Finding the Right String Length for a Dropping Mass

[Masaharustin]

Homework Statement

My group and I have been tasked with choosing a string length so that a mass attached to two springs and the string, dropped from 4.29 meters, will fall within 25 cm of the ground. On the day of the drop we will be given the mass. We will use two springs that we already have and within ten minutes before the drop, must calculate the correct string length.
Constants:
Mass
drop height
the two springs (although the order in which they are used can be changed, we have taken data on both combinations)

*The only thing we can change is the length of the string from which the two springs and mass are hanging.

Homework Equations

Hooke's Law: k= mg/x
x = √(2U/k) * U is the spring's potential energy
u = .5kx^2

The Attempt at a Solution

The data we have taken so far as well as the calculated spring constants are in this google document.
https://docs.google.com/spreadsheet/ccc?key=0AlOf8KvTeCTrdHBxaldGXzB6WWo5RXVSbTAzTmt5VUE

With the information we have now we can predict the stretch of a stationary spring. However, we cannot figure out how to predict the stretch when taking into account the force generated by the mass' fall from 4.29 m.

We would very much appreciate it if someone could simply point us in the right direction on how to go about this, we've kind of been thrown in the deep end. Thanks.

 

[genericusrnme]

What conserved quantities are there going to be?

 

[Masaharustin]

Sorry what do you mean by conserved quantities?

Thanks for the reply.

 

[kushan]

The quantities which are not lost in the system

 

[Masaharustin]

This is a high school assignment, so I think [hope] we're not dealing with lost quantities.

EDIT: We made headway on the problem, air resistance is negligible. Are we correct in thinking that this equation applies?
ΔE = 0

-½ k x² + m g (h + x) = 0

 

[gneill]

This is a high school assignment, so I think [hope] we're not dealing with lost quantities.

EDIT: We made headway on the problem, air resistance is negligible. Are we correct in thinking that this equation applies?
ΔE = 0

-½ k x² + m g (h + x) = 0

Conservation of energy should apply to a good approximation, at least for the first "bounce" and before much energy can be lost to heat through mechanical flexing of the springs.

Can you describe the precise setup for the "bungee" trial in more detail? It looks like you've got two different springs that are to be attached in series. When will you get to know the order of their attachment?

When you measured your spring displacements, were they 'end to end' measurements (attachment point to attachment point)? Did they include allowances for whatever means is required to connect them end to end, to loads, or to fixed attachment points?

Where will the added string be attached? At the top of the springs or at the bottom between the last spring and the load mass?

How exactly is the drop to be performed? Will the load mass be dropped from the height of the fixed top spring attachment with the springs initially unloaded, or in some other fashion?

How will you include the mass of the springs themselves in the calculations?