Name: wedges and self-locking stability
Uploaded: 2025-05-22T09:06:04.000Z
Duration: 1 min 24 s
Channel: JoVE

Uma cunha é uma máquina útil para ajustar a elevação de peças estruturais ou mecânicas, proporcionando estabilidade para objetos pesados e dividindo um corpo em duas partes.
Considere usar uma cunha para levantar uma laje pesada.
A cunha amplifica a força aplicada em uma força muito maior direcionada quase perpendicular à força aplicada.
Existem sete incógnitas, incluindo a força aplicada para o movimento da cunha e seis forças normais e de atrito.
Eles podem ser determinados usando quatro equações de equilíbrio de força aplicadas à cunha e à laje e três equações de atrito aplicadas em cada superfície de contato.
Para abaixar a laje, as forças de atrito atuam no sentido oposto.
Desde que o coeficiente de atrito seja muito pequeno ou o ângulo da cunha seja grande, a força aplicada deve atuar à direita para segurar a laje.
Se a força aplicada for removida e as forças de atrito segurarem o bloco, a cunha é considerada autotravante. Esta condição é válida apenas quando o ângulo da cunha é menor que o dobro do ângulo feito pelas forças de reação.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica: Estática. Décima quarta edição, Nova Jersey: Pearson. Pág. 430-431.</li>
	<li>Meriam, J.L., Kraige, L.G. e Bolten, J.N.(2016). Engenharia Mecânica: Estática e Dinâmica. Oitava Edição, Cingapura: John Wiley & Sons. Pág. 353-354.</li>
	<li>Cerveja, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. e Self, B.P. (2016). Mecânica vetorial para engenheiros. Décima primeira edição, Nova York: McGraw-Hill Education. Pág. 450.</li>
</ol>

cunhas

Uma cunha é uma máquina simples que serve para diversos propósitos, como ajustar a elevação de partes estruturais ou mecânicas, fornecer estabilidade para objetos pesados e dividir um corpo em duas partes. Essa ferramenta versátil pode amplificar uma força aplicada, tornando mais fácil manipular objetos grandes ou pesados.

Considere usar uma cunha para levantar uma laje pesada. Aqui, a cunha funciona convertendo a força aplicada em uma força muito maior direcionada quase perpendicular à força inicial. Essa amplificação permite o levantamento de objetos pesados com um esforço mínimo.

Existem sete fatores desconhecidos envolvidos no movimento da cunha: a força aplicada e seis forças normais e de atrito. Nos diagramas de corpo livre, o peso da cunha é frequentemente negligênciado, pois é pequeno em comparação com a carga.

<img alt="Figure 1" src="/files/ftp_upload/14317/14317_PT_Figure_1v2.svg" style="text-align: center; height: 300px;" />

Esses desconhecidos podem ser determinados usando quatro equações de equilíbrio de forças aplicadas à cunha e à laje, e as três equações de atrito restantes (F1, F2, F3) aplicadas em cada superfície de contato são dadas pelo coeficiente de atrito de produto e suas respectivas forças normais.

<img alt="Equation 1" src="/files/ftp_upload/14317/14317_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />

<img alt="Equation 2" src="/files/ftp_upload/14317/14317_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

<img alt="Equation 3" src="/files/ftp_upload/14317/14317_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" />

<img alt="Equation 4" src="/files/ftp_upload/14317/14317_PT_Equation_4v2.svg" style="text-align: center; height: 13px;" />

Ao resolver essas equações, pode-se obter uma compreensão da relação entre a força aplicada e o movimento resultante da cunha.

Ao abaixar a laje, as forças de atrito agem no sentido oposto. Desde que o coeficiente de atrito seja muito pequeno ou o ângulo da cunha seja grande, a força aplicada deve agir para a direita para segurar a laje no lugar. Esse equilíbrio de forças garante que a cunha permaneça estável e mantenha sua posição enquanto suporta o peso da laje.

Em certas condições, a cunha pode ser considerada auto-travante. Isso ocorre quando a força aplicada é removida e apenas as forças de atrito podem segurar o bloco no lugar. A condição de auto-travamento é válida apenas quando o ângulo da cunha é inferior ao dobro do ângulo formado pelas forças de reação.

Nesse caso, a geometria da cunha e o atrito entre as superfícies de contato trabalham juntos para prevenir movimentos indesejados ou deslizamentos.

A propriedade de auto-travamento de uma cunha pode ser vantajosa em várias aplicações, pois proporciona estabilidade e segurança adicionais ao manipular objetos pesados. Por exemplo, em projetos de construção ou engenharia, uma cunha auto-travante pode ajudar a garantir que os componentes estruturais permaneçam firmemente no lugar durante a montagem ou ajustes.

Cunhas

Uma cunha é uma máquina simples que serve a vários propósitos, como ajustar a elevação de peças estruturais ou mecânicas, proporcionando estabilidade para peças pesadas ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Friction

Atrito

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Wedges

wedges and self-locking stability

A wedge is a simple machine that can lift, support, and split heavy objects. It can also change the height of structural or mechanical parts. Because it amplifies force, a wedge makes it easier to move or hold large loads with less effort.

