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Investigating the Physics of Bunjee Jumping

Extracts from this document...

Introduction

Investigating Bungee Jumping

By Justine Hyu

Abstract: The association of Hooke’s law with elastic were investigated by hanging masses off an elastic cord, and measuring the extensions. A graph of the results was made to determine Hooke’s constant which would later be applied to certain calculations. Then a model bungee jump was created to measure the motions and energies involved with bungee jumping. From the results gathered, calculations and predictions were made in order to provide the foundation of the construction, and properties of real bungee cords which could be applied when jumping off the Story Bridge.

Aim: To investigate the factors and properties associated with a bungee cord, in order to design a suitable model bungee jump, which will be applied as the basis for an actual bungee jump attraction on the Story Bridge.

Introduction and Background Information:

This investigation into bungee jumping was initiated as a result of a company’s proposal to construct a bungee jump attraction on the Story Bridge. Bungee jumping is a popular extreme sport which originated from the Pentecost Islands of Vanuatu, where the men tied vines around their ankles and jumped from a height as a test of courage. Today bungee jumping consists of an elastic cord secured to a platform and a variety of other equipment. Modern bungee jumping, with an elastic cord, demonstrates Hooke’s Law and consists of a variety of energy transformations. According to Hooke’s law the spring constant is theoretically linear, and is calculated by k=F÷image06.png, therefore is the gradient of the line which passes through the origin.

There are many important variables to consider when designing a bungee jump such as Hooke’s (spring)

...read more.

Middle

image06.png -0.887

F=?

image06.pngimage06.png=15.72m

F=9.74×15.72- 0.985

  =153.112-0.985

  =152.127N→15.52kg

To accommodate a wide range of clients it is more efficient to have two bungee cords. One which supports a maximum of approximately 90kg and the other which holds a maximum of approximately 150kg.

So far it has been calculated:

Story Bridge measurements:

Actual length of cord (2 parallel): 17.12m

Max extension of cord: 15.72m

Length of extended cord: 32.84m

Max mass: 15.52kg →152.523N

Constant: 9.74Nm¯¹

Bungee cord 1

Length: 17.12m

Max extension of cord: 15.72m

Length of extended cord: 32.84m

Max mass: 90kg →882N

Constant:?

image11.jpg

If the strands of elastic in parallel are the same, each individual strand of elastic will have the same constant, which contributes to the greater overall constant of the parallel strands working together. For example if a strand of elastic had a constant of 5 Nm¯¹ a cord which consisted of four of these strands would have a constant of 5 + 5 + 5 + 5, or in other words the number of strands multiplied by the constant 4×5=20 Nm¯¹. If the strands are in parallel and a force is applied, each strand will share the force equally. So if there is eight strands in parallel and a 40N force applied, each individual strand will support 5N.

Each string has the same constant:

Therefore if 2 strings have a constant of 9.74Nm¯¹

One string must have half of that, so the constant of one string is 4.87Nm¯¹

If the cords are in parallel they share the force equally:

Therefore if 2 strings extend 15.72m with a force of 152.523N

One string would extend 15.72m with a force 76.06N

Number of chords needed to support 882N (90kg):

882÷76.06= 11.59→for convenience use 12 cords in parallel

The actual mass supported by 12 cords in parallel:

  12×76.06= 912.72N→93.135kg

Constant of 12 strings:

12×4.87= 58.44 Nm¯¹

Length (12 cords parallel): 17.12m

Max extension of cord: 15.72m

Length of extended cord: 32.84m

Max mass: 93.135kg →912.72N

Constant: 58.44 Nm¯¹

...read more.

Conclusion

  KE=0

    v =2.896 ms¯¹

     t =0.295s

  KE =1.258 GPE=1.155 J

 EPE=0

 EPE =0.752 J

      F=-2.94N

GPE=0

   KE=0

 EPE=0.034 J

      F=-2.94m

GPE=0

   KE=0

1

93.135kg

912.72N

GPE=29973.82 J

EPE=0

  KE=0

     v=18.32 ms¯¹

   KE=15629.096 J

GPE=14348.01 J

 EPE=0

EPE=7220.79 J

     F=-912.72N

GPE=0

   KE=0

EPE=329.882 J

     F=-912.72m

GPE=0

   KE=0

2

155.22kg

1521.2N

GPE=49954.76 J

EPE=0

  KE=0

     v=18.32 ms¯¹

   KE=26042.19 J

GPE=23912.57 J

 EPE=0

EPE=12034.67 J

     F=-1521.2 N

GPE=0

   KE=0

EPE=549.8 J

     F=-1521.2N

GPE=0

   KE=0

Conclusion:

This experiment was conducted in order to investigate the important features involved with bungee jump, with the intention of using the results and calculations as a foundation to produce suitable bungee cords, accommodating a range of clients, jumping from the Story Bridge. The association of Hooke’s law and the experimented elastic cord was investigated by trialling different masses and calculating extensions. From the collected results, a model bungee jump was created and a position-time graph was accumulated. These results were carefully analysed and utilised as the basis of further calculations and predictions. Equations were formed to determine the parameters of actual bungee cords which could be applied to the Storey Bridge. The maximum motions and energies experienced were calculated. This experiment could be altered to make further improvements and to increase accuracy of the gathered results. Predominantly, the expected results were derived from this experiment, and the aim was fulfilled.

Bibliography:

Butlin, Chris. 2000, Salters Horners Advanced Physics: Stretching and Springing, Heinemann, New York, p40-42.

Menz, P. 1993, ‘The Physics of Bungee Jumping’, BUNGEE.COM, viewed 14 March 2008, < http://www.bungee.com/bzapp/press/pt.html>.

Murphy, Pat. 1998, ‘Science, Fantasy and Science Fiction, SF Site, viewed 14 March 2008,< http://www.sfsite.com/fsf/1998/pmpd9806.htm>.

Story Bridge Adventure Climb, 2008, ‘The Bridge’, Story Bridge Adventure Climb, viewed 16 March 2008,< http://www.storybridgeadventureclimb.com.au/the_climb_the_bridge.html>.

Walding, Richard. 2004, New Century Senior Physics Concepts in Context  Second Edition, Oxford University Press, Australia.

Wikipedia the Free Encyclopaedia, 2008, ‘Hooke’s Law’, viewed 16 March 2008, < http://en.wikipedia.org/wiki/Hooke's_law>.

...read more.

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