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62-431: Mechanically, a seesaw is a lever which consists of a beam and fulcrum with the effort and load on either side. The most common playground design of seesaw features a board balanced in the center. A person sits on each end, and they take turns pushing their feet against the ground to lift their side into the air. Playground seesaws usually have handles for the riders to grip as they sit facing each other. One problem with

124-638: A ( F A ⋅ e A ⊥ ) − b ( F B ⋅ e B ⊥ ) = a F A − b F B , {\displaystyle F_{\theta }=\mathbf {F} _{A}\cdot {\frac {\partial \mathbf {v} _{A}}{\partial {\dot {\theta }}}}-\mathbf {F} _{B}\cdot {\frac {\partial \mathbf {v} _{B}}{\partial {\dot {\theta }}}}=a(\mathbf {F} _{A}\cdot \mathbf {e} _{A}^{\perp })-b(\mathbf {F} _{B}\cdot \mathbf {e} _{B}^{\perp })=aF_{A}-bF_{B},} where F A and F B are components of

186-426: A b . {\displaystyle MA={\frac {F_{2}}{F_{1}}}={\frac {a}{b}}.\!} This relationship shows that the mechanical advantage can be computed from ratio of the distances from the fulcrum to where the input and output forces are applied to the lever, assuming a weightless lever and no losses due to friction, flexibility or wear. This remains true even though the "horizontal" distance (perpendicular to

248-403: A b . {\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}}.} This is the law of the lever , which was proven by Archimedes using geometric reasoning. It shows that if the distance a from the fulcrum to where the input force is applied (point A ) is greater than the distance b from fulcrum to where the output force is applied (point B ), then the lever amplifies

310-432: A and b are distances from the fulcrum to points A and B and if force F A applied to A is the input force and F B exerted at B is the output, the ratio of the velocities of points A and B is given by a / b so the ratio of the output force to the input force, or mechanical advantage, is given by This is the law of the lever , which Archimedes formulated using geometric reasoning. It shows that if

372-406: A and b are distances from the fulcrum to points A and B and the force F A applied to A is the input and the force F B applied at B is the output, the ratio of the velocities of points A and B is given by a/b , so we have the ratio of the output force to the input force, or mechanical advantage, is given by: M A = F B F A =

434-485: A toothed belt drive, the number of teeth on the sprocket can be used. For friction belt drives the pitch radius of the input and output pulleys must be used. The mechanical advantage of a pair of a chain drive or toothed belt drive with an input sprocket with N A teeth and the output sprocket has N B teeth is given by The mechanical advantage for friction belt drives is given by Chains and belts dissipate power through friction, stretch and wear, which means

496-401: A fixed point. The lever operates by applying forces at different distances from the fulcrum, or a pivot. As the lever rotates around the fulcrum, points further from this pivot move faster than points closer to the pivot. Therefore, a force applied to a point further from the pivot must be less than the force located at a point closer in, because power is the product of force and velocity. If

558-436: A mechanical power transmission scheme. It is common for mechanical advantage to be manipulated in a 'collapsed' form, via the use of more than one gear (a gearset). In such a gearset, gears having smaller radii and less inherent mechanical advantage are used. In order to make use of non-collapsed mechanical advantage, it is necessary to use a 'true length' rotary lever. See, also, the incorporation of mechanical advantage into

620-433: A pair of meshing gears for which the input gear has N A teeth and the output gear has N B teeth is given by This shows that if the output gear G B has more teeth than the input gear G A , then the gear train amplifies the input torque. And, if the output gear has fewer teeth than the input gear, then the gear train reduces the input torque. If the output gear of a gear train rotates more slowly than

682-427: A power source, is frictionless, and is constructed from rigid bodies that do not deflect or wear. The performance of a real system relative to this ideal is expressed in terms of efficiency factors that take into account departures from the ideal. The lever is a movable bar that pivots on a fulcrum attached to or positioned on or across a fixed point. The lever operates by applying forces at different distances from

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744-425: A tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for this is the law of the lever . Machine components designed to manage forces and movement in this way are called mechanisms . An ideal mechanism transmits power without adding to or subtracting from it. This means the ideal machine does not include

