



Home /
Puzzle
Help / 





This is a very unusual puzzle, and
it has nice logic in it. We've got just a few great explanations to
this puzzle and now would like to present the winning answers. 





Solution by Bryan Feir 


The answer, I believe, comes
from two facts: the first is the concept of 'stiction'. It often
requires significantly more force to overcome the static friction of a
stationary object to start it moving than it does to keep it moving
once it already is.
The second is that the couplings between railway cars are not fixed
links, but have a certain amount of 'play' in them. The old standard
doublehook structure:
___
/ \
 / / 
\___/



allows the cars to be
connected and disconnected easily when they're close together, but
when the train is under power, the hooks lock together in such a way
to make it almost impossible to disconnect. A fairly simple mechanical
safety feature.
Since the train had been under power before the new locomotive was
added, all of the couplings would be locked together at full
extension. Therefore, the new locomotive would have to overcome the
stiction of every freight car at the same time. This would require a
much higher force than just pulling the train.
When the locomotive starts backing up, it is only pushing on the first
car; overcoming that stiction is relatively easy. Eventually that
coupling gets compressed as much as it can, and the second car gets
pushed back, and so on. The locomotive only has to overcome the
stiction of each car individually, added to the total weight of the
train once it gets that far back.
The same applies once the locomotive starts moving forward again: only
the first car's stiction must be overcome at first, until the coupling
reaches full extension. Each car starts moving at a slightly different
time, thus the extra force required to start the motion is spread out
over the length of time it takes for the train as a whole to reach
full extension. 





Solution by Geoffrey Mayne 


When the new engine first
connected, all of the couplings were in their extended state. To begin
moving, it needed to move all 100 cars at once. By backing up, it put
slack into some or all of the couplings. After doing this, it goes
forward accelerating one car at a time. How do I know there is slack
in the couplings? The train could never have backed up in the first
place if their weren't. 





Solution by RockyABQ 


Backing the locomotive
compressed all the couplers rearward. Then, when the locomotive moved
forward, it only had to pull the first car until the slack was taken
out in the forward direction. This continued with all the cars. The
additional velocity provided the momentum to overcome the inertia and
static friction of all the cars. 





Solution by Jim Haines 


This is a hoary old one!
A locomotive doesn't have the power to start a train moving all at
once. There must be slack in the couplings so that the locomotive
starts the first car and takes up the slack between the first and
second cars, then the moving locomotive and first car start the second
car moving, taking up the slack between cars two and three, and so on
until the entire train is moving.
Normally, when a locomotive brakes to a halt, all the cars close up so
all the slack in the coupling is available for the necessary
sequential start when the locomotive moves off again.
Somehow, during the swapping of one locomotive for another, the cars
were pulled apart, probably by the 2 nd locomotive shunting into them
when hooking up, jolting them apart. A slow backup will have closed
the cars together again so when they finally moved off they did so
sequentially. 





Solution by Michele Ely 


When the train engine backed
up the cars moved closer together so that when the engine began to
take off it was only pulling one car at a time picking up momentum as
it progressed. 





Last Updated: September 30, 2007 
Posted: July 14, 2002 









