Inclined plane
Overview

The inclined plane is one of the original six simple machine
Simple machine
A simple machine is a mechanical device that changes the direction or magnitude of a force.In general, they can be defined as the simplest mechanisms that use mechanical advantage to multiply force. A simple machine uses a single applied force to do work against a single load force...

s; 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
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...

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.
Discussions
Encyclopedia
The inclined plane is one of the original six simple machine
Simple machine
A simple machine is a mechanical device that changes the direction or magnitude of a force.In general, they can be defined as the simplest mechanisms that use mechanical advantage to multiply force. A simple machine uses a single applied force to do work against a single load force...

s; 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
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...

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
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

, the same amount of mechanical energy
Mechanical energy
In physics, mechanical energy is the sum of potential energy and kinetic energy present in the components of a mechanical system. It is the energy associated with the motion and position of an object. The law of conservation of energy states that in an isolated system that is only subject to...

is required to lift a given object by a given distance, except for losses from friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

, but the inclined plane allows the same work to be done with a smaller force exerted over a greater distance.

## 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 truck
Truck
A truck or lorry is a motor vehicle designed to transport cargo. Trucks vary greatly in size, power, and configuration, with the smallest being mechanically similar to an automobile...

s. Siege
Siege
A siege is a military blockade of a city or fortress with the intent of conquering by attrition or assault. The term derives from sedere, Latin for "to sit". Generally speaking, siege warfare is a form of constant, low intensity conflict characterized by one party holding a strong, static...

ramps gave ancient armies the ability to walk up bringing heavy equipment to the tops of high walls. Chutes and slide
Playground slide
Playground slides are found in parks, schools, playgrounds and backyards. The slide may be flat, or half cylindrical or tubular to prevent falls. Slides are usually constructed of plastic or metal and they have a smooth surface that is either straight or wavy...

s allow fragile objects, including humans, to be safely lowered from a vertical rise by countering gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

al force with the normal force
Normal force
In mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...

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 funnel
Funnel
A funnel is a pipe with a wide, often conical mouth and a narrow stem. It is used to channel liquid or fine-grained substances into containers with a small opening. Without a funnel, spillage would occur....

s are formed by planes shaped into an inverted pyramid
Pyramid
A pyramid is a structure whose outer surfaces are triangular and converge at a single point. The base of a pyramid can be trilateral, quadrilateral, or any polygon shape, meaning that a pyramid has at least three triangular surfaces...

or cone
Cone (geometry)
A cone is an n-dimensional geometric shape that tapers smoothly from a base to a point called the apex or vertex. Formally, it is the solid figure formed by the locus of all straight line segments that join the apex to the base...

shape to concentrate granular or fluid material at the apex.

Eliminating friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of 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
Free-fall
Free fall is any motion of a body where gravity is the only force acting upon it, at least initially. These conditions produce an inertial trajectory so long as gravity remains the only force. Since this definition does not specify velocity, it also applies to objects initially moving upward...

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 roller coaster
Roller coaster
The roller coaster is a popular amusement ride developed for amusement parks and modern theme parks. LaMarcus Adna Thompson patented the first coasters on January 20, 1885...

s roll down inclined tracks to achieve high speeds. In the sports of luge
Luge
A Luge is a small one- or two-person sled on which one sleds supine and feet-first. Steering is done by flexing the sled's runners with the calf of each leg or exerting opposite shoulder pressure to the seat. Racing sleds weigh 21-25 kilograms for singles and 25-30 kilograms for doubles. Luge...

, bobsled, sledding
Sledding
Sledding , sledging , sleding or tobogganing is a common activity in wintry areas, similar to sliding, but in a prone or seated position requiring a device or vehicle generically known in the US as a sled or in other countries as a sledge or toboggan...

, and skiing
Skiing
Skiing is a recreational activity using skis as equipment for traveling over snow. Skis are used in conjunction with boots that connect to the ski with use of a binding....

, 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.

