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Screw (simple machine)
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A screw is one of the six simple machines. All screws are helical inclined planes. A screw can convert a rotational force (torque) to a linear force and vice versa. The ratio of threading determines the mechanical advantage of the machine. More threading increases the mechanical advantage. A rough comparison of mechanical advantage can be done by taking the circumference of the shaft of the screw and divide by the distance between the threads.

A screw is a shaft with a helical groove or thread formed on its surface and provision at one end to turn the screw. Its main uses are as a threaded fastener used to hold objects together, and as a simple machine used to translate torque into linear force. It can also be defined as an inclined plane wrapped around a shaft.

Screws come in a variety of shapes and sizes for different purposes.
Thread as found on a screw.

[edit] Examples

* Lead screws and ball screws are specialized screws for translating rotational to linear motion.
* Automated garage doors, where a motor drives a long finely threaded shaft at relatively high speed and lifts the heavy door at a slower rate.
* Archimedes' screw and worm gears are examples of this machine.


Wedge (mechanical device)
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Wood splitting wedge
Classification Hand tool
Used with Sledgehammer
Related Chisel
Splitting maul

A wedge is a triangular shaped tool, a compound and portable inclined plane, and one of the six classical simple machines. It can be used to separate two objects or portions of an object, lift an object, or hold an object in place. It functions by converting a force applied to its blunt end into forces perpendicular to its length. The mechanical advantage of a wedge is given by the ratio of its length to its width.[1] 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.

* 1 History
* 2 Examples for lifting and separating
* 3 Examples for holding fast
* 4 Mechanical advantage
* 5 References
* 6 See also
* 7 External links

[edit] History

The origin of the wedge is unknown likely because it has been in use for over 9000 years. 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.

[edit] Examples for lifting and separating

Wedges can be used to lift heavy objects, separating them from the surface they rest on. 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 the grain. A narrow wedge with a relatively long taper used to finely adjust the distance between objects is called a shim, and is commonly used in carpentry.

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.

[edit] Examples for holding fast
An insect nest is wedged in between two stones to hold it in place.

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 the bottom of the door and the wedge, and the wedge and the floor (or other surface).

[edit] Mechanical advantage
Cross-section of a wedge with its length oriented vertically. A downward force produces horizontal forces extending outward.

The mechanical advantage of a wedge can be calculated by dividing its length by its width as follows:

MA={L \over W}

The more "acute" (narrow) the angle of a wedge, the greater the ratio of its length to its width, and thus the more mechanical advantage it will yield.

However, in an elastic material such as wood, friction may bind a narrow wedge more easily than a wide one. This is why the head of a splitting maul has a much wider angle than that of an axe.


From Wikipedia, the free encyclopedia
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Sister project Look up fulcrum in
Wiktionary, the free dictionary.

Fulcrum may refer to one of the following.

* Fulcrum, the pivot on which a lever moves
* Fulcrum Wheels, a bicycle wheel manufacturer, based in Italy
* Fulcrum (drumming), part of a percussionist's grip
* MiG-29 Fulcrum or Mikoyan MiG-29, a Soviet fighter aircraft
* Fulcrum (Anglican think tank), a Church of England think tank
* Fulcrum (newspaper), a student newspaper at the University of Ottawa
* Fulcrum (annual), a United States literary periodical, an annual of poetry and aesthetics
* Fulcrum Technologies, a former Canadian search engine, now part of Open Text Corporation
* Fulcrum (Chuck), the enemy spy organization on the TV series Chuck

This disambiguation page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.
Complex Machines
By Sharon Fabian
1 Let's say you already know about the six simple machines: inclined plane, wedge, screw, lever, wheel and axle, and pulley. You've probably figured out that these six machines were invented ages and ages ago. So what has been happening since then? Did someone invent simple machine number 7, 8, 9, 10, and so on? How many simple machines do we have by now? Hundreds? Thousands?

