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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 up to 149 miles per hour. Not only does this 92 second ride have a total length of 2200 meters and a vertical drop of 51.5 meters, 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 roller coasters are all different from one another, they all follow the same basic principle. The system's potential energy is increased by gaining altitude. Then, gravity takes over, causing most of the potential energy to be converted into kinetic energy. Any of the leftover energy that has not been converted into kinetic energy by the end of the ride is energy 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*}

In the equation, 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 to the top of a 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 roller coaster can reach?
3. How is the energy in the system distributed when one of the carts on the roller coaster goes through an upside down loop?

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