806-578: A word or syllable is doubled, often with a different vowel. Reduplication is typical of words that indicate repeated activity, such as riding up and down on a seesaw. In the southeastern New England region of the United States, it is sometimes referred to as a tilt or a tilting board . According to Michael Drout , "There are almost no 'Teeter-' forms in Pennsylvania , and if you go to western West Virginia and down into western North Carolina there

868-516: Is a band of 'Ridey-Horse' that heads almost straight south. This pattern suggests a New England term that spread down the coast and a separate, Scots-Irish development in Appalachia. 'Hickey-horse' in the coastal regions of North Carolina is consistent with other linguistic and ethnic variations." In the early 2000s, seesaws were removed from many playgrounds in the United States, citing safety concerns. However, some people have questioned whether or not

930-553: Is a direct Anglicisation of the French ci-ça , meaning literally, this-that , seemingly attributable to the back-and-forth motion for which a seesaw is known. The term may also be attributable to the repetitive motion of a saw. It may have its origins in a combination of "scie" – the French word for "saw" with the Anglo-Saxon term "saw". Thus "scie-saw" became "see-saw". Another possibility

992-447: Is evident from the recesses in the large blocks and the handling bosses which could not be used for any purpose other than for levers. The earliest remaining writings regarding levers date from the 3rd century BC and were provided, by common belief, by the Greek mathematician Archimedes , who famously stated "Give me a lever long enough and a fulcrum on which to place it, and I shall move

1054-415: Is lessened. T 1 = F 1 a , T 2 = F 2 b {\displaystyle {\begin{aligned}T_{1}&=F_{1}a,\quad \\T_{2}&=F_{2}b\!\end{aligned}}} where F 1 is the input force to the lever and F 2 is the output force. The distances a and b are the perpendicular distances between

1116-482: Is one of the six simple machines identified by Renaissance scientists. A lever amplifies an input force to provide a greater output force, which is said to provide leverage , which is mechanical advantage gained in the system, equal to the ratio of the output force to the input force. As such, the lever is a mechanical advantage device , trading off force against movement. The word "lever" entered English around AD 1300 from Old French : levier . This sprang from

1178-405: Is operated by applying an input force F A at a point A located by the coordinate vector r A on the bar. The lever then exerts an output force F B at the point B located by r B . The rotation of the lever about the fulcrum P is defined by the rotation angle θ in radians. Let the coordinate vector of the point P that defines the fulcrum be r P , and introduce

1240-481: Is the generalized coordinate that defines the configuration of the lever, and the generalized force associated with this coordinate is given by F θ = F A ⋅ ∂ v A ∂ θ ˙ − F B ⋅ ∂ v B ∂ θ ˙ =

1302-412: Is the situation of the apparent appearance, disappearance, and re-emergence of the person, seated opposite one's position, as they, seemingly, "rise" and "fall", against a changing, oscillating background - therefore: "I see you", followed by, "I saw you". In the northern inland and westernmost region of the United States, a seesaw is also called a "teeter-totter." According to linguist Peter Trudgill ,

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1364-449: The actual mechanical advantage (AMA) is defined by a factor called efficiency , a quantity which is determined by experimentation. As an example, using a block and tackle with six rope sections and a 600 lb load, the operator of an ideal system would be required to pull the rope six feet and exert 100  lb F of force to lift the load one foot. Both the ratios F out / F in and V in / V out show that

1426-447: The ancient Near East c.  5000 BC , when it was first used in a simple balance scale . In ancient Egypt c.  4400 BC , a foot pedal was used for the earliest horizontal frame loom . In Mesopotamia (modern Iraq) c.  3000 BC , the shadouf , a crane-like device that uses a lever mechanism, was invented. In ancient Egypt , workmen used the lever to move and uplift obelisks weighing more than 100 tons. This

1488-469: The IMA is six. For the first ratio, 100  lb F of force input results in 600  lb F of force out. In an actual system, the force out would be less than 600 pounds due to friction in the pulleys. The second ratio also yields a MA of 6 in the ideal case but a smaller value in the practical scenario; it does not properly account for energy losses such as rope stretch. Subtracting those losses from

