# Falling Elevators

1. Jun 10, 2004

### suffian

edit::
nm, i figured it out. i forgot to account for the weight of elevator in the "If static friction.. " part. thx anyway. i'm sorry i can't delete the post.
::edit

I hit a brick wall over yet another problem concerning energy methods, basically a mismatch between my answer and the book's. I would appreciate whoever has the time to look this over and guess where I might be going wrong.

Anyway, here's the problem verbatim:

Begin with work-energy formula:
\begin{align*} \Delta K =& \, W_\text{gravity} + W_\text{friction} + W_\text{spring} \\ 0 - \frac{1}{2}mv^2 =&\, mgX - fX - \frac{1}{2}kX^2 \end{align*}

Quadratic formula to find compression distance X (neglect neg ans):
$$X = \frac{1}{k} (mg - f + \sqrt{ (mg-f)^2 +kmv^2 })$$

If static friction will hold elevator at X, then it follows:
$$F = kX \leq f \text{ or } X \leq \frac{f}{k}$$
$$X = \frac{1}{k} (mg - f + \sqrt{ (mg-f)^2 +kmv^2 }) \leq \frac{f}{k}$$

Manipulate to find assertion about spring constant:
$$k \leq \frac{f}{mv^2} (3f - 2mg)$$
$$k \leq \frac{[17000 \text{ N}]}{[2000 \text{ kg}][25 \text{ m/s}]^2} (3[17000 \text{ N}] - 2[2000 \text{ kg}][9.80 \text{ m/ss}])$$
$$k \leq 160 \text{ N/m}$$

So, answer is not the same.

edit::
nm, i figured it out. i forgot to account for the weight of elevator in the "If static friction.. " part. thx anyway. i'm sorry i can't delete the post.
::edit

Last edited by a moderator: Jun 10, 2004