On the first peg, there acts a force m g from
the towel, downwards. There is a tension T2
from the centre part of the washing line and
a tension T1 from the left side of the washing
line. On the second peg, there is again a
force m g acting down due to the towel, tension
T2 from the centre part of the washing line
and a tension T3 acting from the right part
of the washing line. The numbers on the parts
of the washing line in the first diagram correspond
to the tensions in those parts. By symmetry,
T1 must equal T3. Now, considering one half
of the washing line from the centre to one
of the poles, there is a total length 2 b
between these two points. Along the washing
line, there is a distance a, and then a second
distance a but at an angle theta to the horizontal.
This gives a horizontal distance of 2b - a
between one peg and the pole. The angle theta
is also the angle between the tensions, T1
and T3 and the horizontal. From the diagram,
we can see that cos(theta) must equal 2b minus
a divided by a. Since the system is in equilibrium,
using Newton's first law, the resultant force
must be 0. Therefore, resolving vertically
on either of the pegs gives T1 sin(theta)
is equal to mg. Resolving horizontally on
either of the pegs gives T1 cos(theta) equals
T2. It is the same on either of the pegs since
T1 is equal to T3. We can now solve these
three simultaneous equations.
