3/T^2
(670 900 000)^3/16 = r_Io^3

Orbital radius of Io is therefore 670 900 000/cbrt(16) = 2.7*10^8m correct to 2 s. f.
Which is the distance between it's center and Jupiter.

(This would be a multiple choice question in the exam room and thus not require you to provide the significant figures)
--------------------
NEXT QUESTION:
A basketball is thrown with an initial velocity of u at an angle of 45 degrees. There is a basketball hoop whose centre positioned 30m away from the athlete and its hoop is 3.0m high. If the ball was thrown 1.85m above the ground, determine the velocity required so that the basketball will enter the centre at exactly the hoop. (4)

(You may assume that the hoop's diameter is sufficient enough to allow the basketball to pass through)

14. ## Re: HSC Physics Marathon 2016

Describe the motion of a water rocket, mentioning both Newtons 3rd law, and the conservation of momentum. Hence explain the effects of changing the volume of water.

15. ## Re: HSC Physics Marathon 2016

When the water rocket ejects water to propel itself, this creates a force pair that can be described by Newton's 3rd Law. According to this law, the force of ejection will be equal in magnitude but opposite in direction to the force acting upon the body of the water rocket. We can write this like so:

$-F_{water} = F_{rocket}$

Because F = ma = m∆v/t, then this can be rewritten as:

$-\frac{m\Delta v}{t}_{water} = \frac{m\Delta v}{t}_{rocket}$

Given that this model works over the same time period, then $t_{water} = t_{rocket}$. We can multiply both sides by $t_{water}$ to realise the following:

$-m\Delta v_{water} = m\Delta v_{rocket}$
$-p_{water} = p_{rocket}$

Thus the rocket's motion follows the law of conservation of momentum, where the momentum of the water it propels is equal to its own momentum over a given time period.

As the rocket continues to fly, the mass of water that it propels will increase as the mass of water it has left decreases. Presuming that the velocity it ejects the water at is constant, then as it continues to fly, the magnitude of the left hand side of the equation ($p_{water}$) will increase. The right hand side of the equation ($p_{rocket}$) will increase in response. However, the mass component of $p_{rocket}$ will be decreasing, so the magnitude of the velocity will increase. This is acceleration.

I'm not sure about whether the acceleration is constant or not. I'm going to presume it isn't, but if someone knows this please let me know!

Question

A football is kicked from flat ground on a windless day. It flies through the air over 30 metres, and lands after 4 seconds. What was the maximum height it reached, and what was the angle it was launched at? [3 marks]

At least I think this one works.

16. ## Re: HSC Physics Marathon 2016

Originally Posted by Glyde
Describe the motion of a water rocket, mentioning both Newtons 3rd law, and the conservation of momentum. Hence explain the effects of changing the volume of water.
Question skipping?

17. ## Re: HSC Physics Marathon 2016

Just because it's windless doesn't mean there's no air resistance...

18. ## Re: HSC Physics Marathon 2016

Originally Posted by onlyhuwyouknow
Because F = ma
$Note that this is technically not the case if the mass is not constant. The general equation is \bold{F} = m\frac{\mathrm{d} \bold{v}}{\mathrm{d}t}+ \bold{v}\frac{\mathrm{d}m}{\mathrm{d}t}.$

19. ## Re: HSC Physics Marathon 2016

$If we instead assume that the force provided by the water is a constant F_W, water is ejected out at a constant rate of k>0 (dimensions are mass per unit time), then the mass of the water-rocket at time t is m(t) = M_0 - kt for 0\leq t < \frac{M_W}{k}, where M_W is the mass of the water at the start and M_0 = M_W + M_R, where M_R is the mass of the rocket if it were empty. In this time interval, we have the net force on the object being F_W - m(t)g (water-force minus weight force, assuming the approximation of constant gravity), and this is equal to the time derivative of momentum by the generalised Newton's law. Therefore,$

$\frac{\mathrm{d}}{\mathrm{d}t}\left(m(t) v \right)= F_W - m(t) g, where v is the velocity of the water-rocket (upwards is positive direction), and 0\leq t <\frac{M_W}{k}$

\begin{align*}\Rightarrow m(t) v &= \int \left( F_W - \left(M_0 - kt \right) g \right) \text{ d}t \\ \Rightarrow \left( M_0 - kt \right) v &= F_W t - \frac{g \left(M_0 -kt \right)^2 }{ -2k} +C.\\ \end{align*}

