Inclined plane

Straight ramps used to construct an Egyptian pyramid. As the pyramid gets higher, the ramp is made longer, to maintain a manageable slope of the inclined plane.

Examples of various types of ramps used to construct pyramids. From left to right: Zig-zagging ramp (Holscher), ramp utilizing the incomplete part of the superstructure (Dieter Arnold), and a spiraling ramp supported by the superstructure (Mark Lehner).

The inclined plane is one of the classical simple machines; as the name suggests, it is a flat surface whose endpoints are at different heights. By moving an object up an inclined plane rather than directly from one height to another, the amount of force required is reduced, at the expense of increasing the distance the object must travel. The mechanical advantage of an inclined plane is the ratio of the length of the sloped surface to the height it spans; this may also be expressed as the cosecant of the angle between the plane and the horizontal.

History

The inclined plane is one of the simple machines of antiquity, the physical operations of which were first theorized by Archimedes in the second century B.C.E., and then further explained by Hero of Alexandria in the first century C.E..

Inclined planes are often confused with wedges; while loads are moved along stationary inclined planes, wedges themselves move stationary loads. (Examples of early wedges include prehistoric axes, spears, and arrowheads.)

Around 2600 B.C.E., inclined planes in the form of ramps were used, at least in part, to raise the blocks of stone that make up the Great Pyramid. Between 1900 B.C.E. and 1400 B.C.E., inclined planes might also have been used to elevate and place large stone crosspieces at Stonehenge.

Before the advent of inclined planes, levers, pulleys, cranes, gears, and belts, heavy objects had to be hoisted, moved, and positioned by brute force.

Examples of inclined planes

Examples where "inclined planes" are to be found: ramp, sloping roads and hills, windshield, funnel, water slide, 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 machine based on the inclined plane is a blade, where 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. Other examples: aircraft wings, helicopter rotors, propellers used in aircraft, boats or pumps, windmills, water wheels, turbine blades, rotary fan blades, and machine screws, a ramp that is attached to the back of the moving van, or a children's slide.

Physics of the inclined plane

Key:
N = Normal force that is perpendicular to the plane
m = Mass of object
g = Acceleration due to gravity
θ (theta) = Angle of elevation of the plane, measured from the horizontal
f = frictional force of the inclined plane.

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. There are three forces acting on the body (neglecting air resistance): The normal force ('N') exerted by the plane onto the body, the force due to gravity ('mg' - acting vertically downwards) and the frictional force ('f') acting parallel to the plane. The gravitational force may be visualised as two components: A force parallel to the plane ('mgSinθ') and a force acting into the plane ('mgCosθ') which is equal and opposite to 'N'. If the force acting parallel to the plane ('mgSinθ') is greater than the frictional force 'f' - then the body will slide down the inclined plane - otherwise it will remain stationary. When the slope angle ('θ') is zero, sinθ is also zero so the body does not move.

See also

• Construction
• Machine
• Pyramid

References

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External links

• An interactive simulation of Physics inclined plane

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