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

[NicholasAllen]

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

 

[minger]

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:
$$F = k\Delta x$$
Without the original length, you cannot find $$\Delta x$$ and therefore the instantaneous force exerted on the mass by the cord.

 

[NicholasAllen]

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 ?

 

[minger]

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.

 

[Hologram0110]

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...

 

[Curl]

If you don't know the natural length, you must know the elasticity constant.