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Mechanical Equilibrium
Mechanical Equilibrium
Published: 2015/08/22
Channel: PhysicsandAstronomy UKY
Thermodynamics Equilibrium- Chemical, Mechanical and Thermal Equilibrium-
Thermodynamics Equilibrium- Chemical, Mechanical and Thermal Equilibrium-
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CHAPTER # 2   MECHANICAL EQUILIBRIUM   HEWITT
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Mechanical Equilibrium Screencast
Published: 2015/08/07
Channel: ScienceMrLash
Mechanical Equilibrium
Mechanical Equilibrium
Published: 2012/08/28
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Hewitt-Drew-it! PHYSICS 1. Equilibrium Rule  Hewitt-Drew-it!
Hewitt-Drew-it! PHYSICS 1. Equilibrium Rule Hewitt-Drew-it!
Published: 2012/07/11
Channel: mellenstei
Example of Mechanical equilibrium with torque
Example of Mechanical equilibrium with torque
Published: 2010/10/29
Channel: Mr Bdubs Math and Physics
Introduction to Equilibrium
Introduction to Equilibrium
Published: 2015/06/19
Channel: Flipping Physics
Lecture 01 Mechanical Equilibrium: Dynamic and Static  Equilibrium
Lecture 01 Mechanical Equilibrium: Dynamic and Static Equilibrium
Published: 2013/10/06
Channel: TDarcyPhysics
Mechanical Equilibrium
Mechanical Equilibrium
Published: 2014/02/18
Channel: jkruz1675
What is MECHANICAL EQUILIBRIUM? What does MECHANICAL EQUILIBRIUM mean?
What is MECHANICAL EQUILIBRIUM? What does MECHANICAL EQUILIBRIUM mean?
Published: 2016/10/12
Channel: The Audiopedia
Thermodynamics 34   Mechanical Equilibrium and Ideal Gas Law
Thermodynamics 34 Mechanical Equilibrium and Ideal Gas Law
Published: 2015/09/18
Channel: Des Chimistes
Static Equilibrium, or What to do when nothing at all is happening | Doc Physics
Static Equilibrium, or What to do when nothing at all is happening | Doc Physics
Published: 2012/09/25
Channel: Doc Schuster
AS Physics Solving Equilibrium Problems
AS Physics Solving Equilibrium Problems
Published: 2014/01/25
Channel: Kate Wainwright
Balancing Torques (mechanical equilibrium)
Balancing Torques (mechanical equilibrium)
Published: 2011/11/03
Channel: Gregory Mack
Lecture 01 Mechanical Equilibrium Problem Solving
Lecture 01 Mechanical Equilibrium Problem Solving
Published: 2013/10/05
Channel: TDarcyPhysics
Mechanical Engineering: Particle Equilibrium (1 of 19) Addition of Forces - Graphically
Mechanical Engineering: Particle Equilibrium (1 of 19) Addition of Forces - Graphically
Published: 2015/06/18
Channel: Michel van Biezen
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mechanical equilibrium examples
Published: 2015/10/11
Channel: Andrew Berryman
Mechanical Engineering: Particle Equilibrium (7 of 19) Tension of Cables Attached to Hanging Object
Mechanical Engineering: Particle Equilibrium (7 of 19) Tension of Cables Attached to Hanging Object
Published: 2015/06/20
Channel: Michel van Biezen
Exam 1 Problem 1 (Boiling at Elevated Pressures and Mechanical Equilibrium)
Exam 1 Problem 1 (Boiling at Elevated Pressures and Mechanical Equilibrium)
Published: 2016/03/15
Channel: UF Teaching Center
MCAT Force Equilibrium and Free Body Diagrams
MCAT Force Equilibrium and Free Body Diagrams
Published: 2015/02/18
Channel: Leah4sciMCAT
Thermodynamic Equilibrium
Thermodynamic Equilibrium
Published: 2013/02/17
Channel: chunkan yu
Mechanical Engineering: Particle Equilibrium (2 of 19) Addition of Forces - Component
Mechanical Engineering: Particle Equilibrium (2 of 19) Addition of Forces - Component
Published: 2015/06/18
Channel: Michel van Biezen
Mechanical Engineering: Particle Equilibrium (13 of 19) Pulleys and Mechanical Advantage
Mechanical Engineering: Particle Equilibrium (13 of 19) Pulleys and Mechanical Advantage
Published: 2015/06/23
Channel: Michel van Biezen
Mechanical Engineering: Particle Equilibrium (11 of 19) Why are Pulleys a Mechanical Advantage?
Mechanical Engineering: Particle Equilibrium (11 of 19) Why are Pulleys a Mechanical Advantage?
Published: 2015/06/23
Channel: Michel van Biezen
Mechanical Engineering: Equilibrium of Rigid Bodies (6 of 30) Find F=? M=? Ex.1, 2-Dimensions
Mechanical Engineering: Equilibrium of Rigid Bodies (6 of 30) Find F=? M=? Ex.1, 2-Dimensions
