Person hanging over a ledge counterbalanced by a chair

[gmtarknoid]

Hi All,

This isn't a homework problem, but this forum seemed proper for this question. I'm a professional firefighter in California. We just learned this bailout technique and I'm curious as to the science behind why it works. Any insight would be greatly appreciated. Thanks!

-David Anderson

Homework Statement

A FF (m=90kg) is forced to bail out of a window due to extreme heat conditions. He ties off his mass-less rappel rope to a 5kg chair. In order for this procedure to work, the chair cannot move at all while he is rappelling down it. What variables make this work? Is it simply just the friction on the rope? Also, is there a critical angle theta that will make the system catastrophically fail? In other words, if the rope is parallel to the building and perpendicular to the floor (firefighter simply hanging straight up and down), does that make any difference than say if theta was 30 degrees (firefighter assumes classic rappel position)?

Homework Equations

W=mg (probably need to separate into x and y components)
W=T1

The Attempt at a Solution

 

[gneill]

Presumably the chair back is going to act as a lever, pivoting at the widow edge. The center of mass (C.O.M.) of the chair will be well below the pivot, probably located just below the seat level and just back from the center of the seat.

For the sake of argument, say that the chair is initially level with its back pressed against the wall. Its center of mass is located 45cm below the pivot point and 24cm out from the wall. The rope is tied to the top of the chair, and there's 1cm of chair back extending above the window sill (so that's the lever arm for the rope tension). Note that may be less than 1cm depending upon circumstances. This is just for illustration.

You should be able to calculate the torques about the pivot point given your other relevant data.