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49-616: The Mahanoy Plane was a railroad Incline plane located along northern edge of the borough of Frackville , Schuylkill County, Pennsylvania in the Coal Region of the United States. GPS coordinates of the abandoned site are, DMS: N 40° 47’ 14.817” W 76° 13’ 58.652” -or- DD: 40.7874493, -76.232959. The Mahanoy and Broad Mountain Railroad , predecessor of the Reading Company opened

98-532: A funicular or cable railway a railroad car is pulled up a steep inclined plane using cables. Inclined planes also allow heavy fragile objects, including humans, to be safely lowered down a vertical distance by using the normal force of the plane to reduce the gravitational force . Aircraft evacuation slides allow people to rapidly and safely reach the ground from the height of a passenger airliner . Other inclined planes are built into permanent structures. Roads for vehicles and railroads have inclined planes in

147-467: A funicular or cable railway , such as the Johnstown Inclined Plane . Inclined planes are widely used in the form of loading ramps to load and unload goods on trucks, ships and planes. Wheelchair ramps are used to allow people in wheelchairs to get over vertical obstacles without exceeding their strength. Escalators and slanted conveyor belts are also forms of an inclined plane. In

196-546: A paved ramp 6 km (3.7 miles) long, the Diolkos , to drag ships overland across the Isthmus of Corinth . However the inclined plane was the last of the six classic simple machines to be recognised as a machine. This is probably because it is a passive and motionless device (the load is the moving part), and also because it is found in nature in the form of slopes and hills. Although they understood its use in lifting heavy objects,

245-515: A sliding or prismatic joint . The origin of the wedge is not known. In ancient Egyptian quarries , bronze wedges were used to break away blocks of stone used in construction. Wooden wedges that swelled after being saturated with water were also used. Some indigenous peoples of the Americas used antler wedges for splitting and working wood to make canoes , dwellings and other objects. Wedges are used to lift heavy objects, separating them from

294-423: A wedge is given by the ratio of the length of its slope to its width. Although a short wedge with a wide angle may do a job faster, it requires more force than a long wedge with a narrow angle. The force is applied on a flat, broad surface. This energy is transported to the pointy, sharp end of the wedge, hence the force is transported. The wedge simply transports energy in the form of friction and collects it to

343-409: Is H = 1 meter and its length is L = 5 meters, then the mechanical advantage is which means that a 20 lb force will lift a 100 lb load. The Liverpool Minard inclined plane has the dimensions 1804 meters by 37.50 meters, which provides a mechanical advantage of so a 100 lb tension force on the cable will lift a 4810 lb load. The grade of this incline is 2%, which means the angle θ

392-399: Is dissipated as heat by friction, W fric {\displaystyle W_{\text{fric}}} , so less work is done on the load. Due to conservation of energy , the sum of the output work and the frictional energy losses is equal to the input work Therefore, more input force is required, and the mechanical advantage is lower, than if friction were not present. With friction,

441-552: Is not completely tight. The forces exerted by the hanging part of the chain need not be symmetrical because the hanging part need not retain its shape when let go. Even if the chain is released with a zero angular momentum, motion including oscillations is possible unless the chain is initially in its equilibrium configuration, a supposition which would make the argument circular. Inclined planes have been used by people since prehistoric times to move heavy objects. The sloping roads and causeways built by ancient civilizations such as

490-458: Is small enough that sin θ≈tan θ. Wedge (mechanical device) A wedge is a triangular shaped tool , a portable inclined plane , and one of the six simple machines . It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converting a force applied to its blunt end into forces perpendicular ( normal ) to its inclined surfaces. The mechanical advantage of

539-485: Is sometimes called ideal mechanical advantage I M A {\displaystyle \mathrm {IMA} } while the MA when friction is included is called the actual mechanical advantage A M A {\displaystyle \mathrm {AMA} } . If there is no friction between the object being moved and the plane, the device is called an ideal inclined plane . This condition might be approached if

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588-422: Is the coefficient of static friction between the two surfaces, which varies with the material. When no input force is applied, if the inclination angle θ {\displaystyle \theta } of the plane is less than some maximum value ϕ {\displaystyle \phi } the component of gravitational force parallel to the plane will be too small to overcome friction, and