One example is lifting a heavy slab. In that case, the wedge turns the applied force into a much larger force that acts almost perpendicular to the original push. That force change helps raise the load without requiring a large input force.

To analyze wedge motion, there are seven unknowns. These include the applied force, six normal forces, and frictional forces at the contact surfaces. The wedge weight is often ignored in the free-body diagrams because it is small compared with the load.

The unknowns can be found with four force equilibrium equations for the wedge and the slab. Three friction equations, F1, F2, and F3, are then applied at each contact surface. Each friction force equals the coefficient of friction times the normal force at that surface.

The same force balance also explains what happens when the slab is lowered. In that case, the friction forces act in the opposite direction. If the coefficient of friction is very small or the wedge angle is large, the applied force must act to the right to keep the slab in place.

A wedge can also be self-locking. This means that when the applied force is removed, friction alone can hold the block in place. The self-locking condition works only when the wedge angle is less than twice the angle made by the reaction forces.

This stability is useful in many settings. In construction or engineering work, a self-locking wedge can help keep parts firmly in place during assembly or adjustment. The geometry of the wedge and the friction between surfaces work together to reduce slipping and unwanted motion.

Wedges and Self-Locking Stability

dry friction

Dry Friction in Crates and Everyday Motion

Dry friction appears when two solid surfaces touch and try to move past each other. Students can see it when they walk, slide a box across a table, or rub their hands together. Even though it is common, the forces behind it are not easy to see. A simple crate on a rough horizontal floor helps explain the idea. When an external force pushes the crate sideways, two main forces act on it. The normal force acts perpendicular to the surface and helps balance the crate’s weight, while the frictional...

static friction

Static Friction at the Point of Slip

Static friction is the force that keeps two surfaces from starting to slide past each other. It acts when there is a tendency for motion, but not yet actual slipping. This force helps explain everyday actions like walking on the ground and driving a car. A towing example shows how static friction changes as force is applied. A truck pulls a car with a rope, and the car stays still at first. The car is in static equilibrium, which means the forces on it are balanced. Gravity and the normal...

kinetic friction

Sliding Friction Between Moving Surfaces

Kinetic friction is the sliding friction that acts when two surfaces move against each other. It opposes relative motion and acts parallel to the contact surface, in the opposite direction of travel. In the truck and car example, the car first stays still because static friction holds it in place. When the truck’s force becomes greater than the limiting static frictional force, the friction at the contact surface drops to a lower value. The car then begins to slide, and its speed increases. At...

characteristics of dry friction

Static and Kinetic Dry Friction

Dry friction is the resistance between two solid surfaces that move against each other without lubrication or any fluid. A common example is a gardener pushing a wheelbarrow across the ground. The wheel and the ground create dry friction that slows the motion. Before the wheelbarrow starts to move, static friction acts at the contact surface. Static friction is the force that opposes motion before slipping begins, and it helps keep the wheelbarrow stable. It is present only when there is no...

types of friction problems

Dry Friction in Crate, Ladder, and Frame Problems

Dry friction problems often focus on crates, ladders, and frames that are close to slipping. Dry friction is the force that resists relative motion, or the tendency for motion, between two surfaces in contact. In many physics and engineering problems, this force helps keep an object still or defines the point where motion is about to begin. One common case has no clear impending motion. A force may be applied to a crate, but the crate stays at rest. The friction force between the floor and the...

friction: problem solving

Friction on a Banked Road

Friction on a banked road affects whether a bus stays steady while it moves at constant speed. In this problem, a bus with a mass of three megagrams travels on a sloped road. The coefficient of static friction between the tires and the road is 0.5. The goal is to find the maximum bank angle where the bus will not slip or tip. To solve the motion part, the forces on the bus must be shown first. These include gravity, the normal force, and friction. The normal force is the push from the road,...

wedges

A wedge is a simple machine that can lift, support, and split heavy objects. It can also change the height of structural or mechanical parts. Because it amplifies force, a wedge makes it easier to move or hold large loads with less effort. One example is lifting a heavy slab. In that case, the wedge turns the applied force into a much larger force that acts almost perpendicular to the original push. That force change helps raise the load without requiring a large input force. To analyze wedge...

frictional forces on screws

Square-Thread Screw Mechanics and Friction

Square-threaded screws use a helical thread to turn force into lifting motion. They are common fasteners, but they are also useful for transmitting power and motion in machines. A jack with a square-threaded screw lifts heavy loads when force is applied at the handle and the screw turns. A screw can be viewed as a cylindrical shaft with an inclined square ridge wrapped around it. The distance between two neighboring threads is called the pitch. The lead is the distance the screw advances in...

upward impending motion

Screw Jack Force and Friction Analysis

A square-threaded screw jack lifts heavy loads by turning handle force into a twisting moment. Its upward motion depends on overcoming static friction between the screw threads and the jack. To study this motion, the thread can be treated as if it were a block on the groove of the jack after the thread is completely unraveled. A free-body diagram helps show the forces acting on this simplified system. The force at the handle creates a horizontal force that pushes the movable thread up the...

