2. Introduction
Bungee jumping involves jumping from a tall
structure while connected to a large elastic cord
The tall structure is usually a fixed object, such as
a building, bridge or crane in some cases it can
also be a mobile medium such as a hot air
balloon or helicopter that has the ability to hover.
3. Design Specification
Material used:
4’ length of 1.5mm electrical wire
rubber bands
a hook
a 2” x 2” x 2” wooden block
a plastic plate of 1” of water
5’ wooden stand
4. Spring constant
This was obtained by measuring the original
length of the rubber band and then adding the
2*2*2 cubic block and measuring its extension.
(Xe- Xo)=X
F=ma
Hence the spring constant K = (ma)/x
Using m= 0.060kg, a = g = 9.8, Xe- Xo=0.005m
K=(.06x9.8)/.005
=117.6N/m
5. What is the stiffness of a chain of N
rubber bands?
W K1
KN
Nd N
The stiffness of a chain of
Nd rubber bands is inversely
proportional to the number
of bands
W
6. Where are we?
We have the stiffness of
an average rubber band
K1
W K1
KN
We have the length of Nd N
an average rubber band
L1
We have a way to
predict the slack length
and stiffness of a chain
of N rubber bands
LN NL1
7. Conservation of Energy gives drop distance as
a function of the # N of RBs
1 K AV
wh K N (h LN )2 where K N and LN NLAV
2 N
2
w w w
h LN 2 LN
KN KN KN
2
w w w
N L1 2 L1
K1 K1 K1
8. Essentially:
½ kx2 = ½ mv2 + mgh,
where m=mass of block, v= velocity of block during
motion, h=height above datum level for the system
Substituting values determined for k and x, we get:
½ (k/2n)(h-nL)2 = ½ mv2 + mgh
So, ½ (117/2n)(0.0229-.072n)2 = ½ 0.06x(4.89)2 +
(0.06x9.8x0.279)
Solving gives n = 1.2 bands
Note velocity, v determined from conservation of energy mgH= ½
mv2 + mgh
9. At equilibrum point, v = u + at
However initial velocity =0, so using v=5.04s (from
conservation of energy for first system)
T = 5.04/9.8 = 0.5s
For oscillation, T (period) = 2(pi)√m/k
=0.15s
So time to reach water = 0.5 + (.15/2) = 0.6s
From experiment, time to settle (come to rest) =
4.7s
Also Lifetime of system, bands fail after 3-4
attenpts.
10. Sources of Errors
- Length not true due to looping and hooks
- Also system is not fixed so energy dissipated (eg
dampening effect of water.