2 Lets look at a bicycle for an example. A bicycle is a much newer machine than the simple lever that a cave man used to move a big old rock, but its not as new as, say, a laptop computer. Where does a bicycle fit into the world of machines? Well, a bicycle is not number 7, or 100, or even 1000. A bicycle is actually a combination of several of those six basic simple machines. A bicycle gear is actually a combination of simple machines all by itself. A gear is a wheel, but the teeth on the gear are little wedges. What other simple machines can you find on a bicycle?

3 Gears, along with other simple machines, make up many of the machines you use every day. Some examples are the lawn sprinkler, a watch, and the gearbox in a car.


Electrical resistance
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A 750-kΩ resistor, as identified by its electronic color code. An ohmmeter could be used to verify this value.

The electrical resistance of an object is a measure of its opposition to the passage of a steady electrical current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material.

Discovered by Georg Ohm in the late 1820s[1], electrical resistance shares some conceptual parallels with the mechanical notion of friction. The SI unit of electrical resistance is the ohm, symbol Ω. Resistance's reciprocal quantity is electrical conductance measured in siemens, symbol S.

The resistance of a resistive object determines the amount of current through the object for a given potential difference across the object, in accordance with Ohm's law:

I = {V \over R}


R is the resistance of the object, measured in ohms, equivalent to J·s/C2
V is the potential difference across the object, measured in volts
I is the current through the object, measured in amperes

For a wide variety of materials and conditions, the electrical resistance does not depend on the amount of current through or the amount of voltage across the object, meaning that the resistance R is constant for the given temperature. Therefore, the resistance of an object can be defined as the ratio of voltage to current:

R = {V \over I}

In the case of nonlinear objects (not purely resistive, or not obeying Ohm's law), this ratio can change as current or voltage changes; the ratio taken at any particular point, the inverse slope of a chord to an I–V curve, is sometimes referred to as a "chordal resistance" or "static resistance".[2][3]

* 1 Resistance of a conductor
o 1.1 DC resistance
o 1.2 AC resistance
* 2 Causes of resistance
o 2.1 In metals
o 2.2 In semiconductors and insulators
o 2.3 In ionic liquids/electrolytes
o 2.4 Resistivity of various materials
o 2.5 Band theory simplified
* 3 Differential resistance
* 4 Temperature-dependence
* 5 Measuring resistance
* 6 See also
* 7 References
* 8 External links

[edit] Resistance of a conductor

[edit] DC resistance

The resistance R of a conductor of uniform cross section can be computed as

R = {\ell \cdot \rho \over A} \,


ℓ is the length of the conductor, measured in meters

A is the cross-sectional area, measured in square meters

ρ (Greek: rho) is the electrical resistivity (also called specific electrical resistance) of the material, measured in Ohm · meter. Resistivity is a measure of the material's ability to oppose electric current.

For practical reasons, any connections to a real conductor will almost certainly mean the current density is not totally uniform. However, this formula still provides a good approximation for long thin conductors such as wires.

[edit] AC resistance

If a wire conducts high-frequency alternating current then the effective cross sectional area of the wire is reduced because of the skin effect. If several conductors are together, then due to proximity effect, the effective resistance of each is higher than if that conductor were alone.

[edit] Causes of resistance

[edit] In metals

A metal consists of a lattice of atoms, each with a shell of electrons. This can also be known as a positive ionic lattice. The outer electrons are free to dissociate from their parent atoms and travel through the lattice, creating a 'sea' of electrons, making the metal a conductor. When an electrical potential difference (a voltage) is applied across the metal, the electrons drift from one end of the conductor to the other under the influence of the electric field.

Near room temperatures, the thermal motion of ions is the primary source of scattering of electrons (due to destructive interference of free electron waves on non-correlating potentials of ions), and is thus the prime cause of metal resistance. Imperfections of lattice also contribute into resistance, although their contribution in pure metals is negligible.

