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Inverse Variation Models

Identify and solve y=k/x form equations

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Oh, the Places You'll Go...

Have you ever gotten into a car, truck, bus, or van and wondered how putting some gasoline in the tank, turning a key or pushing a button, and shifting gears enables a metal box on wheels to move you forward?! How does the engine of a motor vehicle actually work to get you from one place to another?

Why It Matters

The core of the engine is the cylinder, and most vehicles have a 4-, 6-, or 8-cylinder engine. The piston, essentially a solid piece of metal, moves up and down inside the cylinder. The engine?s fuel system delivers a mixture of fuel (gasoline) and air to the cylinders, the piston moves down in order to allow the cylinder to completely fill with air (only a small amount of gasoline is needed). Then the piston moves back up and the air/fuel mixture is compressed. When the piston has compressed the air/fuel mixture as much as possible, the spark plug emits a spark and the gasoline/air mixture explodes, driving the piston down. The used air/fuel mixture is released from the cylinder as exhaust, and the process starts again. The compression by the piston is what allows for a larger explosion and the exertion of a greater downward force, thereby enabling the movement of the mechanical parts of the vehicle.

The relationship between the volume of the cylinder and the amount of force produced is an inverse relationship. The smaller the volume of the cylinder (when the piston is compressed as much as possible), the greater the force of the explosion when the gasoline/air mixture is ignited by the spark. Because of this relationship, engines with pistons compressing air in its cylinders can use less gasoline to produce the same amount of force as an engine in which no pressure is produced by the piston. As engineers continue to find innovative ways to exploit the relationship between pressure and force, vehicles will continue to achieve better fuel economy, meaning vehicles will use less and less oil to travel farther.

See for yourself: http://auto.howstuffworks.com/engine.htm

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When a rocket ship takes off from Earth, it needs a tremendous amount of fuel to overcome the force of gravity and start its journey. As the rocket gets closer to the edge of atmosphere it requires less and less fuel because the force of gravity becomes smaller as the rocket travels farther from the Earth's surface. How would you describe the relationship between the force of gravity and the distance an object is from Earth?s surface?

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