Faster than
FREEFALL
?
Yep! You CAN demonstrate acceleration faster than freefall in your classroom. I
got this from
Department of Applied Physics of the Delft University of Technology in the
Netherlands
. (AFTER seeing this on their website,
http://www.tn.tudelft.nl/cdd/
, I was told this appeared in
The Physics Teacher
, Vol 34, Sept '96, pp 368-73.
History
:
Ever ask a Bungee Jumper why he does what he does? I have a buddy who skydives
and bungees. He swears that bungeeing is much more exhilerating. I always
assumed it was simply because of the combination of the falling, deceleration
and complete change of direction toward the bottom of the "bounce". However,
upon finding this little gem and testing it out myself, WOW! Take a look at the
pict.
Note the toilet paper has NOTHING to do with this! You just never know when you
need some... Actually, it's for another demo on "SLOWER than 'g'".
SET-UP
: As you can see, this simply consists of dropping two wooden blocks from a
good height. I use 6 inch long sections of regular ole 2x4 stud stuff. (The TOP
image above is from Delft's Website. The 2nd image is from my classroom. I will
update it to my set-up as soon as I can find my dern new pictures of it.) I
painted the blocks different colors to distinguish them better while falling.
The height I use for the most obvious result is 9 meters - using a high 2nd
floor stairwell at school. It works OK as a quik demo from the top of a 4 m (12
ft, sorta...) ladder in the classroom, but things happen so fast some kids
don't notice the difference. Videotaping helps if you can play it back n
SloMo...
One block is attached to the end of a chain, easily available at your friendly
neighborhood home supply store. The other is free. Loosen the clamp that holds
both in place and watch the fall. The one attached to the chain will invariably
hit the floor first!
THEORY
:
As the end of a bullwhip reaches supersonic speeds by applying only a small
speed to the handle end, a bungee cord internally causes the end to "snap"
faster than normal. The explanations actually vary, but all center around
Conservation of Mechanical Energy and Uncle Newton's 3rd Law of Motion.
An energy examination yields a formula that always yields an 'a' greater than
'g' for the jumper.
According to the equation, a = g(1 + m(4+m)/8), where m is the ratio of the
mass of the bungee (chain) to the mass of the jumper (block), 'a' always yields
a value larger than 'g'.
Intuitive explanations without the ugly math?
-
Well, like a bullwhip, energy from the whole chain is transferred along its
length as it "uncoils". Since the mass of the "uncoiled" part keeps decreasing
and energy MUST be conserved, the KE increases.
-
Or, how 'bout this one; As the chain falls, each link must stop. This must be
caused by an upward force. Due to Uncle Newton's 3rd Law, this upward force is
accompanied by an equal downward force. This downward force causes a slightly
larger acceleration on the remaining mass.
-
Rocket Science? The downward moving part of the chain acts like a rocket -
ejecting its fuel of other links. Since the ejected link is at rest and
actually shot upward from this chain "rocket", the remaining part of the chain
must move faster due to Uncle Newt's 3rd Law OR Conservation of Momentum,
whichever you prefer.
Cool, Huh?
