Name: rigid body force balance in equilibrium
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 28 s
Channel: JoVE

Un cuerpo rígido no sufre ninguna deformación bajo la influencia de fuerzas externas.
Consideremos un tiovivo sometido a una fuerza externa F a una distancia radial perpendicular r, lo que resulta en el momento de una fuerza alrededor del punto O.
Si múltiples fuerzas actúan sobre el tiovivo, la condición de equilibrio se obtiene cuando la suma de todas las fuerzas externas que actúan sobre él es cero.
La otra condición de equilibrio establece que la suma de todos los momentos alrededor del punto O debe ser igual a cero.
Cuando el momento se mide en el punto A, se puede expresar como la suma del momento en el punto O y el producto cruzado de la distancia perpendicular y la fuerza aplicada.
Estas condiciones aseguran que el cuerpo no experimente ningún movimiento de traslación o rotación en equilibrio estático.
Aquí solo se consideran las fuerzas externas, ya que las fuerzas internas dentro del cuerpo rígido tienen la misma magnitud y actúan en direcciones opuestas, cancelándose entre sí debido a la tercera ley del movimiento de Newton.

<ol>
	<li>Cerveza, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. y Self, B.P. (2019). Mecánica vectorial para ingenieros: estática y dinámica. Nueva York: McGraw-Hill. págs. 170</li>
</ol>

condiciones de equilibrio

Conditions of Equilibrium

El equilibrio se refiere a un estado en el cual un cuerpo rígido no está sujeto a ningún movimiento traslacional o rotacional. Este estado se alcanza cuando la fuerza y el momento que actúan sobre un cuerpo rígido son iguales a cero. Cuando el sistema de fuerzas externas da como resultado un efecto neto equivalente a cero, se considera que el cuerpo rígido está en equilibrio. Las fuerzas internas no son consideradas en las condiciones de equilibrio porque ocurren en pares opuestos iguales dentro del cuerpo, cancelándose efectivamente entre sí. Como resultado, estas fuerzas internas no contribuyen al movimiento general o cambio en el movimiento del cuerpo rígido. El equilibrio es determinado por el balance de fuerzas y momentos externos que actúan sobre el cuerpo, ya que son responsables de causar el movimiento traslacional o rotacional. Las condiciones necesarias y suficientes para el equilibrio pueden ser determinadas al igualar la fuerza y el momento resultante a cero. Además, las ecuaciones vectoriales pueden ser reemplazadas por seis ecuaciones escalares al descomponer cada fuerza y momento en sus componentes rectangulares. Esto implica que las componentes de las fuerzas externas en las direcciones x, y, z están balanceadas, y los momentos de las fuerzas externas alrededor de los ejes x, y, z también están balanceados. Si un cuerpo rígido está en equilibrio, el sistema de fuerzas externas no produce ningún movimiento traslacional o rotacional en el cuerpo. Para escribir las ecuaciones de equilibrio para un cuerpo rígido, primero se deben identificar todas las fuerzas que actúan sobre el cuerpo y luego dibujar el correspondiente diagrama de cuerpo libre. Además de las fuerzas aplicadas a una estructura, se deben considerar las reacciones ejercidas sobre la estructura por sus soportes. Identificar correctamente cada reacción puede ayudar a resolver las fuerzas y reacciones desconocidas. El conocimiento de las condiciones de equilibrio es crucial para analizar problemas relacionados con cuerpos rígidos. Al determinar las fuerzas y reacciones desconocidas y utilizar las condiciones necesarias y suficientes para el equilibrio, es posible predecir el comportamiento de los cuerpos rígidos.

Condiciones de equilibrio

El equilibrio se refiere a un estado en el que un cuerpo rígido no está sujeto a ningún movimiento de traslación o rotación. Este estado se alcanza cuando la fuerza y ...

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Equilibrium of a Rigid Body

Equilibrio de un cuerpo rígido

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

rigid body force balance in equilibrium

Rigid body equilibrium depends on a balance of external forces and moments. A rigid body is in equilibrium when it has no translational motion and no rotational motion. This happens when the net force and the net couple acting on the body are both zero.

Internal forces are not used when checking equilibrium. These forces act in equal and opposite pairs inside the body, so they cancel each other. Because of that, they do not affect the overall motion or change in motion of the rigid body.

The external forces and moments determine whether the body stays balanced. These are the forces that can cause translation or rotation. The necessary and sufficient conditions for equilibrium are found by setting the resultant force and the resultant moment equal to zero.

