Hockey Puck Physics - Page 2

asdf · 2003-07-14, 17:34

Does the size of the hill matter?

eepiccolo · 2003-07-14, 17:34

Quote:

Originally Posted by asdf

Does the size of the hill matter?

Nope, or I would have defined it.

asdf · 2003-07-14, 17:37

Then I say that it is uncertain who will win.

NickGlover · 2003-07-14, 18:15

I think the hill size and length of the dip matter.

The 2nd puck will have an advantage over the 1st because of the time it spends travelling at a higher speed. However, it also has a slightly longer distance to travel because of the hills. So, which puck wins depends on how these two factors weigh against each other.

Xyzzy · 2003-07-14, 18:45

My guess is the second puck will accellerate faster initially, and because of this, it will lose energy faster due to the fact that the faster you go the air friction becomes greater... (I mean it is not linear)

I think this is why airplanes have to dive (go faster initially) to slow down faster... I was told this by a pilot who had to land unexpectedly in a field due to a engine failure... He had to scrub off a lot of airspeed and diving did the trick... He also mentioned to me that airspeed and altitude were the only two things that mattered to him, and either could be converted to the other, or something like that...

Well, I'm just guessing I suppose...

eepiccolo · 2003-07-14, 18:56

Oops, I forgot to mention that there is no air drag/friction, either.
If there was, the problem would be indeterminate.

Wacky · 2003-07-14, 18:58

Quote:

Originally Posted by NickGlover

I think the hill size and length of the dip matter.

These factors would affect the magnitude of the difference, but not its existence.

At no point will the horizontal component of the 2nd puck's velocity be less than that of the first puck.

By conservation of energy, the velocity of 2nd puck must be greater when it is below the horizontal reference elevation.

Since the profile must be a continuous function, there must be some region in which the puck is moving horizontally and below the reference elevation.

Therefore, the 2nd puck will arrive first.

NickGlover · 2003-07-14, 20:56

Quote:

Originally Posted by Wackerbarth

These factors would affect the magnitude of the difference, but not its existence.

...

Therefore, the 2nd puck will arrive first.

In case it wasn't clear, I think the hill height, the hill steepness, and the length of the dip all determine which puck will win.

To give an extreme example, consider if the hill is very steep and very high with a relatively short dip length. The steep and high hill will accelarate the 2nd puck to a very high speed, but that won't change the fact that the 1st puck would be finished before the 2nd gets to the bottom of this very high hill.

I actually did some calculations and determined that with a less extreme 45 degree slope and zero length dip (upslope starts right after downslope) that the 2nd puck would win with certain initial speeds. I did use sharp angles that magically transferred the puck's current speed in a new direction; I don't believe a rounded-off angle would significantly change the outcome (and it would have been much harder to do the math for).

Wacky · 2003-07-14, 21:20

Quote:

Originally Posted by NickGlover

Quote:

Originally Posted by Wackerbarth

These factors would affect the magnitude of the difference, but not its existence.

...

Therefore, the 2nd puck will arrive first.

In case it wasn't clear, I think the hill height, the hill steepness, and the length of the dip all determine which puck will win.

To give an extreme example, consider if the hill is very steep and very high with a relatively short dip length. The steep and high hill will accelarate the 2nd puck to a very high speed, but that won't change the fact that the 1st puck would be finished before the 2nd gets to the bottom of this very high hill.

I think that you are missing something here.
If the hill starts too fast, the puck will go ballistic and literally fly off the cliff. The curve is a parabola. If the hill is shallower, the added speed will more than make up for the additional distance. As I said before, the horizontal speed of the second puck is NEVER less than that of the first puck.

Quote:

I actually did some calculations ... I did use sharp angles that magically transferred the puck's current speed in a new direction; I don't believe a rounded-off angle would significantly change the outcome

I think that you are wrong. The transition is critical.

NickGlover · 2003-07-14, 22:16

Ok, now I understand what you are saying, and agree that your conclusion is correct. My problem was that you said the puck does not tumble which I took as a less extreme version of flying off the cliff. I'm guessing you meant that any hill configuration which would cause the puck to leave the surface is invalid (in which case the shape of the hill is relevant). I thought you meant that we didn't have to consider the effects of leaving the surface.

ET_ · 2003-07-14, 22:20

Same initial velocity.
Gravity
No friction.
The momentum gained is lost.

They tie.

Luigi

Where got I wrong? :D

Well, of course... I did not consider that the second puck was quicker for the time it ran in the hole... The second puck wins.

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2003-07-14, 17:34	#12
asdf Sep 2002 2²·3·5 Posts	Does the size of the hill matter?

2003-07-14, 17:37	#14
asdf Sep 2002 2²×3×5 Posts	Then I say that it is uncertain who will win.

2003-07-14, 18:15	#15
NickGlover Aug 2002 Richland, WA 132₁₀ Posts	I think the hill size and length of the dip matter. The 2nd puck will have an advantage over the 1st because of the time it spends travelling at a higher speed. However, it also has a slightly longer distance to travel because of the hills. So, which puck wins depends on how these two factors weigh against each other.

2003-07-14, 18:45	#16
Xyzzy "Mike" Aug 2002 2⁵·257 Posts	My guess is the second puck will accellerate faster initially, and because of this, it will lose energy faster due to the fact that the faster you go the air friction becomes greater... (I mean it is not linear) I think this is why airplanes have to dive (go faster initially) to slow down faster... I was told this by a pilot who had to land unexpectedly in a field due to a engine failure... He had to scrub off a lot of airspeed and diving did the trick... He also mentioned to me that airspeed and altitude were the only two things that mattered to him, and either could be converted to the other, or something like that... Well, I'm just guessing I suppose...

2003-07-14, 18:56	#17
eepiccolo Dec 2002 Frederick County, MD 2×5×37 Posts	Oops, I forgot to mention that there is no air drag/friction, either. If there was, the problem would be indeterminate.

2003-07-14, 22:16	#21
NickGlover Aug 2002 Richland, WA 2²×3×11 Posts	Ok, now I understand what you are saying, and agree that your conclusion is correct. My problem was that you said the puck does not tumble which I took as a less extreme version of flying off the cliff. I'm guessing you meant that any hill configuration which would cause the puck to leave the surface is invalid (in which case the shape of the hill is relevant). I thought you meant that we didn't have to consider the effects of leaving the surface.

2003-07-14, 22:20	#22
ET_ Banned "Luigi" Aug 2002 Team Italia 3²×5×107 Posts	Same initial velocity. Gravity No friction. The momentum gained is lost. They tie. Luigi Where got I wrong? :D Well, of course... I did not consider that the second puck was quicker for the time it ran in the hole... The second puck wins.