### Indiana Jones vs. Fundamental Law of Conservation of Mechanical Energy

The Indiana Jones movie series is full of scenarios where characters use ropes, chains, and whips to swing from one place to another. From a physics perspective, this swinging motion is a perfect example of the law of conservation of mechanical energy. The law of conservation of mechanical energy states that the total potential and kinetic energy in a system will remain constant as long as the only forces that act on the system are conservative. This law can be written as follows:

*KEi+PEi=KEf+PEf*

Where the initial and final mechanical energy is measured at these points in the swing path:

__Classic Rope Swing__

When starting from rest in the initial position above, the only energy in the system is in the form of potential energy, since kinetic energy is associated with movement. At the bottom of the swing, there is solely kinetic energy in the system since the bottom of the swing path is considered at ground level. Therefore, the change in potential energy as it drops distance (h) is transferred into kinetic energy. The mechanical energy conservation can thus be written as:

*PE*

**i**=KE**i**

- Where PE is measured as mass(m) * acceleration on Earth due to gravity(g) * height (h) Or, (mgh), and the kinetic energy is ½ * m * velocity(v)^2, or (½ mv^2)

The mechanical energy conservation now takes the form of:

mgh=1/2mv^2

Now that there is a foundation to begin analyzing a conservation of mechanial energy scenario, let’s check out a scene from Indiana Jones and the Kingdom of the Crystal Skull. Here is the scene:

What is interesting about this scene is that the car is traveling at a pretty high speed, and the only way for Mutt Williams to gain this speed is if he started from a sufficient height. The height in this scene can be taken from the following moment:

It appears that Mutt only falls about two times his own height. The height of Mutt is 5’9”, which is about 1.75 meters. Using double his height for the potential energy, the total mechanical energy initially can be written as:

__Mechanical Energy Initial__= (72kg)*(9.8m/s^2)*(2)(1.75m) =

**2470J**

It appears that the car is moving at about 50mph, or 22m/s. Is the initial mechanical energy of the system enough to allow Mutt to travel that fast at the bottom of the vine swing?

In order to figure this out, we must rearrange the mechanical energy equation in order to solve for the speed of Mutt at the bottom if the swing.

mgh=1/2mv^2

gh=1/2v^2

(2gh)^½=v

(2*9.8m/s*2*1.75m)^½= 8.30m/s

This speed is about a third of the speed that is necessary for Mutt to actually catch up to the car. This proves that the movie disregarded the fundamental law of conservation of mechanical energy. Although disappointing, it is a crucial aspect of the movie series for Indiana Jones and other characters to perform impossible stunts for the sole purpose of entertainment.

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