Just take a chain, and put
it on a pulley, then, let it fall. It seems simple, doesn't it ? But
now, take a video of it, with a 1000fps camera (fig.1), and you'll see
a really amazing motion : first, a loop, and then, an extremely
violent whiplash. The problem is to understand this motion.
Fig.1 : A chain
of 35g, for 140cm (~0,25g/cm). Filmed with a 1000fps camera.
We had the idea to control the imbalance of the chain on
the first place, and to give the chain a certain mass to carry on
a second time. We found that an imbalance more significant would only
reduce the moment between the launching and the slap (fig.2 and 3). But
the carried mass had an interesting result : when weight's mass is next
to the chain one, the slap is greater than normal (fig.4 and 5). It
shows the importance of acceleration, given here by the mass. We
noticed that with a 100g mass, there's no big differences with a 200g
one (fig.6 and 7).
Fig. 2 and 3 : at the left one, we set an imbalance of 5
cm, and at the
right one, an imbalance of 30 cm. We can see that there's no
significant differences. It's not shown here, but the right one gets to
the whiplash faster than the left one.
Fig.4 ans 5
: the chain on the left carry a 30g mass, and the
chain on the right a 60g one. We can see a slight difference between
the two, and a great one between a chain carrying its own weight
(excluding the mass, there's no imbalance).
Fig. 6 and 7 :
the chain on the left is carrying a 100g mass, and
the chain on the right a 200g one. The difference between the two is
not significant, so we can say that the motion is not amplified when
the mass is heavier than a certain one.
So, with this results, we can say that the acceleration
on the chain is important, but we found other informations. Actually,
we measured forces exerted on the pulley. The vertical one, and the
lateral one (not independently), with a sensor below the pulley. We
found that the vertical force was slowly decreasing, and at a certain
point, reaches 0, and that the lateral one was at the begging over 0,
but not that much, and after the vertical force reaches 0, get to a
high point, that is near to 10 N. This corresponds to the whiplash,
that is extremely violent, and the vertical force reaches 0 because the
chain is in free fall just after the loop. Unfortunately, we don't have
a good measure enough to show it here, because we couldn't separate the
vertical force from the horizontal one. We ended up to think that this
motion is due to the tension on the
chain. The explanation is that we can see a wave that doesn't move when
you look at it from the outside, so this wave has a velocity equal to
chain velocity. Due to this explanation, tension could be what causes
the chain to have this whiplash.