Inclined_plane

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

Roman soldiers constructed an inclined plane out of earth to lay siege to the Masada during the First Jewish-Roman War in 73 CE.

The inclined plane is one of the original six 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 completely vertically, 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 1 divided by the sine of the angle between the plane and the horizontal. Note that due to the conservation of energy, the same amount of mechanical energy is required to lift a given object by a given distance, if frictional losses are ignored.

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 inclined plane problem

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):

1. The normal force (\'N\') exerted by the plane onto the body,
2. the force due to gravity (\'mg\' - acting vertically downwards) and
3. 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.

External links

• An interactive simulation of Physics inclined plane

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