| Mechanics > Work
and Energy > Conservation of Energy |
DCS# 1M40.xx |
| 3 pieces of elastic cord: 0.25 m,
0.50 m, and the bungee jumper's |
202-14-D |
| bungee jumper |
202-14-D |
| eyebolt in unistrut grid |
202 |
| ladder |
201A |
| tape measure |
101-05-E2 |
| 1 kg mass |
202-04-E |
| meter stick |
101-05-F |
| two-meter
stick |
113 |
| balance |
101-05-A |
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 |
8 N/ 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 1-kg mass and tape measure or two-meter stick to
determine the spring constant of a 0.5 m and a 0.25 m piece of
cord. Use these values to determine k for the bungee cord.
The series part of the series
and parallel springs demonstration can be used to show the
relationship between k and L.
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.