Solving Engineering Equation for Bungee Jumper: What's the Answer?

In summary, the problem is to derive an equation for k using the weight of a bungee jumper, the unstretched length of the cord, and the height of the dam. The derived equation is K = (m * g * h) / (h - b), where m is the weight of the jumper, g is the acceleration of gravity, h is the height of the dam, and b is the unstretched length of the cord. This equation can be used to determine the unstretched length of the cord and the spring constant, k, in order to prevent the jumper from hitting the ground.
  • #1
IanL
2
0
I have a problem for an engineering class I am taking. It reads:

Derive an equation for k using the weight of a bungee jumper (170 lbs) the unstretched length of the cord (unknown) and the height of the dam from which the jumper is jumping off of (722 ft)

What I have come up with is:

K=(170lbs*32.2ft/sec^2)/722ft
K=7.58lb ft/sec^2

Is this correct?

What would be the unstretched length of the cord so that the jumper has a speed of 0 when at the bottom of the jump?

If k=7.58, then the unstretched length should be

L=722/7.58
L=95.25

This does not seem possible...
 
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  • #2


i don't know how you justified your spring constant from the acceleration of gravity and the mass of the man.

Although

You can right it as a potential U = mgh + .5k(h-b)2

and the kinetic energy T = .5mv2 which i don't think you need

before the guy jumps mgh is at a maximum if the ground if the point of reference, and

the spring potential is 0 because the cord isn't stretched, but when the cord is stretched such that h=0 then the spring potential is at a max. Thus U is a constant

you know the differential of U with respect to h would be force

0 = mg +k(h-b)
 
  • #3


I understand that. The problem is asking for an equation for K derived from the given information. As I understand it K is the spring constant.

Thus, how would you derive an equation to figure out the unstretched length and the spring constant so that the bungee jumper does not hit the ground?
 

FAQ: Solving Engineering Equation for Bungee Jumper: What's the Answer?

1. How do you determine the appropriate length of a bungee cord for a specific weight?

The appropriate length of a bungee cord can be determined by using the formula: L = (2Wg)/(Ks), where L is the length of the cord, W is the weight of the jumper, g is the acceleration due to gravity, K is the spring constant of the bungee cord, and s is the safety factor (typically between 4-6). By plugging in the values for the weight and safety factor, the length of the bungee cord can be calculated.

2. What is the significance of the spring constant in the equation for bungee jumping?

The spring constant represents the stiffness of the bungee cord. A higher spring constant means that the bungee cord will stretch less, resulting in a shorter length and a lower risk of the jumper hitting the ground. On the other hand, a lower spring constant means the bungee cord will stretch more, resulting in a longer length and a higher risk of the jumper hitting the ground. It is important to choose a suitable spring constant to ensure the safety of the bungee jumper.

3. Is the equation for bungee jumping affected by the location or altitude of the jump?

Yes, the location and altitude can affect the equation for bungee jumping. This is because the acceleration due to gravity varies slightly at different locations and altitudes. However, this difference is usually negligible and does not significantly impact the overall calculation of the bungee cord length.

4. Can the equation for bungee jumping be used for any type of bungee jumping, such as from a bridge or a crane?

Yes, the equation for bungee jumping can be used for any type of bungee jumping as long as the variables are adjusted accordingly. For example, if the bungee jump is from a bridge with a higher height, the length of the bungee cord will need to be longer to accommodate for the increased distance.

5. Are there any other factors that should be considered when calculating the bungee cord length besides the weight and spring constant?

Yes, there are other factors that should be considered when calculating the bungee cord length, such as the elasticity of the bungee cord material and the aerodynamics of the jumper. These factors can impact the stretch and movement of the bungee cord, and should be taken into account for a more accurate calculation.

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