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Running head: PHYSICS APPLICATION 2

PHYSICS APPLICATION 2

The Physics of the Flying Trapeze

Jordan Swe

Physics 1200-01 with Lab

December 9. 2019

The Physics of the Flying Trapeze

Introduction

The flying trapeze is a phenomenon in physics that draws a lot of attention. It is an essential mechanism that is similar to the pendulum motion in a pendulum clock. The flying trapeze, however, requires sharp precision and many years of experience to master.

Pendulum Motion

The trapeze period is the time it takes to finish one full oscillation. As with the motion of a clock, the time period is independent from the amplitude (the height of the swing). The trapeze period is characterized as the distance between the pivot point and the center of mass of the trapeze artist. By closely managing change in the position of the body the trapeze artist alters the length of the pendulum. Consequently, the time of the swing changed. The fundamental body developments of a trapeze artist throughout the full swing is known as “long on the way down, short on the way up.” When an actual flyer hanging from a trapeze bar is considered, it is not the length of the trapeze cables that represent the length of the pendulum. Rather, it is the distance from the pivot (the attachment point at the top) down to the center of mass of the flyer (roughly the hip area). As explained in the quote above, a long pendulum is the result of moving the center of mass of the away from the pivot (straightening and lengthening the body). Alternatively, a short pendulum occurs when the flyer brings the center of mass up towards the pivot. With the trapeze artist this looks like straightening the body, bending the arms, and pulling the body up to the bar. These actions go from long to short. These are the essential movements that enable the flyer complete his tricks by moving his focal point of mass and accordingly shortening and protracting the pendulum through the span of the swing (Rickenbach, 2019). The equation for the period of the swing demonstrates that a longer length will lead to a longer period. You can see that the period only depends on the length and the acceleration due to gravity.

Energies Involved

There are three energy properties dealing with the trapeze: potential energy, chemical energy, and kinetic energy. Potential energy is involved while the trapeze is at the furthest point from the ground. The peak of the swing is where the flyer has the most potential energy. At the bottom of the swing is where the trapeze artist has the most kinetic energy and, consequently, the highest speed (Cavendish, 2017). When a flyer is swinging the energy in the system is fixed. This includes such things as the flyer himself, the bar, the cables, and the pivot. The energy shifts from one form to another, oscillating between kinetic energy and potential energy as the artist swings back and forth. In order for the height of the swing to increase, more energy must be put into the system. At the extreme end of the swing, where the flyer is stationary, all of the energy is in the form of gravitational potential energy (kinetic energy is zero). The formula is:

PE = m X g X h

(m = mass, g = acceleration due to gravity, h = height with respect to the bottom of the swing)

If height is to be increased the energy in the system must be increased since mass and gravity are constant. The required energy comes from chemical energy stored inside the flyer himself. Work must be done in order to add this energy into the swing. In this case work is defined as moving against a force. The formula is:

Work Done = Force X Distance Moved

EDITS STOPPED HERE…nothing below has been edited…

Momentum

Momentum is the impetus gained by a moving body- a quantity of motion of the said body. Because of this, anything with mass and velocity has momentum. The most important role momentum plays in the trapeze is to carry the flyer through his or her pendulum motion as they travel back and forth, and a flyer's momentum can greatly impact their ability to move while on the bar. The momentum of an object can be computed by the equation:

P=mv

(momentum=mass. velocity)

Hence, a heavier flyer traveling at the same velocity as a lighter one will have more momentum. This can be beneficial depending on the type of maneuvers that the flyer is attempting.

Due to this fact, it is a misconception that all trapeze must be small and agile. Some larger flyers are used in maneuvers that require higher momentum and more strength.

The flyer can increase his or her momentum by adding an impulse to the pendulum motion- usually through a hip thrust. A slight thrust at the end of a period can also act as a restoring force to keep the flyer moving at a constant velocity and maintain the more pop period length.

Forces on the flyer

The two forces acting on the flyer are their weight due to gravity and a centripetal force. While they are swinging through the air, the trapezist experiences a centripetal force acting on them that is produced by the bar on their hands. This force acts to pull them towards the center, or the pivot point. It is this mechanism that opposes the propensity for the body of the flyer to move tangentially (Flying-Trapeze n.d). The may additionally experience a fictitious force or centrifugal force pulling downward on their feet/ legs. The swing, it will feel very difficult for them to try to lift their legs because they are going to feel much heavier than they actually are. This force that they feel will decrease at the peak of their swing when their velocity decreases, and it will feel much easier to pull up their legs. Gravity, however, is still pulling the flyer down, which is why they always pull their legs up at an angle.

Rotational Motion after Release

Several maneuvers carried out by the trapeze artists are effected while away from the bar and after letting go while flying through the air without the hindrance of whatsoever kind. Both of twisting and flipping use the rotation around an axis placed centrally. For one to get the required angular momentum required to carry out the maneuvers, there must be an impulse injected on the flyer’s body. This generates inertia force for the requisite motion for rotation and can be done by kicking the legs or using the arms to pull on the bar.

References

Cavendish, R. (2017). The First Flying Trapeze is Performed. History Today. History Today, and Web, 28.

https://www.flying-trapeze.com/physics-of-flying-trapeze/

https://www.flying-trapeze.com/physics-of-flying-trapeze/8-articles-by-alastair-pilgrim/10-investigation-3-the-swinging-trapeze

Rickenbach, T. (2019). SCIENCE POLICY: The Flying Trapeze. Bulletin of the American Meteorological Society, 100(4), 692-698.