The tensioning force is M * g ( 1 + cos (deflection))
where deflection is angle from the vertical.
This is the sum of gravity and centripetal force
They add or subtract, so that
Max force is at the vertical position (cos(0) =1) as
described here in detail:
Search terms: Forces Pendulum
As myoarin-ga commented, fairly thin steel cable (1.2 mm diameter) can
BONUS : use calculator build into google seacrh engine to get:
you enter: cos(180 degrees) to get
cos(180 degrees) = -1 (this is rope straight up, total tension zero
g is acceleration of gravity (9.81 m /s /s in 'metric')
1 kg * (9.81 m/s/s) to get weight of 1 kilogram
(140 pounds) * (9.81 m/s/s)
(140 pounds) * (9.81 ((m / s) / s)) = 622.963761 newtons
weight of the man
to get tension at deflection 90 (horizontal) on a swing you enter:
(140 pounds) * (9.81 m/s/s) * (1+cos( 90))
(140 pounds) * (9.81 ((m / s) / s)) * (1 + cos(90)) = 343.830136 newtons
Request for Answer Clarification by
15 Aug 2005 06:05 PDT
Your answer totally ignores tension on the cable due to centriptal
force. I could have figure out that max "static" tension would just be
the weight of the person. That is a no brainer. But because the person
is swinging, there is an angular velocity, therefore, there will be an
added tension due to centriptal force which can be many G's. This
force will depend on weight, initial drop height and cable length. All
that data is provided in the question.
Clarification of Answer by
16 Aug 2005 01:22 PDT
I had said quite clearly:
"This is the sum of gravity and centripetal force"
In the vertical position, formula gives double of the weight.
(gravity alone produces just the weight).
As you correctly pointed out, one has to use his/her brain to figure
this out. Please reread my answer AND elementary explanation
provided, in the in such a mode, this time.
Formula is simple, giving vector sum of gravity and centripetal force,
becouse it is a simple problem.
If you really need clarification, pleast post another RFC
however, considering the price, I cannot to engage in an
a prolonged argument.
Rating is always appreciated.
Clarification of Answer by
16 Aug 2005 22:59 PDT
Thanks for the rating.
We all sometime act on impuls, before thinking things through.
And so here are few notes of CAUTION if you actually build it:
1)You need to use a safety factor, not theoretical limit.
I would guess cable should support at least 6 time the weight of the load.
2) The formula leading to 2 g makes an assumption about the energy of
Clearly, if energy get's higher and higher, the bob swings over the
Centrifugal force= M * v *v /L
will be large compared to
contribution yo the tension due to gravity= M * g *cos (deflection)
Of, course that is not a swing aby more. Energy of a swing is less
then E0=M * g *L = is energy of the bob at horizontal position at
If energy of the swing is more then that, e.g. if you hold the rope
and jump of the point above the horizonal level of the pivot, you are
not restrained by
the rope at first. You will be in the free fall until your vertical
(or parabolic) trajectory intersect the circle of pendulum's path. At
there is a jerk, which can exceed the forces we are considering here and which
depends on elasticity of the rope. It can far exceed the 3g we can get at E0
Finally, a note on terminology: We consider three forces here:
Centripetal is the force 'towards the center' - a reaction of the rope
Centrifugal is the force of inertia, (away from the center)
[fuga is same root as in word refugee = to run away from]
and then, there is gravity.
We are really adding all three - and so, it is more complicated
then I said on the beginning, after all.