1550-491: The IMA or using the first ratio yields the AMA. The ideal mechanical advantage (IMA), or theoretical mechanical advantage , is the mechanical advantage of a device with the assumption that its components do not flex, there is no friction, and there is no wear. It is calculated using the physical dimensions of the device and defines the maximum performance the device can achieve. The assumptions of an ideal machine are equivalent to

1612-424: The chain or belt is the same when in contact with the two sprockets or pulleys: where the input sprocket or pulley A meshes with the chain or belt along the pitch radius r A and the output sprocket or pulley B meshes with this chain or belt along the pitch radius r B , therefore where N A is the number of teeth on the input sprocket and N B is the number of teeth on the output sprocket. For

1674-429: The corresponding backward-directed reaction force on the ground is indicated). A block and tackle is an assembly of a rope and pulleys that is used to lift loads. A number of pulleys are assembled together to form the blocks, one that is fixed and one that moves with the load. The rope is threaded through the pulleys to provide mechanical advantage that amplifies that force applied to the rope. In order to determine

1736-458: The design of certain types of electric motors; one design is an 'outrunner'. As the lever pivots on the fulcrum, points farther from this pivot move faster than points closer to the pivot. The power into and out of the lever is the same, so must come out the same when calculations are being done. Power is the product of force and velocity, so forces applied to points farther from the pivot must be less than when applied to points closer in. If

1798-443: The distance a from the fulcrum to where the input force is applied (point A ) is greater than the distance b from fulcrum to where the output force is applied (point B ), then the lever amplifies the input force. If the distance from the fulcrum to the input force is less than from the fulcrum to the output force, then the lever reduces the input force. To Archimedes, who recognized the profound implications and practicalities of

1860-564: The eagerness of children to play with them, are sometimes used to aid in mechanical processes. For example, at the Gaviotas community in Colombia , a children's seesaw is connected to a water pump . In 2019, a set of seesaws were installed spanning the US-Mexico border fence between El Paso and Ciudad Juárez. Seesaws go by several different names around the world. Seesaw , or its variant see-saw ,

1922-416: The end of the rope, which is A where the input force is applied. Let R be the distance from the axle of the fixed block to the axle of the moving block, which is B where the load is applied. The total length of the rope L can be written as where K is the constant length of rope that passes over the pulleys and does not change as the block and tackle moves. The velocities V A and V B of

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1984-442: The forces and the fulcrum. Since the moments of torque must be balanced, T 1 = T 2 {\displaystyle T_{1}=T_{2}\!} . So, F 1 a = F 2 b {\displaystyle F_{1}a=F_{2}b\!} . The mechanical advantage of a lever is the ratio of output force to input force. M A = F 2 F 1 =

2046-400: The forces that are perpendicular to the radial segments PA and PB . The principle of virtual work states that at equilibrium the generalized force is zero, that is F θ = a F A − b F B = 0. {\displaystyle F_{\theta }=aF_{A}-bF_{B}=0.\,\!} Thus, the ratio of the output force F B to

2108-408: The front and rear sprockets The ratio of the force driving the bicycle to the force on the pedal, which is the total mechanical advantage of the bicycle, is the product of the speed ratio (or teeth ratio of output sprocket/input sprocket) and the crank-wheel lever ratio. Notice that in every case the force on the pedals is greater than the force driving the bicycle forward (in the illustration above,

2170-443: The fulcrum, or pivot. The location of the fulcrum determines a lever's class . Where a lever rotates continuously, it functions as a rotary 2nd-class lever. The motion of the lever's end-point describes a fixed orbit, where mechanical energy can be exchanged. (see a hand-crank as an example.) In modern times, this kind of rotary leverage is widely used; see a (rotary) 2nd-class lever; see gears, pulleys or friction drive, used in

2232-426: The input force F A is obtained as M A = F B F A = a b , {\displaystyle MA={\frac {F_{B}}{F_{A}}}={\frac {a}{b}},} which is the mechanical advantage of the lever. This equation shows that if the distance a from the fulcrum to the point A where the input force is applied is greater than the distance b from fulcrum to

2294-419: The input force. On the other hand, if the distance a from the fulcrum to the input force is less than the distance b from the fulcrum to the output force, then the lever reduces the input force. The use of velocity in the static analysis of a lever is an application of the principle of virtual work . A lever is modeled as a rigid bar connected to a ground frame by a hinged joint called a fulcrum. The lever

