Rock Climbing and Differential Equations: The FallFactor - PowerPoint PPT Presentation

1 / 21
About This Presentation
Title:

Rock Climbing and Differential Equations: The FallFactor

Description:

Rock Climbing and Differential Equations: The Fall-Factor ... Concept in Rock-Climbing' The College Mathematics Journal, v.36, no.2, March, 2005, pp. 135-140. ... – PowerPoint PPT presentation

Number of Views:338
Avg rating:3.0/5.0
Slides: 22
Provided by: dancu3
Category:

less

Transcript and Presenter's Notes

Title: Rock Climbing and Differential Equations: The FallFactor


1
Rock Climbing and Differential Equations The
Fall-Factor
  • Dr. Dan Curtis
  • Central Washington University

2
Based on my article Taking a Whipper The
Fall-Factor Concept in Rock-Climbing The
College Mathematics Journal, v.36, no.2, March,
2005, pp. 135-140.
3
  • Climbers use ropes and protection devices
    placed in the rock in order to minimize the
    consequences of a fall.

4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
  • Intuition says
  • The force exerted on the climber by the rope to
    stop a long fall would be greater than for a
    short fall.
  • According to the lore of climbing, this need not
    be so.

8
protection point
climber
belayer
9
protection point
climber
belayer
10
protection point
climber
belayer
11
L un-stretched length of rope between
climber and belayer.
12
DF
DT
13
The Fall-Factor DT / L
Climbing folklore says The maximum
force exerted by the rope on the climber is
not a function of the distance fallen, but
rather, depends on the fall-factor.
14
Fall-factor about 2/3
15
Fall-factor 2
belay point
16
position at start of fall
0
position at end of free-fall
DF
position at end of fall
DT
x
17
During free-fall
18
when
so
When
After the rope becomes taut, the differential
equation changes, since the rope is now
exerting a force.
19
The solution is
20
Maximum force felt by the climber occurs when
and
21
The maximum force is given by
Write a Comment
User Comments (0)
About PowerShow.com