A blade is that portion of a tool, weapon, or machine with a cutting edge and/or a pointed tip that is designed to cut and/or puncture, stab, slash, chop, slice, thrust, or scrape animate or inanimate surfaces or materials...

is a compound inclined plane, consisting of two inclined planes placed so that the planes meet at one edge. When the edge where the two planes meet is pushed into a solid or fluid substance it overcomes the resistance of materials to separate by transferring the force exerted against the material into two opposing forces normal to the faces of the blade. First known to be used by humans in the knife
Knife
A knife is a cutting tool with an exposed cutting edge or blade, hand-held or otherwise, with or without a handle. Knives were used at least two-and-a-half million years ago, as evidenced by the Oldowan tools...

to separate animal tissue, the blade allowed humans to separate meat, fibers, and other plant and animal materials, with much less force than it would take to tear them by simply pulling them apart. Blades can separate solid material, as with plows that separate soil particles, scissors
Scissors
Scissors are hand-operated cutting instruments. They consist of a pair of metal blades pivoted so that the sharpened edges slide against each other when the handles opposite to the pivot are closed. Scissors are used for cutting various thin materials, such as paper, cardboard, metal foil, thin...

and shears to cut flexible materials, axe
Axe
The axe, or ax, is an implement that has been used for millennia to shape, split and cut wood; to harvest timber; as a weapon; and as a ceremonial or heraldic symbol...

s to separate wood fibers, and chisels and planes
Plane (tool)
A hand plane is a tool for shaping wood. When powered by electricity, the tool may be called a planer. Planes are used to flatten, reduce the thickness of, and impart a smooth surface to a rough piece of lumber or timber. Planing is used to produce horizontal, vertical, or inclined flat surfaces on...

to remove precise portions of wood.

Wedges, saw
Saw
A saw is a tool that uses a hard blade or wire with an abrasive edge to cut through softer materials. The cutting edge of a saw is either a serrated blade or an abrasive...

s and chisels can separate thick and hard materials, such as wood, including solid stone and hard metals, with much less force, less waste of material, and more precision, than crushing
Crusher
A crusher is a machine designed to reduce large rocks into smaller rocks, gravel, or rock dust. Crushers may be used to reduce the size, or change the form, of waste materials so they can be more easily disposed of or recycled, or to reduce the size of a solid mix of raw materials , so that pieces...

. Saws have many chisel-like "teeth" along their cutting surface to transfer linear or circular motion to counteract the normal force of the surface to be cut.
Crushing, the overcoming of material bonds by transferring momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

to a material through the normal force
Normal force
In mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...

of another, harder, object was the only way to cut through a hard material
Obelisk building technology in ancient Egypt
Obelisk making technology in ancient Egypt is an archaeological matter that is quite well understood today. Ancient Egyptian Obelisks are tapering stone pillars which have a square cross-section, were used for ornamental purposes in temples and had religious or socio-political connotations...

before saws, and the materials to make them, were developed.

Drills produce circular holes in solids by rotating a chisel around its center, with the edge is sharpened at opposing angles on either side of the rotation axis, so as to cut in the direction of rotation. Twist drills provide one or more heliacally
Helix
A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...

twisted chisels formed out of grooves cut along the side of the bit, to help evacuate cuttings from the drill hole, by using the same inclined plane principle as the archimedean screw. The water screw, though most likely preexisting Archimedes
Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...

, has been used since ancient times to pump water, and is now also used to move granulated and ground materials, such as wheat, coal, and meat. Screws also join pieces of wood or metal together, by using a helical plane, usually formed by cutting a helical groove into a rod, so that the rod can force itself into the material when it is rotated.

## Calculation of forces acting on an object on an inclined plane

To calculate the forces on an object placed on an inclined plane, consider the three forces acting on it.
1. The normal force
Normal force
In mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...

(N) exerted on the body by the plane due to the force of gravity i.e. mg cos θ
2. the force due to gravity (mg, acting vertically downwards) and
3. the frictional force
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

(f) acting parallel to the plane.

We can decompose the gravitational force into two vectors, one perpendicular to the plane and one parallel to the plane. Since there is no movement perpendicular to the plane, the component of the gravitational force in this direction (mg cos θ) must be equal and opposite to normal force exerted by the plane, N. If the remaining component of the gravitational force parallel to the surface (mg sin θ) is greater than the static frictional force fs – then the body will slide down the inclined plane with acceleration where fk is the kinetic friction force – otherwise it will remain stationary.

When the slope angle (θ) is zero, sin θ is also zero so the body does not move.

The MA or Mechanical advantage(ratio of load to effort) of the inclined plane equals to length of the plane over the height of the plane, in an ideal case where efficiency is 100%.

To calculate the MA (Mechanical Advantage) of an inclined plane, divide the length by the height of the ramp.

M.A=Length of the sloping surface / Height of the plane.(or) 1 / sin θ

Example: The height of the ramp = 1 meter
The length of the ramp = 5 meters
Divide 5 by 1=5 ma= 5

Velocity Ratio= height of the inclined plane / Length of the sloping surface