2356-420: The input gear, then the gear train is called a speed reducer (Force multiplier). In this case, because the output gear must have more teeth than the input gear, the speed reducer will amplify the input torque. Mechanisms consisting of two sprockets connected by a chain, or two pulleys connected by a belt are designed to provide a specific mechanical advantage in power transmission systems. The velocity v of

2418-413: The law of the lever, has been attributed the famous claim, "Give me a place to stand and with a lever I will move the whole world." The use of velocity in the static analysis of a lever is an application of the principle of virtual work . The requirement for power input to an ideal mechanism to equal power output provides a simple way to compute mechanical advantage from the input-output speed ratio of

2480-442: The lengths a = | r A − r P | , b = | r B − r P | , {\displaystyle a=|\mathbf {r} _{A}-\mathbf {r} _{P}|,\quad b=|\mathbf {r} _{B}-\mathbf {r} _{P}|,} which are the distances from the fulcrum to the input point A and to the output point B , respectively. Now introduce

2542-405: The lever equals the power out, and the ratio of output to input force is given by the ratio of the distances from the fulcrum to the points of application of these forces. This is known as the law of the lever . The mechanical advantage of a lever can be determined by considering the balance of moments or torque , T , about the fulcrum. If the distance traveled is greater, then the output force

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2604-404: The mechanical advantage of a block and tackle system consider the simple case of a gun tackle, which has a single mounted, or fixed, pulley and a single movable pulley. The rope is threaded around the fixed block and falls down to the moving block where it is threaded around the pulley and brought back up to be knotted to the fixed block. Let S be the distance from the axle of the fixed block to

2666-422: The moving block. Let F A be the input force applied at A the end of the rope, and let F B be the force at B on the moving block. Like the velocities F A is directed downwards and F B is directed upwards. For an ideal block and tackle system there is no friction in the pulleys and no deflection or wear in the rope, which means the power input by the applied force F A V A must equal

2728-408: The moving block. Mechanical advantage that is computed using the assumption that no power is lost through deflection, friction and wear of a machine is the maximum performance that can be achieved. For this reason, it is often called the ideal mechanical advantage (IMA). In operation, deflection, friction and wear will reduce the mechanical advantage. The amount of this reduction from the ideal to

2790-414: The next, and thus the applied force is transferred from one lever to the next. Examples of compound levers include scales, nail clippers and piano keys. The malleus , incus and stapes are small bones in the middle ear , connected as compound levers, that transfer sound waves from the eardrum to the oval window of the cochlea . The lever is a movable bar that pivots on a fulcrum attached to

2852-399: The point B where the output force is applied, then the lever amplifies the input force. If the opposite is true that the distance from the fulcrum to the input point A is less than from the fulcrum to the output point B , then the lever reduces the magnitude of the input force. Mechanical advantage Mechanical advantage is a measure of the force amplification achieved by using

2914-562: The points A and B are obtained as v A = θ ˙ a e A ⊥ , v B = θ ˙ b e B ⊥ , {\displaystyle \mathbf {v} _{A}={\dot {\theta }}a\mathbf {e} _{A}^{\perp },\quad \mathbf {v} _{B}={\dot {\theta }}b\mathbf {e} _{B}^{\perp },} where e A and e B are unit vectors perpendicular to e A and e B , respectively. The angle θ

2976-426: The points A and B are related by the constant length of the rope, that is or The negative sign shows that the velocity of the load is opposite to the velocity of the applied force, which means as we pull down on the rope the load moves up. Let V A be positive downwards and V B be positive upwards, so this relationship can be written as the speed ratio where 2 is the number of rope sections supporting

3038-429: The power out acting on the load F B V B , that is The ratio of the output force to the input force is the mechanical advantage of an ideal gun tackle system, This analysis generalizes to an ideal block and tackle with a moving block supported by n rope sections, This shows that the force exerted by an ideal block and tackle is n times the input force, where n is the number of sections of rope that support