The larger the cross-sectional area of the conductor, the more electrons are available to carry the current, so the lower the resistance. The longer the conductor, the more scattering events occur in each electron's path through the material, so the higher the resistance. Different materials also affect the resistance.[1]

[edit] In semiconductors and insulators

In metals, the Fermi level lies in the conduction band (see Band Theory, below) giving rise to free conduction electrons. However, in semiconductors the position of the Fermi level is within the band gap, approximately half-way between the conduction band minimum and valence band maximum for intrinsic (undoped) semiconductors. This means that at 0 Kelvin, there are no free conduction electrons and the resistance is infinite. However, the resistance will continue to decrease as the charge carrier density in the conduction band increases. In extrinsic (doped) semiconductors, dopant atoms increase the majority charge carrier concentration by donating electrons to the conduction band or accepting holes in the valence band. For both types of donor or acceptor atoms, increasing the dopant density leads to a reduction in the resistance. Highly doped semiconductors hence behave metallic. At very high temperatures, the contribution of thermally generated carriers will dominate over the contribution from dopant atoms and the resistance will decrease exponentially with temperature.

[edit] In ionic liquids/electrolytes

In electrolytes, electrical conduction happens not by band electrons or holes, but by full atomic species (ions) traveling, each carrying an electrical charge. The resistivity of ionic liquids varies tremendously by the concentration - while distilled water is almost an insulator, salt water is a very efficient electrical conductor. In biological membranes, currents are carried by ionic salts. Small holes in the membranes, called ion channels, are selective to specific ions and determine the membrane resistance.

[edit] Resistivity of various materials
Main article: electrical resistivities of the elements (data page)
Material Resistivity, ρ
Metals 10 - 8
Semiconductors variable
Electrolytes variable
Insulators 1016
Superconductors 0 (exactly)

[edit] Band theory simplified
Electron energy levels in an insulator.

Quantum mechanics states that the energy of an electron in an atom cannot be any arbitrary value. Rather, there are fixed energy levels which the electrons can occupy, and values in between these levels are impossible. The energy levels are grouped into two bands: the valence band and the conduction band (the latter is generally above the former). Electrons in the conduction band may move freely throughout the substance in the presence of an electrical field.

In insulators and semiconductors, the atoms in the substance influence each other so that between the valence band and the conduction band there exists a forbidden band of energy levels, which the electrons cannot occupy. In order for a current to flow, a relatively large amount of energy must be furnished to an electron for it to leap across this forbidden gap and into the conduction band. Thus, even large voltages can yield relatively small currents.

[edit] Differential resistance

When resistance may depend on voltage and current, differential resistance, incremental resistance or slope resistance is defined as the slope of the V-I graph at a particular point, thus:

R = \frac {\mathrm{d}V} {\mathrm{d}I} \,

This quantity is sometimes called simply resistance, although the two definitions are equivalent only for an ohmic component such as an ideal resistor. For example, a diode is a circuit element for which the resistance depends on the applied voltage or current.

If the V-I graph is not monotonic (i.e. it has a peak or a trough), the differential resistance will be negative for some values of voltage and current. This property is often known as negative resistance, although it is more correctly called negative differential resistance, since the absolute resistance V/I is still positive. Example of such an element is a tunnel diode.

[edit] Temperature-dependence

Near room temperature, the electric resistance of a typical metal increases linearly with rising temperature, while the electrical resistance of a typical semiconductor decreases with rising temperature. The amount of that change in resistance can be calculated using the temperature coefficient of resistivity of the material.

