Strings

1
Strings
A string can only support tension along the
tangent to the string. It cannot support
compression or shear stress.
Cosine law
b
a
t2
t1
F
2
Tensions
Torque around 1 0.
1
d
q2
q0
3
Stretchy Strings!
b
a
t2
t1
Now a and b are functions of t1 and t2
F
Cannot be solved in closed form. Need some sort
of approximation method.
4
Method of Successive Approximations
Step 1 Assume ki0 solve for ti.
Step 2 Given ti, find new lengths li.
Step 3 Given li, find new tensions ti.
Step 4 Reiterate until desired precision is
achieved.
Works because new length is bounded by previous
two.
5
Hanging Strings
(x2,y2)
For any section along string (tension is always
tangential to curve of string)
F0
(x1,y1)
t
s
q
6
Hanging Strings (2)
7
Hanging Strings (3)
Catenary
Three constants for y1, y2, and l.
8
Hanging Strings (4)
Length
Do different weights give different shapes?
9
Hanging Strings (5)
Do different weights give different shapes?
10
Shape Depends on Length, y1 and y2
See Mathematica Notebook