# Inclined plane

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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 vertical, 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. 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, except for losses from friction, but the inclined plane allows the same work to be done with a smaller force exerted over a greater distance.

## Contents

### Ramps, chutes and slides

An inclined plane is a simple machine that does not move. Many devices based on the principles of the inclined plane allow expending less force to achieve a task. Ramps enable accessing heights that would be too difficult to scale vertically. Ramps allow heavy objects to ascend to, and descend safely from, a high-level bridge. Portable ramps allow easy loading and unloading of high-decked trucks. Siege ramps gave ancient armies the ability to walk up bringing heavy equipment to the tops of high walls. Chutes and slides allow fragile objects, including humans, to be safely lowered from a vertical rise by countering gravitational force with the normal force provided by a stiff surface at an angle to the gravitational vector. Airplane rescue slides allow people to quickly reach the ground safely, without the danger of jumping from a height. The addition of the normal force and gravity vectors causes the sliding object to move parallel to surface of the slide, so a slide can be used to move objects through a distribution system from one area to another. Hoppers and funnels are formed by planes shaped into an inverted pyramid or cone shape to concentrate granular or fluid material at the apex.

Eliminating friction from a slide increases the maximum speed at which an object can move down the slide, while the acceleration of the moving object can be controlled to any degree by varying the angle of the slide. Because of this, slides are one of the most common and popular forms of entertainment. A well-polished slide can allow a human to move at a high speed with no effort, even experience near free-fall acceleration, yet arrive on the ground safely because the angle of slide can be varied along its length to end up parallel to the ground, so the forward motion of the slider can be slowly arrested by friction. The metal slide is a popular piece of playground equipment, and towering water slides employ liquid lubrication to reduce friction even further. Wheeled cars of rollercoasters roll down inclined tracks to achieve high speeds. In the sports of luge, bobsled, sledding, and skiing, participants accelerate to extremely high speeds utilizing only the inclined plane, whether a mountain slope provided by nature, or a chute lined with near-frictionless ice. Mountains are another example of an inclined plane.