4 ms·

> pontificate about things that are too small or too dark and far away to see I was bitten by this last week. I am enrolled in an aops physics course, titled M

by dxbydt 2y ago

> pontificate about things that are too small or too dark and far away to see I was bitten by this last week. I am enrolled in an aops physics course, titled Mechanics. So the last time I took any Mechanics was 40 years ago as a high school student in India. Most of the curriculum then was about stuff banging into each other aka collisions, & asking what happens to the result. Like some golf ball rolls down an inclined plane at some angle theta & hits a identical stationary ball & the objects stick together & we're supposed to compute where they end up. I was curious what American students learn, so I enrolled in this aops course. Last week's assignment asks me - under which scenario will conservation of momentum make an accurate prediction. The 3 scenarios are - truck collides with car, eagle comes to rest at perch after flying from far away, and two galaxies colliding into each other to form a third megagalaxy. I naturally picked truck & car - so aops knocks off 2 points for the wrong answer! Apparently if a truck collides with a car there will be so much thermal energy produced by the friction of the road, any prediction you make about the final velocity of the car assuming conservation of momentum will be bogus. So then I pick eagle coming to rest - aops knocks off 2 more points for the wrong answer! Apparently when eagle comes to land, it will open its giant wings to create air resistance, so momentum won't be conserved. Ok so that leaves the 2 galaxies. I pick that & get my correct answer, a pathetic score of 3/7. I'm left wondering how do we even know this is correct. Galaxies are too far away to observe. How is one supposed to compute the mass of 2 separate galaxies, & then find their moving velocities accurately, & then find the final velocity of the combined galaxy, & thus confirm momentum was conserved ? Seems very far fetched. I would rather go with the car & truck.

lilyball 2y ago
With the car & truck, and with the eagle, a lot of energy is lost into the environment. With two galaxies colliding, there is no environment to speak of. They're in space, and space is as close to a perfect vacuum as one might reasonably imagine. So the only real escape for energy is light, but I don't think there's any reason to believe colliding galaxies will produce absurd amounts of excess light (if it did we'd have observed it). Therefore the energy of the collision is preserved within the system, and so conservation of momentum will produce an accurate prediction.
- dxbydt 2y ago
  I have zero issues with your logical reasoning - its the same reasoning aops gives. I'm simply asking - how do you know for sure that this actually happens in practice ? Like, have we observed such a thing ? I'm genuinely curious, no snark. If all we have is reasoning, with zero observation, then its equivalent to what JFK says in Oliver Stone's picture - "Theoretical physics can prove that an elephant can hang from a cliff with its tail tied to a daisy."
  - lilyball 2y ago
    I have no idea if we've observed it. Galaxy collisions take a very long time, I'm not sure how we'd ever be in a position to observe both the starting state and result. That said, the point of the law of conservation of momentum is we don't need to observe it to know that it happens. Momentum is conserved, that's a fact. So the question becomes, what is it that makes this law not produce a good prediction about a scenario? And the answer is that when the scenario involves other factors that can take kinetic energy away from the system. In the car & truck scenario, we have friction with the road as a pretty huge factor, that removes a lot of energy. Even without a collision, friction is why a car needs to constantly burn fuel in order to keep moving at the same speed. So it should be no surprise that a car & truck collision will lose a ton of energy to friction. In the eagle landing scenario, that's not even a simple collision between the eagle and the branch, the eagle uses its wings to slow down, and the branch is fixed to a tree and absorbs the remaining energy. An eagle landing on a branch is an eagle that comes to rest on the branch, it doesn't just not conserve momentum it gets rid of all of it. But in the colliding galaxies scenario, there's no surface to have friction with, there's no wings beating against air, there's no tree anchoring one of the objects in place, nothing to absorb any energy, no environment to dissipate energy in. Without anything to get rid of kinetic energy, conservation of momentum will predict the results.
    - saagarjha 2y ago
      That is, until gravitation waves carry away the energy :)
saagarjha 2y ago
TIL AoPS has physics classes now
- dxbydt 2y ago
  i am essentially a rayiner on steroids, in that i believe america has absolutely nothing meaningful to offer to the world at large other than aops and rsm. its such an extraordinary institution. large number of international signups - so tons of indian and chinese kids burning the midnight oil solving woot alongside their american compatriots. just an amazing, spectacular creation all around. if the nobel committee had any brains, rusczyk would have gotten atleast a peace prize by now.
  - saagarjha 2y ago
    "I am essentially a rayiner on steroids" has to be the most unhinged thing I have read on this site today lmao
trashtester 2y ago
> conservation of momentum make an accurate prediction. Accurate prediction of what? If it's the velocity and location in the end state, the best answer is the eagle (once it comes to rest). The momentum of Earth is so huge that the eagle will end up precisely on the perch (if we disregard the inability of a living bird to be completely still) For the cars, the exact end state depends on many other factors, as you say. Finally, for the colliding galaxies, there may be some uncertainty about how dark matter and dark energy (or their absence) affect galaxy collisions. This may be beyond the understanding of whoever wrote the test, though.

