A tall bald student (height 2.1 meters and mass 95.1 kg) decides to try bungee j

Question

A tall bald student (height 2.1 meters and mass 95.1 kg) decides to try bungee jumping from a bridge. The bridge is 36.7 meters above the river and the "bungee" is 25.3 meters long as measured from the attachment at the bridge to the foot of jumper. Treat the "bungee" as an ideal spring and the student as a 2.1-meter rod with all the mass at the midpoint. This particular student desires to stay dry and he jumps from the bridge in a standing position. What is the minimum spring constant of the "bungee" that will allow the student to get as close as possible to the water but still stay dry? Assume that he begins at a standing position and "falls" from the bridge.

Please help! Thanks!

Explanation / Answer

The total distance student  will fall is:
h = (36 m) - (2.1 m) = 33.9 m

The change in gravitational potential energy over that distance will be
PEg = (95.1 kg)×(9.8 m/s²)×(33.9 m) =31594 J

The stretching distance of the cord is:
d = (33.9 m) - (25.3 m) = 8.6 m

At that stretching, the change in gravitational potential energy

(31594 J) = k × (8.6 m)² / 2
k = 854 N/m < - - - - - - - - - - - - - - - - - - answer

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.