20030817, 00:37  #1 
Jun 2003
The Texas Hill Country
3^{2}·11^{2} Posts 
The Railroad Puzzles
Number 1:
Out in West Texas there are many miles of perfectly straight track. Let us assume that some night we go out and select a section of perfectly welded track without any joints. We securely anchor each end of a section that is exactly 1 mile long. The next afternoon is a typical "scorcher" and the sun heats the track causing it to expand. Assume that the one mile of track is lengthened by only one foot (0.02%). Further assume that all the intermediate ties are loose and the track raises vertically to accomodate the extra length. If we allowed the track the make abrupt bends, it could instantly jump up six inches and then abruptly drop six inches to include the extra length. Or it could go up 3 inches, return to the normal elevation and make a second similar 3 inch step. Or it could make 4 steps of 1.5 inches, etc. But, steel rail does not have those characteristics. So assume that it raises up in a smooth circular arc. The high point will be at the middle and it will slowly decend toward each end. The question is: "How high will the midpoint be above its nominal location?" 
20030817, 00:43  #2 
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
Number 2:
A freight train is exactly one mile long at rest. If it is travelling at 60 miles per hour, how long will it be? PS: This was an actual question on the final exam of a physics course. 
20030817, 01:06  #3 
Aug 2003
Snicker, AL
7·137 Posts 
I'll raise one question just for the fun of it. Years ago I was told that railroad track does not expand in the lengthwise direction rather it expands in width and height. Your posted question is based on the length expanding. Am I to presume that this is just a mental exercise, not a question based on fact?
On the second question, I presume you are wanting to apply Einsteins equations to the train. Fusion 
20030817, 01:27  #4  
Jun 2003
The Texas Hill Country
3^{2}·11^{2} Posts 
Quote:
Quote:
Yes, I think that you should consider "The Lorentz Transformation". 

20030817, 01:34  #5  
"William"
May 2003
New Haven
3·787 Posts 
Quote:
Or perhaps the person was trying to say that the overall length of a multirail stretch does not change because the expansion gaps absorb the difference. 

20030817, 01:42  #6  
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
Quote:
(And after you do the math, you too may wonder just how they make "welded rail" work. In olden days, the "clickityclack of the railroad track" was because of those gaps.) 

20030818, 04:28  #7 
Sep 2002
1421_{8} Posts 
How could only going 60 MPH be enough to make the train any longer in a measureable sense? I thought Einstein's theories only dealt with speed at or near that of light.

20030818, 04:59  #8 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{3}×7×167 Posts 
In regards to puzzle 2:
Using a North American style frieght train, we could esimate how much longer the train would be. When the train is stopped it is exactly 5280' long and all the couplers are in the "clopased" state. As the train starts up the engine(s) begin to pull the couplers into the running position. With a rough figure of 3" expansion per coupler. For the purposes of the test figure the 'old fashion' 60' box cars (and engine). This gives us 88 total cars (and engine). Giving 87 couplings. 87 x 3 = 261" = 21.75' 5280 + 21.75 = 5300.75' total length at any non relativistic speed. 
20030818, 05:46  #9 
Aug 2003
Snicker, AL
1677_{8} Posts 
Re the train question:
Presuming that the train is exactly 5280 feet long at rest and that its length is fixed i.e. it doesn't stretch due to couplings, etc. If the train accelerates to 60 mph, it would shrink by about .0002 feet in length. If it accelerated to 1/2 lightspeed, it would shrink much more dramatically For all practical purposes, the train stays the same length as it approaches light speed, its frame of reference shrinks though so an outside observer thinks the train is shorter. What happens when a relativistic object meets another relativistic object head on? What if a relativistic object (that weighed just one pound at rest) struck the earth doing .8C? Relativistic object is defined as anything moving more than half the speed of light. 
20030818, 09:19  #10 
Jul 2003
41 Posts 
In terms of relativity the length of the train depends on the frame of reference used to measure it.
In the train's frame of reference it is always 1 mile long, no matter how it's moving. In the frame of reference of the tracks, the train would be shorter by three thousands of an inch. But the question doesn't specify which frame you're using so it's meaningless as an exam question (unless you want the answer "it depends"). Puzzles, of course, on the other hand, tend to over or under specify the conditions as part of the puzzle  in this case my answer is "I don't know". Graeme 
20030818, 10:25  #11  
Aug 2002
Richland, WA
2^{2}·3·11 Posts 
Quote:


Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
logic puzzles  science_man_88  Puzzles  0  20110328 17:31 
Jigsaw Puzzles  davar55  Puzzles  10  20080409 18:48 
Some puzzles  fetofs  Puzzles  32  20051026 18:32 
Circle Puzzles 1  mfgoode  Puzzles  18  20050711 11:51 
Puzzles without solutions  Orgasmic Troll  Puzzles  12  20030716 09:36 