The vector equations for equilibrium can also be written as six scalar equations. Each force and moment is resolved into rectangular components. This means the external force components in the x, y, and z directions must balance, and the moments about the x, y, and z axes must also balance.

To write equilibrium equations for a rigid body, first identify all forces acting on it. Then draw a free-body diagram. The reactions from supports must also be included. Correctly identifying each reaction helps solve unknown forces and reactions in structures.

Rigid Body Force Balance in Equilibrium

conditions of equilibrium

Rigid body equilibrium depends on a balance of external forces and moments. A rigid body is in equilibrium when it has no translational motion and no rotational motion. This happens when the net force and the net couple acting on the body are both zero. Internal forces are not used when checking equilibrium. These forces act in equal and opposite pairs inside the body, so they cancel each other. Because of that, they do not affect the overall motion or change in motion of the rigid body. The...

support reactions

Types of Structural Supports

Types of structural supports control how a coplanar force system moves and reacts under load. A coplanar force system is a set of forces that all lie in the same plane. The supports create reactions at the point of contact. These reactions help keep a structure stable under external forces. Supports work by stopping translation with an equal and opposite force. They can also stop rotation by applying a couple moment in the opposite direction. In structural design, these reactions are important...

internal forces and center of gravity

Forces Inside a Body and Balance

Internal forces and the center of gravity help explain how objects stay in balance. These mechanics ideas matter for structures, machines, and vehicles that must remain stable under different loads and conditions. Internal forces are created inside a body when its particles interact. They can appear as tension, compression, or shear forces. These forces act in collinear pairs with equal magnitude and opposite direction. Between connected parts, they cancel each other and help keep the body in...

alternative sets of equilibrium equations

alternative-sets-of-equilibrium-equations

Equilibrium Conditions for a Supported Plate

Equilibrium conditions for a supported plate are used to describe when forces and moments balance. In this state, the plate has no net movement and no rotation. Engineers use these equations to study how structures behave under external loads. In many cases, the standard equilibrium equations are enough. But some systems need an alternative set of equations to match the geometry of the support points. A rectangular plate supported at points A, B, and C is one example. For this plate, the...

two force member

Two-Force Body Equilibrium

A two-force body is a rigid body acted on by only two external forces. In equilibrium, those two forces must have the same magnitude, the same line of action, and opposite directions. This balance is what keeps the body at rest. For a plate with forces F1 and F2 applied at points A and B, equilibrium means the sum of moments about any axis is zero. If moments are summed about point A, the moment from F2 must be zero. That means the line of action of F2 must pass through point A. The same idea...

three force member

Solving a Three-Force Member Example

A three-force member is a rigid body acted on by three forces at three points. The forces must have concurrent lines of action. If the forces are parallel, their lines of action stay parallel instead. A dumpster provides the example used here. It is connected to a pin support at point A and to a pin on a hydraulic cylinder at point B. The hydraulic cylinder acts as a two-force member in equilibrium. The dumpster weight acts through the center of gravity, and the support reaction acts at point...

equations of equilibrium in three dimensions

equations-of-equilibrium-in-three-dimensions

Checking Force Balance in 3D Structures

Checking force balance in 3D structures is a key step when a system is at rest. The vector and scalar equations of equilibrium are used to test whether a body is stable and will not collapse or fall apart. These equations give a clear way to study the forces acting on a body. The vector equations of equilibrium require the vector sum of all external forces on a body to equal zero. They also require the vector sum of the couple moments and the moments of all forces about a point to equal zero.

support reactions in three dimensions

3D Support Types for Stability and Motion

Support reactions in three dimensions keep structures stable and in equilibrium. They stop unwanted translation and rotation, so a design can handle external forces safely and work as intended. These reactions are important in many structures and systems. A ball and socket joint is one support that allows free rotation about any axis. It does not provide a moment that resists turning. At the same time, it restricts motion in space with three reaction forces along the three dimensions. A...

constraints and statical determinacy

Constraints in Structural Equilibrium

Constraints in structural engineering control how a body can move and help keep it in mechanical equilibrium. A constraint is a restriction on motion. When the right number of constraints is used, the system can stay balanced with the fewest supports needed. A system with the proper number of supports is called statically determinate. In that case, the unknown reaction forces can be found from equations of equilibrium. These systems are the easiest to analyze and design because the forces can...

key terms and concepts

Learn how rigid body equilibrium is determined by balanced external forces and moments, free-body diagrams, and support reactions in high school physics.

Rigid Body Force Balance in Equilibrium | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Rigid Body Force Balance in Equilibrium

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