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Bungee Jump (no: Strikk-hopp)

Surprisingly (also for many physicist) you can have an acceleration greater than g (the acceleration of gravity) when you make a bungee jump.

In the video to the left we simulate a bungee jump, but this time with just two chains.
To the left you see a two meter long chain.
To the right you see a four meter long chain, but you see this last one makes a bow at the bottom and goes up again.
Both chains have a marker on the top so we more easily can follow the movement.

Both chains are dropped at the same time.
The marker (and the chain) to the left will be falling with an acceleration equal to the acceleration of gravity (g).
The marker to tre right will be falling with an acceleration greater than the acceleration of gravity (g).
Notice especially the acceleration of the right marker just before it reaches the bottom of the chain bow.

Click 'Start' and you can see a video of the real Bungee Jump experiment.

Here some real bungee jumps: 001 002

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The Physical Explanation of Bungee Jump:

In the figure 1 we have two chains, the one to the left straight down and the other to the right in a bow up again.
Both chains have a mark on the top to see the movement.
The mark to the left will fall down with an acceleration equal g.
The mark to the right will fall down with an acceleration greater than g.

The correct form of Newton's Second Law is: F = (d/dt)(mv).
Many people (also some physicists) believe that Newton's Second Law is F = ma.
That is only correct if the mass of the system we are stydying is constant.
If the mass is not constant, then we have to use the general form of Newton's Second Law: F = (d/dt)(mv).
In the figure we choose the chain under mark 2 (marked by a red recatngle) as our system and we are going to use Newton's Second Law on this system.

The solution of the acceleration from Newton's Second Law.

In the bottom of chain 2, we have only horizontal forces.
After we drop the chain, the gravity force G = mg is the only vertical force on our system.
The g-vector and v-vector both have the same direction (vertically downwards) and the mass m is positive.
Since the mass of our system decreases (that is dm/dt is negative), the acceleration a of our system will be greater than g.

You see that the mark 2 has greater acceleration than mark 1.

More details about The physics of Bungee Jump

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