At lower temperatures (less than the Debye temperature), the resistance of a metal decreases as T5 due to the electrons scattering off of phonons. At even lower temperatures, the dominant scattering mechanism for electrons is other electrons, and the resistance decreases as T2. At some point, the impurities in the metal will dominate the behavior of the electrical resistance which causes it to saturate to a constant value. Matthiessen's Rule (first formulated by Augustus Matthiessen in the 1860s; the equation below gives its modern form) [4][5] says that all of these different behaviors can be summed up to get the total resistance as a function of temperature,

R = R_\text{imp} + a T^2 + b T^5 + cT \,

where Rimp is the temperature independent electrical resistivity due to impurities, and a, b, and c are coefficients which depend upon the metal's properties. This rule can be seen as the motivation to Heike Kamerlingh Onnes's experiments that lead in 1911 to discovery of superconductivity. For details see History of superconductivity.

The electric resistance of a typical intrinsic (non doped) semiconductor decreases exponentially with the temperature:

R= R_0 e^{-aT}\,

Extrinsic (doped) semiconductors have a far more complicated temperature profile. As temperature increases starting from absolute zero they first decrease steeply in resistance as the carriers leave the donors or acceptors. After most of the donors or acceptors have lost their carriers the resistance starts to increase again slightly due to the reducing mobility of carriers (much as in a metal). At higher temperatures it will behave like intrinsic semiconductors as the carriers from the donors/acceptors become insignificant compared to the thermally generated carriers.

The electric resistance of electrolytes and insulators is highly nonlinear, and case by case dependent, therefore no generalized equations are given.

[edit] Measuring resistance

An instrument for measuring resistance is called an ohmmeter. Simple ohmmeters cannot measure low resistances accurately because the resistance of their measuring leads causes a voltage drop that interferes with the measurement, so more accurate devices use four-terminal sensing.
Mechanical advantage
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In physics and engineering, mechanical advantage (MA) is the factor by which a mechanism multiplies the force or torque put into it. Generally, the mechanical advantage is calculated as follows:

MA = \frac{\text{distance over which effort is applied}}{\text{distance over which the load is moved}}

or more simply:

MA = \frac{\text{output force}}{\text{input force}}

The first equation shows that the force exerted IN to the machine multiplied by the distance moved IN will always be equal to the force exerted OUT of the machine multiplied by the distance moved OUT. For example, using a block and tackle with 6 ropes, and a 600 pound load, the operator would be required to pull the rope 6 feet, and exert 100 pounds of force to lift the 600 pound load 1 foot.

The second equation is a simplified formula based just on the forces in and out. Using the example above, 100 pounds of force IN results in 600 pounds of force OUT, an MA of 6. Both of these equations calculate only the ideal mechanical advantage (IMA) and ignore any losses due to friction.

The actual mechanical advantage (AMA) includes those frictional losses. The difference between the two is the mechanical efficiency of the system.

* 1 Simple machines
o 1.1 Pulleys
o 1.2 Screws
* 2 Types
o 2.1 Ideal mechanical advantage
o 2.2 Actual mechanical advantage
* 3 See also
* 4 References
o 4.1 Notes
o 4.2 Bibliography
* 5 External links

[edit] Simple machines
Beam balanced around a fulcrum

The following simple machines exhibit a mechanical advantage:

* The beam shown is in static equilibrium around the fulcrum. This is due to the moment created by vector force "A" counterclockwise (moment A*a) being in equilibrium with the moment created by vector force "B" clockwise (moment B*b). The relatively low vector force "B" is translated in a relatively high vector force "A". The force is thus increased in the ratio of the forces A : B, which is equal to the ratio of the distances to the fulcrum b : a. This ratio is called the mechanical advantage. This idealised situation does not take into account friction. For more explanation, see also lever.

* Wheel and axle notion (e.g. screwdrivers, doorknobs): A wheel is essentially a lever with one arm the distance between the axle and the outer point of the wheel, and the other the radius of the axle. Typically this is a fairly large difference, leading to a proportionately large mechanical advantage. This allows even simple wheels with wooden axles running in wooden blocks to still turn freely, because their friction is overwhelmed by the rotational force of the wheel multiplied by the mechanical advantage.

* Pulley: Pulleys change the direction of a tension force on a flexible material, e.g. a rope or cable. In addition, pulleys can be "added together" to create mechanical advantage, by having the flexible material looped over several pulleys in turn. Adding more loops and pulleys increases the mechanical advantage.

