Bungee Jump-Springs and Energy

In summary, a person with a mass of 90kg bungee jumps off a bridge 80m above the water using a bungee chord with a length of 25m and a spring constant of 30 N/m. The minimum distance they will be from the surface of the water is 102m, assuming the spring constant is actually 300 N/m. This was confirmed by a discussion with a TA at OSU.
  • #1
Furby
21
0
Bungee Jump--Springs and Energy

Homework Statement



A person bungee jumps off a bridge.
The person's mass is 90kg.
The height of the bridge above the water is 80m.
The bungee chord has a length of 25m.
The bungee chord's spring constant is 30 N/m.
What is the minimum distance the person will be from the surface of the water?

Homework Equations



PEs=1/2*k*x2
PEg=m*g*h

The Attempt at a Solution



I assigned the point of jump at the height of the bridge as y=0, thus as the jumper falls his PEg increases, becoming more negative. Kinetic energy is growing at the same rate until 25m, the chord's equilibrium point, where the chord will begin to stretch and exert a force on the jumper opposite to gravity.

Afterwards the kinetic energy begins to convert to PEs always growing in equal value to the constantly increasing PEg. Thus at the end, or 'bottom' of the person's jump, he will no longer have any KE, and thus:

mgh=1/2*kx2
h=25+x

Use some algebra and you get a quadratic:

15x2-882x-22050=0

x=77.715m

Which add the initial 25m and you get 102m, obviously exceeding the 80m height. The bungee jumper would then easily hit the water. I solved the problem another way assigning y=0 at the point of greatest KE (25m) and set PEg to be 0 at this point as well, and received the same answer.

My first assumption is that there was a typo and the problem is intended to have a 300 N/m spring constant, but I'm curious to see if I did anything wrong?
 
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  • #2


That is correct. My TA did the same problem in discussion today. Do you go to OSU?
 
  • #3


It looks spot-on, just some bad numbers.
 

FAQ: Bungee Jump-Springs and Energy

1. How do bungee jump-springs work?

Bungee jump-springs work by storing potential energy when they are stretched to their maximum length. When a person jumps, the potential energy is converted to kinetic energy as the jumper falls, and the spring recoils back to its original length, slowing the jumper's descent and preventing them from hitting the ground.

2. Are there different types of bungee jump-springs?

Yes, there are different types of bungee jump-springs that vary in their elasticity and strength. Some springs are designed for shorter jumps, while others are better suited for longer jumps. It is important to choose the right type of spring for a safe and enjoyable bungee jumping experience.

3. How is the energy of a bungee jump-spring calculated?

The energy of a bungee jump-spring can be calculated using the formula E = 1/2kx^2, where E is the energy in joules, k is the spring constant, and x is the displacement (change in length) of the spring. The spring constant is a measure of the spring's stiffness, and it varies depending on the type and size of the spring.

4. What safety precautions are taken with bungee jump-springs?

There are several safety precautions that are taken with bungee jump-springs, including regular inspections and maintenance of the springs, using high-quality materials, and following strict safety protocols during jumps. It is also important for jumpers to have proper training and wear appropriate safety gear.

5. Can bungee jump-springs ever break?

While bungee jump-springs are designed to be strong and durable, they can break if they are not properly maintained or if they are subjected to excessive force. That is why it is important for bungee jumping companies to follow strict safety regulations and for jumpers to only use equipment that has been properly inspected and approved.

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