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# Conservation of Energy

## The amount of energy in a closed system never changes.

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Practice Conservation of Energy

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The World's Fastest Roller Coaster

### The World’s Fastest Roller Coaster

Credit: Sarah Ackerman
Source: http://www.flickr.com/photos/sackerman519/8638541154/

Known as the fastest roller coaster in the world, Formula Rossa accelerates its riders to 149 mph. Not only does this 92 second ride have a total length of 2200 m and a vertical drop of 51.5 m, but its passengers will experience almost 5.0Gs!

#### Amazing But True

Credit: Jeremy Thomson
Source: http://www.flickr.com/photos/rollercoasterphilosophy/3228818023/

The energy equation lets engineers determine how fast a roller coaster can travel [Figure2]

• While almost every roller coaster is different, they all follow the same basic principle. The system's potential energy is increased and then gravity is allowed to take over, causing most of the potential energy to be converted into kinetic energy. Any of the energy that is not converted into kinetic energy by the end of the ride is energy that has been lost due to friction.
• The energy at any given point along the ride is given as:

Kinitial+Uinitial+Wext=Kfinal+Ufinal\begin{align*}K_{initial}+U_{initial}+W_{ext}=K_{final}+U_{final}\end{align*}

Where K\begin{align*}K\end{align*} and U\begin{align*}U\end{align*} represent the kinetic and potential energies respectively. W\begin{align*}W\end{align*} represents any work that is done on the ride by external forces (friction/air resistance). Using this equation and the principle that energy must be conserved, engineers are able to determine how fast they can make the ride as well as how sharp each turn can be.

#### What Do You Think?

Using the information provided above, answer the following questions.

1. Why do most roller coasters start by bringing the passengers up a really large incline?
2. Does the Wext\begin{align*}W_{\text{ext}}\end{align*} in the above equation serve to increase or decrease the speed at which the riders on a roller coaster can reach?
3. How is the energy in the system distributed when one of the carts on the roller coaster go through an upside down loop?

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