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Energy Transformation

Date: 02/13/2003 at 09:25:48
From: Angela
Subject: Energy Transformation

Can you explain the formula for energy transformation on a roller 
coaster?

I am mathematically challenged and can't help my 12-yr-old with his 
homework. We found a formula on the Internet, but I can't help him 
explain it.


Date: 02/13/2003 at 11:44:28
From: Doctor Edwin
Subject: Re: Energy Transformation

Hi, Angela.

I'm not sure which formula you're dealing with, but the first one 
that springs to mind is

  E = mgh

This says that the energy you get from your height is equal to the 
mass of the object, times the force of gravity, times the height. 
That kind of makes intuitive sense, doesn't it? If you double the 
strength of gravity, you get twice as much energy out of the fall. 
Likewise if you double the mass of the object or the height of the 
ride.

Let's say we're in a car that weighs 200 Kg and a roller coaster 
that's 100m high. Gravity is 9.8m/sec^2, so your energy will be

  E =  m    *   g   *  h

               9.8m
  E = 200Kg * ------ * 100m
               sec^2 

  E = 196,000 Kg m^2/sec^2

Now the units are kind of weird, I'll admit. But they make sense. It's 
mass (Kg) times distance (m) times acceleration (m/sec^2). So if 
you're pushing something and you know the mass, and you know how much 
you were accelerating it, and you know how far you pushed it, then you 
know how much energy you must have expended.

That messy conglomeration, Kg m^2/sec^2, comes up often enough that 
physicists gave it a name. 1 Kg m^2/sec^2 is equal to 1 Joule.

So in our example above, the rollercoaster converts the height of the 
car into 196 KiloJoules of energy.

Incidentally, I got as far as Kg m^2/sec^2 and thought, "There must 
be a better way to write that." I went to www.convertit.com, and 
typed that in on the left side. It took some jiggering to get the 
format right - I had to change it to Kg * m^2/sec^2. But when I 
pressed the button, it came out with 1 Joule on the right side.

I hope this helps. Please write back if you have any more questions.

- Doctor Edwin, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Physics/Chemistry

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