* Screw: A screw is essentially an inclined plane wrapped around a cylinder. The run over the rise of this inclined plane is the mechanical advantage of a screw.[1]

[edit] Pulleys
An example of a rope and pulley system illustrating mechanical advantage.

Consider lifting a weight with rope and pulleys. A rope looped through a pulley attached to a fixed spot, e.g. a barn roof rafter, and attached to the weight is called a single fixed pulley. It has an MA = 1 (assuming frictionless bearings in the pulley), meaning no mechanical advantage (or disadvantage) however advantageous the change in direction may be.

A single movable pulley has an MA of 2 (assuming frictionless bearings in the pulley). Consider a pulley attached to a weight being lifted. A rope passes around it, with one end attached to a fixed point above, e.g. a barn roof rafter, and a pulling force is applied upward to the other end with the two lengths parallel. In this situation the distance the lifter must pull the rope becomes twice the distance the weight travels, allowing the force applied to be halved. Note: if an additional pulley is used to change the direction of the rope, e.g. the person doing the work wants to stand on the ground instead of on a rafter, the mechanical advantage is not increased.

By looping more ropes around more pulleys we can continue to increase the mechanical advantage. For example if we have two pulleys attached to the rafter, two pulleys attached to the weight, one end attached to the rafter, and someone standing on the rafter pulling the rope, we have a mechanical advantage of four. Again note: if we add another pulley so that someone may stand on the ground and pull down, we still have a mechanical advantage of four.

Here are examples where the fixed point is not obvious:

* A velcro strap on a shoe passes through a slot and folds over on itself. The slot is a movable pulley and the MA = 2.
* Two ropes laid down a ramp attached to a raised platform. A barrel is rolled onto the ropes and the ropes are passed over the barrel and handed to two workers at the top of the ramp. The workers pull the ropes together to get the barrel to the top. The barrel is a movable pulley and the MA = 2. If there is enough friction where the rope is pinched between the barrel and the ramp, the pinch point becomes the attachment point. This is considered a fixed attachment point because the rope above the barrel does not move relative to the ramp. Alternatively the ends of the rope can be attached to the platform.
* Block and tackle: MA = 3
* Inclined plane: MA = length of slope ÷ height of slope

[edit] Screws

The theoretical mechanical advantage for a screw can be calculated using the following equation:[2]

MA = \frac{\pi d_m}{l}


dm = the mean diameter of the screw thread
l = the lead of the screw thread

Note that the actual mechanical advantage of a screw system is greater, as a screwdriver or other screw driving system has a mechanical advantage as well.

[edit] Types

There are two types of mechanical advantage:

1. Ideal mechanical advantage (IMA)
2. Actual mechanical advantage (AMA)

[edit] Ideal mechanical advantage

The ideal mechanical advantage (IMA), or theoretical mechanical advantage, is the mechanical advantage of an ideal machine. It is usually calculated using physics principles because there is no ideal machine.

The IMA of a machine can be found with the following formula:

IMA = \frac {D_E} {D_R}


DE equals the effort distance (the distance from the fulcrum to where the effort is applied)
DR equals the resistance distance (the distance from the fulcrum to where the resistance is applied)

[edit] Actual mechanical advantage

The actual mechanical advantage (AMA) is the mechanical advantage of a real machine. Actual mechanical advantage takes into consideration real world factors such as energy lost in friction.

The AMA of a machine is calculated with the following formula:

AMA = \frac {R} {E_\text{actual}}


R = resistance force
Eactual = actual effort force


From Wikipedia, the free encyclopedia
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For the band, see Pulley (band). For the village, see Pulley, Shropshire. For the American photographer, see Gerald P. Pulley.
Pulleys on a ship. In this context, pulleys are usually known as blocks.

