| Mechanics
> Work and Energy > Conservation of Energy |
DCS# 1M40.xx |
| elastic cord |
202-02-C3 |
| bungee jumper |
SAF |
| eyebolt
in unistrut nut |
202-01-C6 |
| ladder |
218 |
| tape
measure |
101-05-E2 |
| 1 kg weight hanger with pointer |
202-04-E |
| meter
stick |
101-05-F |
Use
energy conservation to determine the maximum length of elastic cord
that will allow a stuffed gingerbread man to safely bungee jump from
the hook near the ceiling of the lecture hall. The gingerbread
man will
drop with zero initial velocity from the hook, with one end of an
elastic cord tied around his feet and the other end tied
to the hook. Calculate the length of cord that
will stop his fall just above the
floor.
| mass
of jumper, m |
0.50
kg |
| initial
velocity of jumper, vo |
0
m/s |
| release
height of jumper*, h |
2.9
m |
| spring
constant of cord, k |
7.7
N/m / m * Lo |
| unstretched
length of cord, Lo |
? |
*This
is the height of the hook above the floor minus the length of the
gingerbread man: 3.3 - 0.4 m.
Use
the weight hanger and tape measure to determine the spring constant of
the piece of cord.
Initially the KE and elastic PE are zero, and the energy is entirely gravitational PE. At the bottom of the jump, when the gingerbread man is momentarily at rest at h = 0, the energy is entirely elastic potential energy of the cord. Neglecting air resistance and friction, the initial mechanical energy is equal to the final mechanical energy:
mgh = (1/2) k (h-Lo)2.
Use
the precut cord of the calculated length to test the prediction.