self-locking screw

Screw Jack Self-Locking Behavior

A square-threaded screw jack can hold a heavy load because of its self-locking behavior. This feature makes the device more reliable when it is used to lift large weights or apply a strong force. If the screw keeps its position after the turning moment is removed, the jack is self-locking. Self-locking happens because friction changes the way the forces act on the thread. The friction force reverses direction, and the reaction force moves to the other side of the thread’s normal. In this case,...

screw: problem solving

Screw Torque and Self-Locking

Screw torque and self-locking are analyzed by looking at a threaded screw shaft and a plate gear. The shaft has a mean radius and a lead. The plate gear also has a mean radius. The coefficient of static friction between the screw and the gear is part of the setup. The first step is to find the static friction angle, φ. This angle is defined by the coefficient of static friction. Next, the lead angle is calculated from the lead and the mean radius of the shaft. It gives the screw geometry...

frictional forces on flat belts

Flat Belt Tension and Friction

Flat belt tension and friction control how power moves from one pulley to another. Flat belts are used in many industrial systems to transmit power between pulleys. As the belt wraps around the pulleys, the tension changes because of friction between the belt and the pulley surface. When a pulley turns counterclockwise, the belt side moving away from the pulley has the higher tension, called T2. The side moving toward the pulley has the lower tension, called T1. To estimate these tensions, the...

flat belts: problem solving

Flat Belt Forces and Pulley Moment

Flat belts transmit power from one pulley to another, and the forces on the belt help determine the moment on a pulley. In this example, a belt wraps around pulleys A and B, with radii of 30 cm and 10 cm. The belt meets the pulleys at a 20 degree angle from the horizontal, which sets up the force balance in the system. As pulley B rotates clockwise, it drives pulley A. That motion creates tension T2 on one side of the belt and tension T1 on the other side. The belt-to-surface contact angle, β,...

pivot bearings

Axial Load Support in Pivot Bearings

Pivot bearings support axial loads on a rotating shaft. A bearing helps two parts move relative to each other while reducing friction and wear. In this design, the pivot is placed at the end of the shaft to carry the axial thrust. The pivot surface can be flat, conical, or truncated, depending on the application. In a flat pivot bearing, the axial load is spread over the bearing area. The pressure is uniform and can be found by dividing the load by the area. To study the forces more closely,...

collar bearings

Friction Torque in Collar Bearings

Collar bearings support axial loads on rotating shafts, and their friction helps determine the torque needed to start motion. They are used in many machines and may have a single collar or multiple collars, depending on the application and load needs. For a single collar bearing under an axial load, the contact area is the ring-shaped region between the external radius and the internal radius of the collar. If the bearing is assumed to support the load evenly, the uniform normal pressure is...

journal bearings

Friction Moment in Journal Bearings

Journal bearings support rotating shafts and axles while helping keep them stable. They are used in machines such as engines, turbines, and pumps. Their job is to reduce friction, wear, and vibration. A journal bearing works by keeping a thin film of lubricant between the bearing surface and the rotating shaft. This film limits direct contact and lowers frictional force. The video uses a rope winch with dry or only partly lubricated journal bearings to show the idea. As the spool turns...

bearings: problem solving

Double-Collar Bearing Torque Calculations

Double-collar bearing torque calculations show how friction and axial force affect bearing performance. Engineers use these calculations to test whether the bearing can handle the forces and moments it experiences during operation. This helps them choose and design bearings for specific applications and setups. For a double-collar bearing with set dimensions and an axial force applied, the maximum frictional moment can be found with a standard expression. The equation is rearranged, and the...

rolling resistance

Tire Deformation and Rolling Resistance

Tire deformation and rolling resistance explain why a rolling wheel still needs a driving force. When a solid cylinder or tire rolls on a rigid surface, the normal force is perpendicular to the surface at the contact point. But real materials are not perfectly rigid, so the surface pushes back with a spread of normal pressures instead of one single force. A hard cylinder on a softer surface compresses the material under it. As the cylinder moves forward, the material in front of the contact...

rolling resistance: problem solving

Lawn Roller Force Calculation

Rolling resistance is the force that makes a rolling object harder to move across a surface. It is also called rolling friction. It comes from deformation in the object and the surface that touch each other. Internal friction, hysteresis, and other energy losses in the materials also play a role. Because of this force, extra energy is needed to keep a wheel, tire, or ball moving. The video applies this idea to a lawn roller. The roller has a mass of 100 kg, a radius of 25 cm, and a coefficient...

key terms and concepts

Learn how wedges amplify force, lift heavy slabs, and stay in place through friction. Explore equilibrium, contact forces, and self-locking stability.

Wedges and Self-Locking Stability | JoVE K12

O JoVE Core Mechanical Engineering oferece vídeos animados concisos e de fácil compreensão que abrangem tópicos-chave como equilíbrio, forças, análise de treliças e mecânica estrutural. Explore suas aplicações no mundo real e observe esses conceitos em ação por meio de experimentos conduzidos por cientistas.

mechanical engineering

Wedges and Self-Locking Stability

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