Published: 2015/08/23
Channel: Michel van Biezen
Mechanical Engineering: Particle Equilibrium (12 of 19) Pulleys and Mechanical Advantage
Mechanical Engineering: Particle Equilibrium (12 of 19) Pulleys and Mechanical Advantage
Published: 2015/06/23
Channel: Michel van Biezen
Example of Mechanical equilibrium with torque #2
Example of Mechanical equilibrium with torque #2
Published: 2010/10/29
Channel: Mr Bdubs Math and Physics
Netural Stable Unstable Equilibrium Mechanical Engineering Lectures Notes
Netural Stable Unstable Equilibrium Mechanical Engineering Lectures Notes
Published: 2015/10/08
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Mechanical Engineering: Particle Equilibrium (9 of 19) Forces on a Bracket
Mechanical Engineering: Particle Equilibrium (9 of 19) Forces on a Bracket
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Channel: Michel van Biezen
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Mechanical Engineering: Equilibrium of Rigid Bodies (1 of 30) Introduction
Published: 2015/08/18
Channel: Michel van Biezen
Mechanical Engineering: Equilibrium of Rigid Bodies (9 of 32) Find F=? M=? Ex.4, 2-Dimensions
Mechanical Engineering: Equilibrium of Rigid Bodies (9 of 32) Find F=? M=? Ex.4, 2-Dimensions
Published: 2015/08/26
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Static Equilibrium Problems (part II)
Static Equilibrium Problems (part II)
Published: 2009/10/17
Channel: lasseviren1
Chapter 2 and 3 Particle Equilibrium Dot product, 3-D Particle Equilibrium
Chapter 2 and 3 Particle Equilibrium Dot product, 3-D Particle Equilibrium
Published: 2015/04/30
Channel: STATICS THE EASY WAY
Mechanical Engineering: Particle Equilibrium (17 of 19) Determining Angles in 3-Dimension
Mechanical Engineering: Particle Equilibrium (17 of 19) Determining Angles in 3-Dimension
Published: 2015/06/25
Channel: Michel van Biezen
Ladder Example for Static Equilibrium
Ladder Example for Static Equilibrium
Published: 2013/09/30
Channel: cstephenmurray
Rotational Equilibrium Problems
Rotational Equilibrium Problems
Published: 2015/02/19
Channel: Daniel M
Mechanical Engineering: Particle Equilibrium (5 of 19) Beam and Cable Under Tension
Mechanical Engineering: Particle Equilibrium (5 of 19) Beam and Cable Under Tension
Published: 2015/06/19
Channel: Michel van Biezen
Static and Dynamic Equilibrium
Static and Dynamic Equilibrium
Published: 2012/12/22
Channel: AK LECTURES
Mechanical Engineering: Equilibrium of Rigid Bodies (2 of 30) Forces & Moments at Connections 1
Mechanical Engineering: Equilibrium of Rigid Bodies (2 of 30) Forces & Moments at Connections 1
Published: 2015/08/19
Channel: Michel van Biezen
Mechanical Engineering: Equilibrium of Rigid Bodies (5 of 30) Finding Contact Forces
Mechanical Engineering: Equilibrium of Rigid Bodies (5 of 30) Finding Contact Forces
Published: 2015/08/22
Channel: Michel van Biezen
Engineering Mechanics (MSBTE) - Equilibrium
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Published: 2015/12/16
Channel: No - KT
Translational Equilibrium
Translational Equilibrium
Published: 2012/09/07
Channel: Vector Shock
Mechanical Engineering: Equilibrium of Rigid Bodies (3 of 30) Forces & Moments at Connections 2
Mechanical Engineering: Equilibrium of Rigid Bodies (3 of 30) Forces & Moments at Connections 2
Published: 2015/08/20
Channel: Michel van Biezen
A Level Physics: Mechanics: Forces in Equilibrium
A Level Physics: Mechanics: Forces in Equilibrium
Published: 2016/02/23
Channel: Burrows Physics
Physics, Static Equilibrium, Hanging Sign No. 5
Physics, Static Equilibrium, Hanging Sign No. 5
Published: 2014/12/07
Channel: Step-by-Step Science
Mechanical Engineering: Particle Equilibrium (14 of 19) Vectors in 3-Dimensions Explained
Mechanical Engineering: Particle Equilibrium (14 of 19) Vectors in 3-Dimensions Explained
Published: 2015/06/24
Channel: Michel van Biezen
Mechanical Engineering: Equilibrium of Rigid Bodies (4 of 30) Forces & Moments at Connections 3
Mechanical Engineering: Equilibrium of Rigid Bodies (4 of 30) Forces & Moments at Connections 3
Published: 2015/08/21
Channel: Michel van Biezen
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WIKIPEDIA ARTICLE

