Inclined plane

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This article deals with the physical structure. For related terms, see canal inclined plane, cable railway, funicular, or fixed-wing aircraft (airplane).

An inclined plane is a plane surface set at an angle, other than a right angle, against a horizontal surface. The inclined plane permits one to overcome a large resistance by applying a relatively small force through a longer distance than the load is to be raised. In civil engineering the slope (ratio of rise/run) is often referred to as a grade or gradient. An inclined plane is one of the commonly-recognized simple machines.

[edit] Examples of inclined planes

Examples of inclined planes are [[ramps, sloping roads and hills, chisels, hatchets, plows, air hammers, carpenter's planes, and wedges. The most canonical example of an inclined plane is a sloped surface; for example a roadway to bridge a height difference.

Another simple machines based on the inclined plane include the blade, in which two inclined planes placed back to back allow the two parts of the cut object to move apart using less force than would be needed to pull them apart in opposite directions.

Aircraft wings, helicopter rotors, propellers used in aircraft and boats, windmills, water wheels, turbine blades, and fans are also specialised examples of inclined planes.

[edit] History

The ramp or inclined plane was useful in building early stone edifices, roads and aqueducts. It was also used for military assault of fortified positions. It was invented by the ancient egyptians as was the lever and the clock.

Experiments with inclined planes helped early physicists such as Galileo Galilei quantify the behavior of nature with respect to gravity, mass, acceleration, etc.

Detailed understanding of inclined planes and their use helped lead to the understanding of how vector quantities such as forces can be usefully decomposed and manipulated mathematically. This concept of superposition and decomposition is critical in many modern fields of science, engineering, and technology.

[edit] Physics inclined plane problem

The inclined plane gives rise to a common elementary physics exercise. Consider an object placed on an inclined plane, and describe mathematically the forces acting upon that object.

The picture below has 3 force vectors (neglecting air resistance and the mass sliding down the inclined plane).

The first vector is the normal force, which is perpendicular to the surface upon which the object rests. It is also the force that is stopping the object from accelerating at gravity's full acceleration (On Earth, the AVERAGE gravity acceleration is approximately 9.8 meters/seconds squared).

The second vector is gravity, the attractive force exerted on the object by the planet. Within the gravity vector, there are two components, horizontal and vertical force in the inclined plane perspective. As you can see the angle is on the lower left corner.

What happens if we make that angle zero degrees? The plane will be horizontal and the only force acting on it is gravity (pointing downwards)and normal force (pointing upwards). The only trigonometric function that makes zero degree = 1 is cosine, so cosine must be the vertical force. With this fact, we can go back to the inclined plane and use the cosine function to find the vertical force, and the sine function to find the horizontal force.

The inclined plane is also in contact with the block, and the contact causes friction. So the third vector is friction. Since the block is sliding downwards, the friction vector is going the opposite of the horizontal force of gravity.

Taking all these vectors into consideration, we can say the normal force and the vertical component of gravity balances out, because it is not accelerating upwards nor downwards, but sideways. And since, friction is going the opposite direction of the horizontal gravity force, the whole equation is $mg \sin \theta\ - f = mA$ . The mA part is derived from Newton's laws of motion.