The amount of heat generated in the bungee cord is substantial.?

Question

A bored college student decides to try bungee jumping. He attaches an elastic bungee cord to his ankles and happily jumps off a tall bridge across a river. He ends up barely touching the water before the cord jerks him back up. What is the mass m of the student? The length of the relaxed cord is y(e); the distance from the bridge to the river surface is y(0) (where y(0) > y(e)), and the spring constant of the elastic cord is k.
Which objects are reasonable to include in the system in this problem? a,the bridge b,the student c,the bungee cord d,the air
e,the river f,the planet earth g,the moon h,the sun
Which assumptions are reasonable to make in this problem?
The student can be treated as a particle moving with constant speed. The student can be treated as a particle moving with constant acceleration. The student cannot be treated as a particle. The air resistance is substantial. The air resistance is negligible.The amount of heat generated in the bungee cord is subs

Answer 1

If you idealize the motion without any resistance and an idealized spring representing the bungee cord, then the potential energy lost in the drop of the student from the bridge to the river is
m*g*y(0)

The energy then stored in the bungee at the moment the velocity of the student is zero, is:
.5*k*(y(0)-y(e))^2

this includes the earth, the student, and the bungee cord, and the relative vertical distance from the bridge to the river.

The other factors such as the moon and the sun will have negligible effect on the student's motion.

Air resistance could be a factor depending on the distance from the bridge to the river. Since air resistance creates a drag force, there will be energy loss due to this force which will reduce the extension of the bungee cord resulting in a hand in the water versus a face plunk. F=d*v^2
The terminal velocity of a skydiver presenting maximal area to the fall is about 40 m/s, which requires more than 800 feet of free fall. Since the maximum velocity occurs in the early stages of deccelartion due to the force of the bungee, air resistance is unlikely to be a major factor. The highest bridge in the world is Royal Gorge, Colorado U.S.A. , which is 950 feet from road surface to the gorge floor. If the bored college student forgets to attach the cord, they will plunge into the ground at about 95 miles per hour.

Heating the bungee is unlikely to be a factor since the cord is relatively light and suseptible to melting. The amount of heat that would be measurable as a loss in potential energy would likely cause spontaneous combustion in the cord.

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Answer 2

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