$Plugging in the initial condition of v=0 at t=0 and solving for C, we find that C=-\frac{gM_0^2}{2k}.$

$So the velocity of the water-rocket is v(t) = \frac{F_W t}{M_0 - kt}+ \frac{g \left(M_0 -kt\right)^2}{2k}-\frac{gM_0^2}{2k} = \frac{F_W t}{M_0 - kt} + \frac{g\left(k^2 t^2 - 2M_0 k t\right)}{2k}\Rightarrow v(t) = \frac{F_W t}{M_0 - kt} + \frac{g t \left(kt - 2M_0 \right)}{2} for 0\leq t < \frac{M_W}{k} . After this time, its motion is simply that of an object moving just under the force gravity. (We have ignored friction and air resistance etc.).$

20. ## Re: HSC Physics Marathon 2016

Calculate the maximum height a water rocket reaches if it is shot straight up in the air and the total time of flight is 2.57sec

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21. ## Re: HSC Physics Marathon 2016

Integrand decides casually to visit an alternate universe to investigate the laws of physics. Upon his arrival he notices something quite strange... objects are no longer attracted but rather repel each other... Integrand in his space rocket decides to undergo a few experiments.

1) Explain why Integrand dies upon his arrival without testing his results and if he was able to survive how he would be able to safely conduct his experiments.
2)If Integrand wants to commit to the sling shot manoeuvre explain why the object/planet in which the sling shot effect is used must be moving.
3) Discuss the problems associated with the new universe in regards to space travel.
4) Would Newton's Universal Law of Gravity still apply ? Explain.

22. ## Re: HSC Physics Marathon 2016

Originally Posted by Drsoccerball
Integrand decides casually to visit an alternate universe to investigate the laws of physics. Upon his arrival he notices something quite strange... objects are no longer attracted but rather repel each other... Integrand in his space rocket decides to undergo a few experiments.

1) Explain why Integrand dies upon his arrival without testing his results and if he was able to survive how he would be able to safely conduct his experiments.
2)If Integrand wants to commit to the sling shot manoeuvre explain why the object/planet in which the sling shot effect is used must be moving.
3) Discuss the problems associated with the new universe in regards to space travel.
4) Would Newton's Universal Law of Gravity still apply ? Explain.
The electromagnetic and two nuclear forces should be sufficient to prevent Integrand from dying immediately. Gravity only dominates at larger scales.

23. ## Re: HSC Physics Marathon 2016

The electromagnetic and two nuclear forces should be sufficient to prevent Integrand from dying immediately. Gravity only dominates at larger scales.
His particles in his body are now all repulsive and since $F=\frac{Gm_1m_2}{r^2}$ as r is very very very small it produces large amount of force ripping Integrand up exploding him :P

24. ## Re: HSC Physics Marathon 2016

Originally Posted by Drsoccerball
His particles in his body are now all repulsive and since $F=\frac{Gm_1m_2}{r^2}$ as r is very very very small it produces large amount of force ripping Integrand up exploding him :P
Yes, but the combined forces of the electromagnetic field, strong and weak nuclear fields exceeds the miniscule anti-gravitational force from the tiny masses of each individual atom. The Earth will explode, not Integrand, as the negative curvature created by the warping of space-time is large enough to send the Earth scattering apart, but not large enough to send Integrand scattering apart. He might get gastrointestinal distress though.

25. ## Re: HSC Physics Marathon 2016

Originally Posted by Drsoccerball
Integrand decides casually to visit an alternate universe to investigate the laws of physics. Upon his arrival he notices something quite strange... objects are no longer attracted but rather repel each other... Integrand in his space rocket decides to undergo a few experiments.

1) Explain why Integrand dies upon his arrival without testing his results and if he was able to survive how he would be able to safely conduct his experiments.
2)If Integrand wants to commit to the sling shot manoeuvre explain why the object/planet in which the sling shot effect is used must be moving.
3) Discuss the problems associated with the new universe in regards to space travel.
4) Would Newton's Universal Law of Gravity still apply ? Explain.
For (2), surely a planet would not even be able to form in this alternate universe? (at least via accretion?) Or is this simply hypothetical?

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