Trapeze artists gained popularity by performing at the
circus, swinging high above the ground. The trapeze and trapeze artist can be modeled as a simple pendulum because the artist is
basically a mass at the end of a string, which in this case is the trapeze made
of a horizontal bar hanging by two cables. I assumed that
the trapeze artist doesn’t move his body, but hangs straight in line with the
middle of the bar. I wanted to
determine the maximum speed that the trapeze artist moves. Air resistance was ignored.

I estimated the mass of the trapeze artist to be 65 kg and
the mass of the horizontal bar to be 4 kg (the mass of the cables is
negligent). Therefore, the mass of
the trapeze system is 69 kg. The
cables connecting the horizontal bar to the ceiling are 4.2 m long and the
trapeze artist is 1.6 m tall. The
trapeze artist starts by standing on a platform. I assumed that the platform was 4.5 meters above the
floor. The man is modeled as a
point mass and his center of mass is assumed to be half of his body
length. Therefore, the distance of
the trapeze system is 4.5 m + (1.6 m/2) = 5.3 m from the floor.

The trapeze artist starts by standing on a platform at the
highest point of his swing.
Therefore, while standing on the platform, at rest, the trapeze artist
has his maximum potential energy.

PE = mgh = (69 kg)(9.8 m/s

^{2})(5.3 m) = 3.6 x 10^{3}J
When the trapeze artist swings to the lowest height in his
swing, he is at his maximum speed and his maximum kinetic energy. The trapeze artist is at his lowest
potential energy here. I assumed
that there are no nonconservative forces.
I also assumed that the trapeze system was now at a height of 4.6 m from
the floor.

One trick performed on a swinging trapeze, which is a
trapeze in which the trapeze artist starts from rest and swings the trapeze
himself, instead of creating the swing by walking off the high platform (this
is a flying trapeze), is the stand seats-off. In this trick, the trapeze artist first stands upright on
the bar, swings, and eventually finishes hanging upside down from the bar with
his feet. I assumed the angle of
the trapeze artist’s swing to be 50°.
To determine the maximum speed at which the trapeze artist swings, I
used the same formula as above.
This time the height is the height of the “pendulum” or the trapeze
system, which is the length of the cables plus half of the performer’s height
(4.2 m + (1.6 m/2) = 5.0 m. The
performer starts from rest.

Now I want to find the maximum velocity of the trapeze
artist after he starts falling. I
estimated that the performer fell 2.2 m. First, I have to find the potential energy before the
performer falls. I ignored the
mass of the bar.

PE = mgh = (65 kg)(9.8 m/s

^{2})(5.0m – (5.0 m * cos(50°))) = 1137 J
The PE at the bottom of the fall is:

PE = mgh = (65 kg)(9.8 m/s

^{2})(-2.2 m) = -1401 J
The PE is negative because the man is falling down.

The trapeze artist has a large increase in velocity when he
performs this trick.

Sources:

http://newyork.trapezeschool.com/resources/inv1.php

http://www.flying-trapeze.com/The-Physics-of-Flying-Trapeze/the-swinging-trapeze.html

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