by dxbydt 2y ago

lilyball 2y ago

With the car & truck, and with the eagle, a lot of energy is lost into the environment. With two galaxies colliding, there is no environment to speak of. They're in space, and space is as close to a perfect vacuum as one might reasonably imagine. So the only real escape for energy is light, but I don't think there's any reason to believe colliding galaxies will produce absurd amounts of excess light (if it did we'd have observed it). Therefore the energy of the collision is preserved within the system, and so conservation of momentum will produce an accurate prediction.

dxbydt 2y ago
I have zero issues with your logical reasoning - its the same reasoning aops gives. I'm simply asking - how do you know for sure that this actually happens in practice ? Like, have we observed such a thing ? I'm genuinely curious, no snark. If all we have is reasoning, with zero observation, then its equivalent to what JFK says in Oliver Stone's picture - "Theoretical physics can prove that an elephant can hang from a cliff with its tail tied to a daisy."
- lilyball 2y ago
  I have no idea if we've observed it. Galaxy collisions take a very long time, I'm not sure how we'd ever be in a position to observe both the starting state and result. That said, the point of the law of conservation of momentum is we don't need to observe it to know that it happens. Momentum is conserved, that's a fact. So the question becomes, what is it that makes this law not produce a good prediction about a scenario? And the answer is that when the scenario involves other factors that can take kinetic energy away from the system. In the car & truck scenario, we have friction with the road as a pretty huge factor, that removes a lot of energy. Even without a collision, friction is why a car needs to constantly burn fuel in order to keep moving at the same speed. So it should be no surprise that a car & truck collision will lose a ton of energy to friction. In the eagle landing scenario, that's not even a simple collision between the eagle and the branch, the eagle uses its wings to slow down, and the branch is fixed to a tree and absorbs the remaining energy. An eagle landing on a branch is an eagle that comes to rest on the branch, it doesn't just not conserve momentum it gets rid of all of it. But in the colliding galaxies scenario, there's no surface to have friction with, there's no wings beating against air, there's no tree anchoring one of the objects in place, nothing to absorb any energy, no environment to dissipate energy in. Without anything to get rid of kinetic energy, conservation of momentum will predict the results.
  - saagarjha 2y ago
    That is, until gravitation waves carry away the energy :)

saagarjha 2y ago

TIL AoPS has physics classes now

dxbydt 2y ago
i am essentially a rayiner on steroids, in that i believe america has absolutely nothing meaningful to offer to the world at large other than aops and rsm. its such an extraordinary institution. large number of international signups - so tons of indian and chinese kids burning the midnight oil solving woot alongside their american compatriots. just an amazing, spectacular creation all around. if the nobel committee had any brains, rusczyk would have gotten atleast a peace prize by now.
- saagarjha 2y ago
  "I am essentially a rayiner on steroids" has to be the most unhinged thing I have read on this site today lmao

trashtester 2y ago

> conservation of momentum make an accurate prediction. Accurate prediction of what? If it's the velocity and location in the end state, the best answer is the eagle (once it comes to rest). The momentum of Earth is so huge that the eagle will end up precisely on the perch (if we disregard the inability of a living bird to be completely still) For the cars, the exact end state depends on many other factors, as you say. Finally, for the colliding galaxies, there may be some uncertainty about how dark matter and dark energy (or their absence) affect galaxy collisions. This may be beyond the understanding of whoever wrote the test, though.