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# The Physics of Bungee Jumping

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## Sarah Mandi

on 28 May 2014

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#### Transcript of The Physics of Bungee Jumping

The Jump
Simple Harmonic Motion
Tension
Bungee
Jumping

The Physics of Bungee Jumping
Factors That Affect
The jump
Spring Constant
Length of Cord
Air Resistance
Weight
Free Fall
Cord Stretches
Oscillation & Retraction
Gravity is the only force
Constant acceleration of 9.81 m/s^2
Bungee cord is relaxed
Force of tension begins acting upon the jumper
When tension > gravity...
Upward acceleration
Jumper slows down
Bungee cord has reached maximum tension
Stronger tension force causes upward acceleration
Jumper stops before rising
Process repeats itself
Begins with zero tension
Increases as jumper approaches maximum length of the cord
Force of tension creates an upward acceleration
Pulls jumper back up to origin

Blue Arrows: constant downward force of gravity

Red Arrows: non-constant force of tension
When hanging from the cord, the jumper undergoes vibrational motion
Hooke's Law: restoring force is directly proportional to the displacement of the mass
F = -kx
Jumper can also behave like a pendulum as they oscillate
Energy
Potential energy is at a maximum when jumper is at rest at origin
As jumper falls, PE converts into KE
As tension increases, PE of the cord increases
Spring Constant (k) determines stiffness of cord/spring
If k is too large, cord will be too stiff and jumper will not experience complete stretch
If k is too small, cord will be too elastic and jumper could hit ground, fling upwards with great acceleration, or cord could snap
If cord is too long, cord could stretch too much and jumper could hit the ground
Oops...
Greater weight causes cord to stretch more
Important to customize the length of the rope to the weight of the jumper so heavy jumpers don't hit the ground in a setup that had been safe for a lightweight jumper
Reason why bungee jumper eventually comes to a stop
In ideal system, jumper would continue to oscillate
Energy is lost during the jump
For purposes of calculations, we will neglect air resistance
To find spring constant:

F = -kx
Elastic Potential Energy Equation
(1/2)kx^2
(1/2)k(H-L)^2
H = stretched length
L = unstretched length
mgh = (1/2)k(H-L)^2
Therefore.....
Gravitational Potential Energy Equation
PE = mgh
Mechanical Energy
Sources:
http://stokes.byu.edu/teaching_resources/bungee.html
http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html