637-444: Is the application of the same force over a wider area of the material to be separated. Other examples of wedges are found in drill bits , which produce circular holes in solids. The two edges of a drill bit are sharpened, at opposing angles, into a point and that edge is wound around the shaft of the drill bit. When the drill bit spins on its axis of rotation, the wedges are forced into the material to be separated. The resulting cut in

686-403: Is the force needed to hold the load motionless on the inclined plane, or push it up at a constant velocity. If the input force is greater than this, the load will accelerate up the plane. If the force is less, it will accelerate down the plane. Where there is friction between the plane and the load, as for example with a heavy box being slid up a ramp, some of the work applied by the input force

735-696: Is the most well-known, because of its originality and use of a string of beads (see box). In 1600, Italian scientist Galileo Galilei included the inclined plane in his analysis of simple machines in Le Meccaniche ("On Mechanics"), showing its underlying similarity to the other machines as a force amplifier. The first elementary rules of sliding friction on an inclined plane were discovered by Leonardo da Vinci (1452-1519), but remained unpublished in his notebooks. They were rediscovered by Guillaume Amontons (1699) and were further developed by Charles-Augustin de Coulomb (1785). Leonhard Euler (1750) showed that

784-424: Is zero. Since the direction of the frictional force is opposite for the case of uphill and downhill motion, these two cases must be considered separately: The mechanical advantage of an inclined plane is the ratio of the weight of the load on the ramp to the force required to pull it up the ramp. If energy is not dissipated or stored in the movement of the load, then this mechanical advantage can be computed from

833-520: The Pennsylvania Historical & Museum Commission erected a historical marker noting the Mahanoy Plane's historic importance. Incline plane An inclined plane , also known as a ramp , is a flat supporting surface tilted at an angle from the vertical direction , with one end higher than the other, used as an aid for raising or lowering a load. The inclined plane is one of

882-414: The ancient Greek philosophers who defined the other five simple machines did not include the inclined plane as a machine. This view persisted among a few later scientists; as late as 1826 Karl von Langsdorf wrote that an inclined plane " ...is no more a machine than is the slope of a mountain ". The problem of calculating the force required to push a weight up an inclined plane (its mechanical advantage)

931-503: The tangent of the angle of repose on an inclined plane is equal to the coefficient of friction . The mechanical advantage of an inclined plane depends on its slope , meaning its gradient or steepness. The smaller the slope, the larger the mechanical advantage, and the smaller the force needed to raise a given weight. A plane's slope s is equal to the difference in height between its two ends, or " rise ", divided by its horizontal length, or " run ". It can also be expressed by

980-482: The Mahanoy Plane on July 16, 1861. The Plane traversed Broad Mountain between the boroughs of Mahanoy Plane and Frackville . With a pitch of 28 degrees at its steepest point, the plane rose 524 feet (160 m) over a distance of 2,460 feet (750 m). A 2,500 horsepower (1,900 kW) engine could hoist a three car trip, equivalent to 200 tons in three minutes. After a fire in 1886, new 6,000 horsepower (4,500 kW) engines were installed. These were supposedly

1029-594: The Romans are examples of early inclined planes that have survived, and show that they understood the value of this device for moving things uphill. The heavy stones used in ancient stone structures such as Stonehenge are believed to have been moved and set in place using inclined planes made of earth, although it is hard to find evidence of such temporary building ramps. The Egyptian pyramids were constructed using inclined planes, Siege ramps enabled ancient armies to surmount fortress walls. The ancient Greeks constructed

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1078-410: The angle the plane makes with the horizontal, θ {\displaystyle \theta } . The mechanical advantage M A {\displaystyle \mathrm {MA} } of a simple machine as defined as the ratio of the output force exerted on the load to the input force applied.The inclined plane the output load force is just the gravitational force of the load object on

1127-402: The bottom of the door and the wedge, and the wedge and the floor (or other surface). The mechanical advantage or MA of a wedge can be calculated by dividing the height of the wedge by the wedge's width: The more acute , or narrow, the angle of a wedge, the greater the ratio of the length of its slope to its width, and thus the more mechanical advantage it will yield. A wedge will bind when

1176-465: The conservation of energy equation above and rearranging To express the mechanical advantage by the angle θ {\displaystyle \theta } of the plane, it can be seen from the diagram (above) that So So the mechanical advantage of a frictionless inclined plane is equal to the reciprocal of the sine of the slope angle. The input force F i {\displaystyle F_{\rm {i}}} from this equation

