Bungee Jumper Oscillation: Determine Spring Constant

In summary, the spring constant for bungee jumping is used to calculate the necessary length of the bungee cord and the maximum distance the jumper will fall before being pulled back up. It can be measured using a spring scale or experiments, and can be affected by factors such as cord length, thickness, material, temperature, and humidity. The spring constant directly impacts the safety of the experience, as a too low or too high constant can lead to injury. However, it is not the only factor and other important factors include the structural integrity of the platform and equipment, proper training, and following safety protocols.
  • #1
lindsk
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A bungee jumper, whose mass is 87 kg, jumps from a tall platform. After reaching his lowest point, he continues to oscillate up and down, reaching the low point two more times in 8.5 s. Ignoring air resistance and assuming that the bungee cord is an ideal spring, determine its spring constant.
 
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What do you think? Can you show us all relevant equations as well as your attempted solution?
 
  • #3


To determine the spring constant of the bungee cord, we can use the equation for simple harmonic motion: T = 2π√(m/k), where T is the period of oscillation, m is the mass of the bungee jumper, and k is the spring constant.

In this scenario, the period of oscillation is 8.5 s, and the mass of the bungee jumper is 87 kg. We can plug these values into the equation and solve for k:

8.5 s = 2π√(87 kg/k)
8.5 s = 2π√(87 kg/k)
4.25 s = π√(87 kg/k)
(4.25 s)^2 = π^2(87 kg/k)
18.0625 s^2 = 87 kg/k
k = (87 kg) / (18.0625 s^2)
k = 4.811 N/m

Therefore, the spring constant of the bungee cord is 4.811 N/m. This value is important as it represents the stiffness of the bungee cord and determines the amount of force it exerts on the bungee jumper during the oscillation. This information can be useful for designing bungee cords for safe and enjoyable bungee jumping experiences.
 

Related to Bungee Jumper Oscillation: Determine Spring Constant

1. What is the purpose of determining the spring constant for bungee jumping?

The spring constant for bungee jumping is used to calculate the necessary length of the bungee cord to ensure a safe and successful jump. It is also used to determine the maximum distance the jumper will fall before the cord reaches its maximum stretch and begins to pull the jumper back up.

2. How is the spring constant measured for bungee jumping?

The spring constant can be measured using a spring scale or by conducting experiments to determine the relationship between the force applied to the bungee cord and the resulting stretch. This can be done by varying the weight of the jumper and measuring the corresponding change in length of the cord.

3. What factors can affect the spring constant for bungee jumping?

The length and thickness of the bungee cord, as well as the material it is made of, can all affect the spring constant. Additionally, the temperature and humidity of the environment can also alter the spring constant.

4. How does the spring constant impact the safety of a bungee jumping experience?

The spring constant directly affects the amount of stretch and recoil of the bungee cord. If the spring constant is too low, the cord may not provide enough resistance and the jumper could hit the ground. Conversely, if the spring constant is too high, the cord could snap or cause excessive recoil, which could also lead to injury.

5. Is the spring constant the only factor that determines the safety of a bungee jumping experience?

No, there are many other important factors that contribute to the safety of bungee jumping, such as the structural integrity of the jumping platform and harness, proper training and equipment, and following safety protocols. The spring constant is just one piece of the puzzle in ensuring a safe and enjoyable bungee jumping experience.

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