3100-438: The power output is actually less than the power input, which means the mechanical advantage of the real system will be less than that calculated for an ideal mechanism. A chain or belt drive can lose as much as 5% of the power through the system in friction heat, deformation and wear, in which case the efficiency of the drive is 95%. Consider the 18-speed bicycle with 7 in (radius) cranks and 26 in (diameter) wheels. If

3162-411: The pull of gravity) of both a and b change (diminish) as the lever changes to any position away from the horizontal. Levers are classified by the relative positions of the fulcrum, effort and resistance (or load). It is common to call the input force "effort" and the output force "load" or "resistance". This allows the identification of three classes of levers by the relative locations of the fulcrum,

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3224-423: The ratio of the number of teeth on each gear, its gear ratio . The velocity v of the point of contact on the pitch circles is the same on both gears, and is given by where input gear A has radius r A and meshes with output gear B of radius r B , therefore, where N A is the number of teeth on the input gear and N B is the number of teeth on the output gear. The mechanical advantage of

3286-424: The resistance and the effort: These cases are described by the mnemonic fre 123 where the f fulcrum is between r and e for the 1st class lever, the r resistance is between f and e for the 2nd class lever, and the e effort is between f and r for the 3rd class lever. A compound lever comprises several levers acting in series: the resistance from one lever in a system of levers acts as effort for

3348-420: The seesaw's design is that if a child allows himself/herself to hit the ground suddenly after jumping, or exits the seesaw at the bottom, the other child may fall and be injured. For this reason, seesaws are often mounted above a soft surface such as foam, wood chips, or sand. Seesaws are also manufactured in shapes designed to look like other things, such as airplanes , helicopters , and animals. Seesaws, and

3410-422: The seesaws should have been removed, indicating the fun provided by seesaws may outweigh the safety risk posed using them. Lever A lever is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge , or fulcrum . A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is divided into three types . It

3472-418: The sprockets at the crank and at the rear drive wheel are the same size, then the ratio of the output force on the tire to the input force on the pedal can be calculated from the law of the lever to be Now, assume that the front sprockets have a choice of 28 and 52 teeth, and that the rear sprockets have a choice of 16 and 32 teeth. Using different combinations, we can compute the following speed ratios between

3534-536: The stem of the verb lever , meaning "to raise". The verb, in turn, goes back to Latin : levare , itself from the adjective levis , meaning "light" (as in "not heavy"). The word's primary origin is the Proto-Indo-European stem legwh- , meaning "light", "easy" or "nimble", among other things. The PIE stem also gave rise to the English word "light". The earliest evidence of the lever mechanism dates back to

3596-419: The system. The power input to a gear train with a torque T A applied to the drive pulley which rotates at an angular velocity of ω A is P=T A ω A . Because the power flow is constant, the torque T B and angular velocity ω B of the output gear must satisfy the relation which yields This shows that for an ideal mechanism the input-output speed ratio equals the mechanical advantage of

3658-399: The system. This applies to all mechanical systems ranging from robots to linkages . Gear teeth are designed so that the number of teeth on a gear is proportional to the radius of its pitch circle, and so that the pitch circles of meshing gears roll on each other without slipping. The speed ratio for a pair of meshing gears can be computed from ratio of the radii of the pitch circles and

3720-473: The term originates from the Norfolk dialect word tittermatorter . A "teeter-totter" may also refer to a two-person swing on a swing seat , on which two children sit facing each other and the teeter-totter swings back and forth in a pendulum motion. Both teeter-totter (from teeter , as in to teeter on the edge ) and seesaw (from the verb saw ) demonstrate the linguistic process called reduplication , where

3782-448: The unit vectors e A and e B from the fulcrum to the point A and B , so r A − r P = a e A , r B − r P = b e B . {\displaystyle \mathbf {r} _{A}-\mathbf {r} _{P}=a\mathbf {e} _{A},\quad \mathbf {r} _{B}-\mathbf {r} _{P}=b\mathbf {e} _{B}.} The velocity of

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3844-404: The world." Autumn Stanley argues that the digging stick can be considered the first lever, which would position prehistoric women as the inventors of lever technology. A lever is a beam connected to ground by a hinge, or pivot, called a fulcrum. The ideal lever does not dissipate or store energy, which means there is no friction in the hinge or bending in the beam. In this case, the power into

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