1225-634: The development of knives for those kinds of tasks. The blade of the knife allowed humans to cut meat, fibers, and other plant and animal materials with much less force than it would take to tear them apart by simply pulling with their hands. Other examples are plows , which separate soil particles, scissors which separate fabric, axes which separate wood fibers, and chisels and planes which separate wood. Wedges, saws and chisels can separate thick and hard materials, such as wood, solid stone and hard metals and they do so with much less force, waste of material, and with more precision, than crushing , which

1274-404: The dimensions of the ramp. In order to show this, let the position r of a rail car on along the ramp with an angle, θ , above the horizontal be given by where R is the distance along the ramp. The velocity of the car up the ramp is now Because there are no losses, the power used by force F to move the load up the ramp equals the power out, which is the vertical lift of the weight W of

1323-410: The distance moved. The mechanical advantage of an inclined plane, the factor by which the force is reduced, is equal to the ratio of the length of the sloped surface to the height it spans. Owing to conservation of energy , the same amount of mechanical energy ( work ) is required to lift a given object by a given vertical distance , disregarding losses from friction , but the inclined plane allows

1372-404: The force multiplied by the displacement an object moves. The work done on the load is equal to its weight multiplied by the vertical displacement it rises, which is the "rise" of the inclined plane The input work is equal to the force F i {\displaystyle F_{\text{i}}} on the object times the diagonal length of the inclined plane. Substituting these values into

1421-521: The form of gradual slopes, ramps, and causeways to allow vehicles to surmount vertical obstacles such as hills without losing traction on the road surface. Similarly, pedestrian paths and sidewalks have gentle ramps to limit their slope, to ensure that pedestrians can keep traction. Inclined planes are also used as entertainment for people to slide down in a controlled way, in playground slides , water slides , ski slopes and skateboard parks . As pointed out by Dijksterhuis, Stevin's argument

1470-444: The grain. A narrow wedge with a relatively long taper , used to finely adjust the distance between objects is called a gib, and is commonly used in machine tool adjustment. The tips of forks and nails are also wedges, as they split and separate the material into which they are pushed or driven; the shafts may then hold fast due to friction. The blade is a compound inclined plane, consisting of two inclined planes placed so that

1519-405: The inclined plane. The wedge can be considered a moving inclined plane or two inclined planes connected at the base. The screw consists of a narrow inclined plane wrapped around a cylinder . The term may also refer to a specific implementation; a straight ramp cut into a steep hillside for transporting goods up and down the hill. This may include cars on rails or pulled up by a cable system;

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1568-413: The load is stationary, neither sliding up or down the plane, whereas with a frictionless inclined plane there is only one particular value of input force for which the load is stationary. A load resting on an inclined plane, when considered as a free body has three forces acting on it: Using Newton's second law of motion the load will be stationary or in steady motion if the sum of the forces on it

1617-444: The load will only move if the net force parallel to the surface is greater than the frictional force F f {\displaystyle F_{\text{f}}} opposing it. The maximum friction force is given by where F n {\displaystyle F_{\text{n}}} is the normal force between the load and the plane, directed normal to the surface, and μ {\displaystyle \mu }

1666-492: The load will remain motionless. This angle is called the angle of repose and depends on the composition of the surfaces, but is independent of the load weight. It is shown below that the tangent of the angle of repose ϕ {\displaystyle \phi } is equal to μ {\displaystyle \mu } With friction, there is always some range of input force F i {\displaystyle F_{\text{i}}} for which

1715-400: The load. The input power pulling the car up the ramp is given by and the power out is Equate the power in to the power out to obtain the mechanical advantage as The mechanical advantage of an inclined plane can also be calculated from the ratio of length of the ramp L to its height H, because the sine of the angle of the ramp is given by therefore, Example: If the height of a ramp

1764-401: The material is in the direction of rotation of the drill bit, while the helical shape of a bit allows the removal of the cut material. Wedges can also be used to hold objects in place, such as engine parts ( poppet valves ), bicycle parts ( stems and eccentric bottom brackets ), and doors . A wedge-type door stop (door wedge) functions largely because of the friction generated between

1813-584: The most powerful engines in the world, later surpassed only by the engines operating the locks on the Panama Canal . Approximately 800 to 900 railroad cars passed over the plane every twenty-four hours. The Mahanoy Plane ceased operation on February 27, 1932, due to the decline of Anthracite and the much easier route through the Mahanoy Tunnel . Foundations are all that remain and there are currently no plans of historical preservation or restoration. There

