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Mechanical Equilibrium
Mechanical Equilibrium
Published: 2015/08/22
Channel: PhysicsandAstronomy UKY
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
CHAPTER # 2   MECHANICAL EQUILIBRIUM   HEWITT
CHAPTER # 2 MECHANICAL EQUILIBRIUM HEWITT
Published: 2015/06/11
Channel: Jan Rothschild
Mechanical Equilibrium
Mechanical Equilibrium
Published: 2012/08/28
Channel: Nancy Foote
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 Equilibrium- Chemical, Mechanical and Thermal Equilibrium-
Thermodynamics Equilibrium- Chemical, Mechanical and Thermal Equilibrium-
Published: 2015/12/19
Channel: Ujjwal Kumar Sen
Example of Mechanical equilibrium with torque
Example of Mechanical equilibrium with torque
Published: 2010/10/29
Channel: Mr Bdubs Math and Physics
Mechanical Equilibrium Screencast
Mechanical Equilibrium Screencast
Published: 2015/08/07
Channel: ScienceMrLash
Mechanical Equilibrium
Mechanical Equilibrium
Published: 2014/02/18
Channel: jkruz1675
Three forces in equilibrium - an easy method
Three forces in equilibrium - an easy method
Published: 2013/03/25
Channel: Beverley Lane
Problems 1 on Equilibrium in Engineering mechanics.
Problems 1 on Equilibrium in Engineering mechanics.
Published: 2015/09/18
Channel: Ekeeda
Unit 4 Lesson 3: Mechanical Equilibrium
Unit 4 Lesson 3: Mechanical Equilibrium
Published: 2016/11/28
Channel: Ian McNair
mechanical equilibrium examples
mechanical equilibrium examples
Published: 2015/10/11
Channel: Andrew Berryman
Lecture 01 Mechanical Equilibrium Problem Solving
Lecture 01 Mechanical Equilibrium Problem Solving
Published: 2013/10/05
Channel: TDarcyPhysics
Balancing Torques (mechanical equilibrium)
Balancing Torques (mechanical equilibrium)
Published: 2011/11/03
Channel: Gregory Mack
Lecture 01 Mechanical Equilibrium Part III
Lecture 01 Mechanical Equilibrium Part III
Published: 2013/10/09
Channel: TDarcyPhysics
What is Definition of Equilibrium in Engineering Mechanism
What is Definition of Equilibrium in Engineering Mechanism
Published: 2015/10/13
Channel: Ekeeda
Example of Mechanical equilibrium with torque #2
Example of Mechanical equilibrium with torque #2
Published: 2010/10/29
Channel: Mr Bdubs Math and Physics
力學平衡mechanical equilibrium
力學平衡mechanical equilibrium
Published: 2013/12/15
Channel: ineedlucky
Introduction to Equilibrium
Introduction to Equilibrium
Published: 2015/06/19
Channel: Flipping Physics
Engineering Mechanics (MSBTE) - Equilibrium
Engineering Mechanics (MSBTE) - Equilibrium
Published: 2015/12/16
Channel: No - KT
Mechanical Engineering: Particle Equilibrium (6 of 19) Worker Pulling on Mass Hanging from Crane
Mechanical Engineering: Particle Equilibrium (6 of 19) Worker Pulling on Mass Hanging from Crane
Published: 2015/06/19
Channel: Michel van Biezen
Lecture 01 Mechanical Equilibrium: Dynamic and Static  Equilibrium
Lecture 01 Mechanical Equilibrium: Dynamic and Static Equilibrium
Published: 2013/10/06
Channel: TDarcyPhysics
Static Equilibrium equal angles two cables
Static Equilibrium equal angles two cables
Published: 2012/10/24
Channel: SciencePi
Static Equilibrium
Static Equilibrium
Published: 2011/10/30
Channel: PhunScience
Thermodynamic Equilibrium
Thermodynamic Equilibrium
Published: 2013/02/17
Channel: chunkan yu
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
Static Equilibrium Sample Problem 2
Static Equilibrium Sample Problem 2
Published: 2012/11/08
Channel: CastleRockResearch
Lab 3 Forces in Equilibrium
Lab 3 Forces in Equilibrium
Published: 2010/08/04
Channel: AUPhysics
[clipvidva]  สมดุลกล Mechanical Equilibrium Part1/5
[clipvidva] สมดุลกล Mechanical Equilibrium Part1/5
Published: 2013/12/22
Channel: clipvidva
Static Equilibrium - Tension, Torque, Lever, Beam, & Ladder Problem - Physics
Static Equilibrium - Tension, Torque, Lever, Beam, & Ladder Problem - Physics
Published: 2016/10/07
Channel: The Organic Chemistry Tutor
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
Thermodynamics 34 : Mechanical Equilibrium and Ideal Gas Law
Thermodynamics 34 : Mechanical Equilibrium and Ideal Gas Law
Published: 2013/09/01
Channel: Adam Beatty
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
Ladder Example for Static Equilibrium
Ladder Example for Static Equilibrium
Published: 2013/09/30
Channel: cstephenmurray
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
Statics Lecture 19: Rigid Body Equilibrium -- 2D supports
Statics Lecture 19: Rigid Body Equilibrium -- 2D supports
Published: 2013/02/18
Channel: Yiheng Wang
MCAT Force Equilibrium and Free Body Diagrams
MCAT Force Equilibrium and Free Body Diagrams
Published: 2015/02/18
Channel: Leah4sciMCAT
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
Netural Stable Unstable Equilibrium Mechanical Engineering Lectures Notes
Netural Stable Unstable Equilibrium Mechanical Engineering Lectures Notes
Published: 2015/10/08
Channel: iProf India
4.4 Pulleys in equilibrium
4.4 Pulleys in equilibrium
Published: 2016/03/28
Channel: Vector In Motion
[clipvidva]  สมดุลกล Mechanical Equilibrium Part3/5
[clipvidva] สมดุลกล Mechanical Equilibrium Part3/5
Published: 2014/01/12
Channel: clipvidva
Mechanical Engineering: Particle Equilibrium (4 of 19) Beam Under Tension
Mechanical Engineering: Particle Equilibrium (4 of 19) Beam Under Tension
Published: 2015/06/19
Channel: Michel van Biezen
NCEA Physics L2 Mechanics: Torque and Equilibrium
NCEA Physics L2 Mechanics: Torque and Equilibrium
Published: 2015/04/29
Channel: LearnCOACH
AS Physics Solving Equilibrium Problems
AS Physics Solving Equilibrium Problems
Published: 2014/01/25
Channel: Kate Wainwright
25.2 Stable and Unstable Equilibrium Points
25.2 Stable and Unstable Equilibrium Points
Published: 2017/06/02
Channel: MIT OpenCourseWare
Mechanical Equilibrium
Mechanical Equilibrium
Published: 2015/03/02
Channel: Rajiv Rajan
Physics - Equilibrium of Force xy-component 1
Physics - Equilibrium of Force xy-component 1
Published: 2010/11/13
Channel: skoolplusplus
Equilibrium of a particle : ExamSolutions
Equilibrium of a particle : ExamSolutions
Published: 2011/10/11
Channel: ExamSolutions
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
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WIKIPEDIA ARTICLE

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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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