A pulley (also called a block) is a mechanism composed of a wheel (called a sheave) with a groove between two flanges around the wheel's circumference. A rope, cable or belt usually runs inside the groove. Pulleys are used to change the direction of an applied force, transmit rotational motion, or realize a mechanical advantage in either a linear or rotational system of motion.

* 1 Belt and pulley systems
* 2 Rope and pulley systems
o 2.1 Types of systems
o 2.2 How it works
* 3 See also

[edit] Belt and pulley systems
Belt and pulley system

A belt and pulley system is characterized by two or more pulleys in common to a belt. This allows for mechanical power, torque, and speed to be transmitted across axes and, if the pulleys are of differing diameters, a mechanical advantage to be realized.

A belt drive is analogous to that of a chain drive, however a belt sheave may be smooth (devoid of discrete interlocking members as would be found on a chain sprocket, spur gear, or timing belt) so that the mechanical advantage is given by the ratio of the pitch diameter of the sheaves only (one is not able to count 'teeth' to determine gear ratio).

[edit] Rope and pulley systems

Also called block and tackles, rope and pulley systems (the rope may be a light line or a strong cable) are characterized by the use of one rope transmitting a linear motive force (in tension) to a load through one or more pulleys for the purpose of pulling the load (often against gravity.) They are often included in the list of simple machines.

In a system of a single rope and pulleys, when friction is neglected, the mechanical advantage gained can be calculated by counting the number of rope lengths exerting force on the load. Since the tension in each rope length is equal to the force exerted on the free end of the rope, the mechanical advantage is simply equal to the number of ropes pulling on the load. For example, in Diagram 3 below, there is one rope attached to the load, and 2 rope lengths extending from the pulley attached to the load, for a total of 3 ropes supporting it. If the force applied to the free end of the rope is 10 lb, each of these rope lengths will exert a force of 10 lb. on the load, for a total of 30 lb. So the mechanical advantage is 3.

The force on the load is increased by the mechanical advantage; however the distance the load moves, compared to the length the free end of the rope moves, is decreased in the same proportion. Since a slender cable is more easily managed than a fat one (albeit shorter and stronger), pulley systems are often the preferred method of applying mechanical advantage to the pulling force of a winch (as can be found in a lift crane).

Pulley systems are the only simple machines in which the possible values of mechanical advantage are limited to whole numbers.

In practice, the more pulleys there are, the less efficient a system is. This is due to sliding friction in the system where cable meets pulley and in the rotational mechanism of each pulley.

It is not recorded when or by whom the pulley was first developed. It is believed however that Archimedes developed the first documented block and tackle pulley system, as recorded by Plutarch. Plutarch reported that Archimedes moved an entire warship, laden with men, using compound pulleys and his own strength.

[edit] Types of systems
Fixed pulley
Movable pulley

These are different types of pulley systems:

* Fixed A fixed or class 1 pulley has a fixed axle. That is, the axle is "fixed" or anchored in place. A fixed pulley is used to change the direction of the force on a rope (called a belt). A fixed pulley has a mechanical advantage of 1. A mechanical advantage of one means that the force is equal on both sides of the pulley and there is no multiplication of force.
* Movable A movable or class 2 pulley has a free axle. That is, the axle is "free" to move in space. A movable pulley is used to multiply forces. A movable pulley has a mechanical advantage of 2. That is, if one end of the rope is anchored, pulling on the other end of the rope will apply a doubled force to the object attached to the pulley.
* Compound A compound pulley is a combination of a fixed and a movable pulley system.
o Block and tackle - A block and tackle is a compound pulley where several pulleys are mounted on each axle, further increasing the mechanical advantage. Block and tackles usually lift objects with a mechanical advantage greater than 2.

[edit] How it works

Diagram 1 - A basic equation for a pulley: In equilibrium, the force F on the pulley axle is equal and opposite to the sum of the tensions in each line leaving the pulley, and these tensions are equal.

