Bungee jump height/spring energy

In summary, customers of mass 53.0 kg will experience a bungee jump from a platform with an unstretched rope length of 52.6 m and spring constant 17.0 n/m. The distance below the platform that the rope will reach during the jump can be calculated using the equations for potential energy and spring energy, along with the assumption that g=9.8 m s-2. The correct equations to use are mgh=0.5kL^2-mgL, where h is the total stretched length of the rope and L is the distance from the platform to the lowest point, as well as PE=mgh and Spring energy=0.5kd^2.
  • #1
Matt123456789
2
0

Homework Statement


Imagine that you have been given the job of desiging a new bungee jumping platform. Customers of mass 53.0 kg will step off a platform, attached to a rope of unstretched length 52.6 m and spring constant 17.0 n/m.

How far below the platform will the end of end of the rope get during a jump? This is the lowest point it will ever reach, not where it settles down.

You may assume that g=9.8 m s-2.

Homework Equations


PE=mgh
KE=0.5mv^2
Spring energy=0.5kd^2

The Attempt at a Solution


- Set the distance from platform to when rope first goes taut as H, distance from H to to lowest point as L
- rearranged equations to get mgh=0.5kL^2-mgL
- also tried mgh=0.5kd^2 and solve for d
- got 90.6 and 91.5, both wrong, no idea what to do now
 
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  • #2
Matt123456789 said:
mgh=0.5kL^2-mgL
I think you're on the right track.
What is answer that is given, which makes you think you're answer is wrong?
 
  • #3
Matt123456789 said:

The Attempt at a Solution


- Set the distance from platform to when rope first goes taut as H, distance from H to to lowest point as L
- rearranged equations to get mgh=0.5kL^2-mgL
You explained the meaning of H and L, but what are h and d?
 
Last edited:
  • #4
The answer i submit is checked and I am told if I am wrong or right, but not what the actual answer is.

h is the total height, and d i think is meant to be L
 
  • #5
Matt123456789 said:
The answer i submit is checked and I am told if I am wrong or right, but not what the actual answer is.

h is the total height, and d i think is meant to be L
In this case, your first equation is wrong, and there are too many unknowns in the second equation.

If you count the potential energy zero at the height of the platform, what is the PE at the deepest position, at depth h? How much is the rope stretched then? What is the elastic energy? What is the speed?
 
  • #6
Matt123456789 said:
h is the total height,
Do you mean the length of the rope?
If so I don't see why your 1st equation could be wrong.
 
  • #7
Suraj M said:
Do you mean the length of the rope?
If so I don't see why your 1st equation could be wrong.
The OP said that h was the total (stretched ) length of the rope, that is, h=H+L:. The equation
mgh=0.5kL^2-mgL
is wrong.
 
  • #8
ehild said:
The OP said that h was the total (stretched ) length of the rope
oh! I thought he said it was the length of the rope,thats why i put the condition
Suraj M said:
Do you mean the length of the rope?
If so ...
I misunderstood, sorry
 

Related to Bungee jump height/spring energy

1. What is the maximum height for a safe bungee jump?

The maximum height for a safe bungee jump can vary depending on several factors such as the weight and age of the jumper, the type of bungee cord used, and the location of the jump. Generally, a safe bungee jump height is considered to be between 50 to 200 feet.

2. How does the height affect the spring energy of a bungee jump?

The height of a bungee jump directly affects the amount of potential energy stored in the bungee cord. The higher the jump, the more potential energy is stored in the cord, resulting in a greater release of kinetic energy when the jumper reaches the bottom of the jump.

3. What is the ideal spring energy for a bungee jump?

The ideal spring energy for a bungee jump is determined by the weight and height of the jumper. The goal is to have enough spring energy to provide a thrilling and safe jump, but not so much that the jumper is at risk of injury. A professional bungee jump operator will calculate the ideal spring energy for each individual jumper.

4. Can the spring energy of a bungee jump be controlled?

Yes, the spring energy of a bungee jump can be controlled by adjusting the length and thickness of the bungee cord. A longer and thinner cord will result in a lower spring energy, while a shorter and thicker cord will have a higher spring energy. Bungee jump operators carefully calculate and control the spring energy to ensure a safe and enjoyable jump for each participant.

5. Is there a limit to how high a bungee jump can be?

There is no set limit to how high a bungee jump can be, but there are practical limitations based on safety and physics. The higher the jump, the more potential risk for injury due to the increased speed and impact at the bottom of the jump. Additionally, at extreme heights, the bungee cord may stretch beyond its maximum capacity, resulting in a less thrilling and potentially dangerous jump. Bungee jump operators carefully consider these factors when determining the maximum height for a jump.

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