Energy TransformationDate: 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/ |
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