From Wikipedia, the free encyclopedia
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An object resting on a surface and the corresponding free body diagram showing the forces acting on the object. The normal force N is equal, opposite, and colliniear to the gravitational force mg so the net force and moment is zero. Consequently, the object is in a state of static mechanical equilibrium.

In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero.[1]:39 By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero.[1]:45–46[2]

In addition to defining mechanical equilibrium in terms of force, there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent. In terms of momentum, a system is in equilibrium if the momentum of its parts is all constant. In terms of velocity, the system is in equilibrium if velocity is constant. In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero.[2] More generally in conservative systems, equilibrium is established at a point in configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero.

If a particle in equilibrium has zero velocity, that particle is in static equilibrium.[3][4] Since all particles in equilibrium have constant velocity, it is always possible to find an inertial reference frame in which the particle is stationary with respect to the frame.

Stability[edit]

An important property of systems at mechanical equilibrium is their stability.

Potential energy stability test[edit]

If we have a function which describes the system's potential energy, we can determine the system's equilibria using calculus. A system is in mechanical equilibrium at the critical points of the function describing the system's potential energy. We can locate these points using the fact that the derivative of the function is zero at these points. To determine whether or not the system is stable or unstable, we apply the second derivative test:

Unstable equilibria
Second derivative < 0
The potential energy is at a local maximum, which means that the system is in an unstable equilibrium state. If the system is displaced an arbitrarily small distance from the equilibrium state, the forces of the system cause it to move even farther away.
Stable equilibria
Second derivative > 0
The potential energy is at a local minimum. This is a stable equilibrium. The response to a small perturbation is forces that tend to restore the equilibrium. If more than one stable equilibrium state is possible for a system, any equilibria whose potential energy is higher than the absolute minimum represent metastable states.
Neutral equilibria
Second derivative = 0 or does not exist
The state is neutral to the lowest order and nearly remains in equilibrium if displaced a small amount. To investigate the precise stability of the system, higher order derivatives must be examined. The state is unstable if the lowest nonzero derivative is of odd order or has a negative value, stable if the lowest nonzero derivative is both of even order and has a positive value, and neutral if all higher order derivatives are zero. In a truly neutral state the energy does not vary and the state of equilibrium has a finite width. This is sometimes referred to as state that is marginally stable or in a state of indifference.

When considering more than one dimension, it is possible to get different results in different directions, for example stability with respect to displacements in the x-direction but instability in the y-direction, a case known as a saddle point. Generally an equilibrium is only referred to as stable if it is stable in all directions.

Statically indeterminate system[edit]

Sometimes there is not enough information about the forces acting on a body to determine if it is in equilibrium or not. This makes it a statically indeterminate system.

Examples[edit]

A stationary object (or set of objects) is in "static equilibrium," which is a special case of mechanical equilibrium. A paperweight on a desk is an example of static equilibrium. Other examples include a rock balance sculpture, or a stack of blocks in the game of Jenga, so long as the sculpture or stack of blocks is not in the state of collapsing.

Objects in motion can also be in equilibrium. A child sliding down a slide at constant speed would be in mechanical equilibrium, but not in static equilibrium (in the reference frame of the earth or slide).

Another example of mechanical equilibrium is a person pressing a spring to a defined point. He or she can push it to an arbitrary point and hold it there, at which point the compressive load and the spring reaction are equal. In this state the system is in mechanical equilibrium. When the compressive force is removed the spring returns to its original state.

The minimal number of static equilibria of homogeneous, convex bodies (when resting under gravity on a horizontal surface) is of special interest. In the planar case, the minimal number is 4, while in three dimensions one can build an object with just one stable and one unstable balance point.[citation needed] Such an object is called a gomboc.

See also[edit]

Notes and references[edit]

  1. ^ a b John L Synge & Byron A Griffith (1949). Principles of Mechanics (2nd ed.). McGraw-Hill. 
  2. ^ a b Beer FP, Johnston ER, Mazurek DF, Cornell PJ, and Eisenberg, ER (2009). Vector Mechanics for Engineers: Statics and Dynamics (9th ed.). McGraw-Hill. p. 158. 
  3. ^ Herbert Charles Corben & Philip Stehle (1994). Classical Mechanics (Reprint of 1960 second ed.). Courier Dover Publications. p. 113. ISBN 0-486-68063-0. 
  4. ^ Lakshmana C. Rao; J. Lakshminarasimhan; Raju Sethuraman; Srinivasan M. Sivakumar (2004). Engineering Mechanics. PHI Learning Pvt. Ltd. p. 6. ISBN 81-203-2189-8. 

Further reading[edit]

  • Marion JB and Thornton ST. (1995) Classical Dynamics of Particles and Systems. Fourth Edition, Harcourt Brace & Company.

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