How Far Will a 76 kg Person Fall with a Doubling Bungee Cord?

  • Thread starter Thread starter NicholasAllen
  • Start date Start date
  • Tags Tags
    Bungee Mathematics
AI Thread Summary
To determine how far a 76 kg person would fall with a bungee cord that stretches to twice its natural length, one must consider the cord's behavior as a spring. The force exerted by the cord can be described using the formula F = kΔx, where k is the spring constant and Δx is the change in length. Without knowing the natural length of the cord, calculating Δx becomes impossible, making it challenging to derive a specific formula. A free body diagram can help visualize the forces acting on the person, leading to an equation where the net force equals zero at rest. Understanding the spring constant in relation to the mass and cord length is essential for further calculations.
NicholasAllen
Messages
5
Reaction score
0
Hi,

I was wondering whether there is a formula in terms of length and mass which would provide how far a person would fall is they were attached to a bungee cord rope which stretched to twice it's natural length when an object of 76 kilos was hung from it at REST from the free end?

I'm finding this difficult as we are not given a natural length... Oh also in this case I am neglecting the height of the person.

I am a Maths C student, so any physics explanations would not be much help as I'm hopeless at physics (whereas quite okay at maths c).

Thanks
 
Engineering news on Phys.org
You're correct about not knowing the unstretched length. One could think of a bungee cord simply as a spring. In that case, the force exerted is:
<br /> F = k\Delta x<br />
Without the original length, you cannot find \Delta x and therefore the instantaneous force exerted on the mass by the cord.
 
So does that mean there is no formula?
Because my maths C teacher is convinced there is, and i need it as a preliminary sort of thing to begin an assignment - maybe it is a formula in terms of x, l and m ?
 
I mean that's the formula for the resistance felt by the person. You could draw a free body diagram; the net force being mass times acceleration. The forces in each direction are mass and the resistance force from the bungee. However, saying that the cord will stretch twice it's length, but not specifying that length will not allow a person to get the change in length of the cord.
 
This can be done by assuming the rope behaves as a spring as minger described.

-Draw free body diagram of the person at rest hanging from the end of the rope using the known condition (76 kg mass, delta x = l)
-> At rest means no acceleration, therefore the vector sum of all forces adds up to zero. This leads to an equation.
-> Solve for spring constant k in terms of l and m

Since this is homework I'm not going to give you the rest of the solution, but hopefully now that you know the spring constant, and what minger described, you can come up with something on your own for the variable mass case...
 
If you don't know the natural length, you must know the elasticity constant.
 

Thread 'Query on Isentropic relationships (such as PV^gamma = constant)'

Hi all, I have a question. So from the derivation of the Isentropic process relationship PV^gamma = constant, there is a step dW = PdV, which can only be said for quasi-equilibrium (or reversible) processes. As such I believe PV^gamma = constant (and the family of equations) should not be applicable to just adiabatic processes? Ie, it should be applicable only for adiabatic + reversible = isentropic processes? However, I've seen couple of online notes/books, and...
View full post »
Thread 'How can I find the cleanout for my building drain?'

Thread 'How can I find the cleanout for my building drain?'

I am a long distance truck driver, but I recently completed a plumbing program with Stratford Career Institute. In the chapter of my textbook Repairing DWV Systems, the author says that if there is a clog in the building drain, one can clear out the clog by using a snake augur or maybe some other type of tool into the cleanout for the building drain. The author said that the cleanout for the building drain is usually near the stack. I live in a duplex townhouse. Just out of curiosity, I...
View full post »

Thread 'Dry sump pump issue'

I have an engine that uses a dry sump oiling system. The oil collection pan has three AN fittings to use for scavenging. Two of the fittings are approximately on the same level, the third is about 1/2 to 3/4 inch higher than the other two. The system ran for years with no problem using a three stage pump (one pressure and two scavenge stages). The two scavenge stages were connected at times to any two of the three AN fittings on the tank. Recently I tried an upgrade to a four stage pump...
View full post »

Similar threads

Bungee jumping and Conservation of energy
Replies
3
Views
2K
Final amplitude with damping of bungee cord
Replies
8
Views
3K
How Does a Bungee Jumper's Energy Change During a Jump?
Replies
14
Views
6K
Max speed and tension of bungee jump?
Replies
3
Views
7K
How would you quantify and predict the efficiency of a bungee cord?
Replies
3
Views
4K
A Closer Look at Bungee Jumping Physics
Replies
26
Views
5K
Bungee jumping with elastic cord and rigid rope
Replies
1
Views
3K
Calculating Bungee Jumping Acceleration: Physics and Calculus Problem Solutions
Replies
2
Views
2K
Spring constant and bungee jumping.
Replies
1
Views
4K
What is the correct spring constant for the bungee cord?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top