Diagram 2 - A simple pulley system - a single movable pulley lifting weight W. The tension in each line is W/2, yielding an advantage of 2.

Diagram 2a - Another simple pulley system similar to diagram 2, but in which the lifting force is redirected downward.

A practical compound pulley corresponding to diagram 2a.

The simplest theory of operation for a pulley system assumes that the pulleys and lines are weightless, and that there is no energy loss due to friction. It is also assumed that the lines do not stretch.
A crane using the compound pulley system yielding an advantage of 4. The single fixed pulley is installed on the crane. The two movable pulleys (joined together) are attached to the hook. One end of the rope is attached to the crane frame, another - to the winch.

In equilibrium, the total force on the pulley must be zero. This means that the force on the axle of the pulley is shared equally by the two lines looping through the pulley. The situation is schematically illustrated in diagram 1. For the case where the lines are not parallel, the tensions in each line are still equal, but now the vector sum of all forces is zero.

A second basic equation for the pulley follows from the conservation of energy: The product of the weight lifted times the distance it is moved is equal to the product of the lifting force (the tension in the lifting line) times the distance the lifting line is moved. The weight lifted divided by the lifting force is defined as the advantage of the pulley system.

It is important to notice that a system of pulleys does not change the amount of work done. The work is given by the force times the distance moved. The pulley simply allows trading force for distance: you pull with less force, but over a longer distance.

In diagram 2, a single movable pulley allows weight W to be lifted with only half the force needed to lift the weight without assistance. The total force needed is divided between the lifting force (red arrow) and the "ceiling" which is some immovable object (such as the earth). In this simple system, the lifting force is directed in the same direction as the movement of the weight. The advantage of this system is 2. Although the force needed to lift the weight is only W/2, we will need to draw a length of rope that is twice the distance that the weight is lifted, so that the total amount of work done (Force x distance) remains the same.

A second pulley may be added as in diagram 2a, which simply serves to redirect the lifting force downward, it does not change the advantage of the system.

Diagram 3 - A simple compound pulley system - a movable pulley and a fixed pulley lifting weight W. The tension in each line is one W/3, yielding an advantage of 3.

Diagram 3a - A simple compound pulley system - a movable pulley and a fixed pulley lifting weight W, with an additional pulley redirecting the lifting force downward. The tension in each line is one W/3, yielding an advantage of 3.

Diagram 4a - A more complicated compound pulley system. The tension in each line is W/4, yielding an advantage of 4. An additional pulley redirecting the lifting force has been added.

Figure 4b - A practical block and tackle pulley system corresponding to diagram 4a. Note that the axles of the fixed and movable pulleys have been combined.

The addition of a fixed pulley to the single pulley system can yield an increase of advantage. In diagram 3, the addition of a fixed pulley yields a lifting advantage of 3. The tension in each line is W/3, and the force on the axles of each pulley is 2W/3. As in the case of diagram 2a, another pulley may be added to reverse the direction of the lifting force, but with no increase in advantage. This situation is shown in diagram 3a.

This process can be continued indefinitely for ideal pulleys with each additional pulley yielding a unit increase in advantage. For real pulleys friction among rope and pulleys will increase as more pulleys are added to the point that no advantage is possible. It puts a limit for the number of pulleys usable in practice. The above pulley systems are known collectively as block and tackle pulley systems. In diagram 4a, a block and tackle system with advantage 4 is shown. A practical implementation in which the connection to the ceiling is combined and the fixed and movable pulleys are encased in single housings is shown in figure 4b.

Other pulley systems are possible, and some can deliver an increased advantage with fewer pulleys than the block and tackle system. The advantage of the block and tackle system is that each pulley and line is subjected to equal tensions and forces. Efficient design dictates that each line and pulley be capable of handling its load, and no more. Other pulley designs will require different strengths of line and pulleys depending on their position in the system, but a block and tackle system can use the same line size throughout, and can mount the fixed and movable pulleys on a common axle.