1862-399: The object is rolling like a barrel , or supported on wheels or casters . Due to conservation of energy , for a frictionless inclined plane the work done on the load lifting it, W out {\displaystyle W_{\text{out}}} , is equal to the work done by the input force, W in {\displaystyle W_{\text{in}}} Work is defined as

1911-409: The plane, its weight F w {\displaystyle F_{\text{w}}} . The input force is the force F i {\displaystyle F_{\text{i}}} exerted on the object, parallel to the plane, to move it up the plane. The mechanical advantage is The M A {\displaystyle \mathrm {MA} } of an ideal inclined plane without friction

1960-462: 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. The blade's first known use by humans was the sharp edge of a flint stone that was used to cleave or split animal tissue, e.g. cutting meat. The use of iron or other metals led to

2009-433: The pointy end, consequently breaking the item. Wedges have existed for thousands of years. They were first made of simple stone. Perhaps the first example of a wedge is the hand axe (see also Olorgesailie ), which is made by chipping stone, generally flint , to form a bifacial edge, or wedge. A wedge is a simple machine that transforms lateral force and movement of the tool into a transverse splitting force and movement of

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2058-656: The power into the wedge equals the power out. Or The velocity of the block is related to the velocity of the wedge by the slope of the side of the wedge. If the angle of the wedge is α then which means that the mechanical advantage Thus, the smaller the angle α the greater the ratio of the lifting force to the applied force on the wedge. This is the mechanical advantage of the wedge. This formula for mechanical advantage applies to cutting edges and splitting operations, as well as to lifting. They can also be used to separate objects, such as blocks of cut stone. Splitting mauls and splitting wedges are used to split wood along

2107-452: The same work to be done with a smaller force exerted over a greater distance. The angle of friction , also sometimes called the angle of repose , is the maximum angle at which a load can rest motionless on an inclined plane due to friction without sliding down. This angle is equal to the arctangent of the coefficient of static friction μ s between the surfaces. Two other simple machines are often considered to be derived from

2156-414: The six classical simple machines defined by Renaissance scientists. Inclined planes are used to move heavy loads over vertical obstacles. Examples vary from a ramp used to load goods into a truck, to a person walking up a pedestrian ramp, to an automobile or railroad train climbing a grade. Moving an object up an inclined plane requires less force than lifting it straight up, at a cost of an increase in

2205-441: The surface upon which they rest. Consider a block that is to be lifted by a wedge. As the wedge slides under the block, the block slides up the sloped side of a wedge. This lifts the weight F B of the block. The horizontal force F A needed to lift the block is obtained by considering the velocity of the wedge v A and the velocity of the block v B . If we assume the wedge does not dissipate or store energy, then

2254-420: The workpiece. The available power is limited by the effort of the person using the tool, but because power is the product of force and movement, the wedge amplifies the force by reducing the movement. This amplification, or mechanical advantage is the ratio of the input speed to output speed. For a wedge, this is given by 1/tanα, where α is the tip angle. The faces of a wedge are modeled as straight lines to form

2303-516: Was a previous “Mahanoy Plane” built in the same general area in 1834 by the Danville and Pottsville Railroad(D&P). This was incline plane Number 5 (of six) and was 345 feet high over 1,625 feet in length. Very quickly, however, the D&;P closed the eastern section of railroad. By 1844, the eastern section, according to Rupp's History of Schuylkill County, was "rotting in the sun." On September 8, 2007,

2352-443: Was apparently not communicated to other philosophers of the time. Girolamo Cardano (1570) proposed the incorrect solution that the input force is proportional to the angle of the plane. Then at the end of the 16th century, three correct solutions were published within ten years, by Michael Varro (1584), Simon Stevin (1586), and Galileo Galilei (1592). Although it was not the first, the derivation of Flemish engineer Simon Stevin

2401-480: Was attempted by Greek philosophers Heron of Alexandria (c. 10 - 60 CE) and Pappus of Alexandria (c. 290 - 350 CE), but their solutions were incorrect. It was not until the Renaissance that the inclined plane was solved mathematically and classed with the other simple machines. The first correct analysis of the inclined plane appeared in the work of 13th century author Jordanus de Nemore , however his solution

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