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In this site, mechanical equilibrium is defined as when there is no net force between the system and the boundary, it is in mechanical equilibrium.

Now, what does it mean by net force? What would happen if there were a net force??

In an isolated system, when there is no net force within anypart of the system, it is called mechanical equilibrium.

Now,what is this? What does this definition want to tell?? What does it want to say by writting any part of the system?? What will happen if mechanical equilibrium doesn't exist in the isolated system??

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    $\begingroup$ Mechanical equilibrium simply means that all forces acting on parts of the system work out to be zero. This includes pressure differences (which, otherwise, would produce a net force). Without mechanical forces the system or its parts are not accelerated according to Newton's laws of motion. Practical examples of thermodynamic systems that are in near-thermal equilibrium but not in mechanical equilibrium are low intensity sound waves or a slowly swinging pendulum in air. As a consequence both systems experience damping of their mechanical movements. $\endgroup$
    – CuriousOne
    Commented Dec 28, 2014 at 6:03
  • $\begingroup$ @CuriousOne: So, that means no part of the system can accelerate,right? $\endgroup$
    – user36790
    Commented Dec 28, 2014 at 12:57
  • $\begingroup$ Nope. No forces, no acceleration. $\endgroup$
    – CuriousOne
    Commented Dec 28, 2014 at 15:22
  • $\begingroup$ Related question by OP: physics.stackexchange.com/q/155271/2451 $\endgroup$
    – Qmechanic ♦
    Commented Dec 28, 2014 at 23:38
  • $\begingroup$ mechanical equilibrium of a point mass simply means no acceleration is observed (in inertial frame) $\endgroup$
    – Shing
    Commented Jul 19, 2015 at 13:20

3 Answers 3

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The picture below can illustrate the concept of static equilibrium. On a pulley hangs an object A on which acts the gravity with the force $G_A$. If on the other end of the cable there is nothing, the system A + cable is not in static equilibrium and A will fall pulling the cable after it. But, if on the other end we hand an object B of the same weight as A, the system will be in equilibrium: nothing moves, and nothing falls.

A net force appears when the weights of A and B are not equal.

Static equilibrium or non-equilibrium

To see this let's write the equations. I consider the positive direction of the forces, upwards, and I write the sign of the forces explicitly.

On the left hand side (LHS) $-G_A$ pulls the cable downwards, and by virtue of the 3rd Newton law the cable pulls the object A with a force of tension, $T_1$, equal in magnitude and opposite in direction to $-G_A$.

(1) $T_1 = +G_A$

On the right hand side (RHS), if there is an object B, there appears a tension force $T_2$ in the cable, also upwards directed.

(2) $T_2 = +G_B$

The two tensions have to be equal, otherwise the cable won't be fully stretched, it will tend to gather on the top of the pulley. For that, one should have $G_A = G_B$. If this equality doesn't hold, the system is not in equilibrium. For instance, assume that $G_A - G_B > 0$. This difference produces a torque on the pulley which rolls the cable. Thus, the object A gets a downward acceleration $a$, and the object B gets the same acceleration (because the length of the cable is constant), but upwards. So, on the LHS we have

(3) $T_1 - G_A = -m_A a$.

On the RHS,

(4) $T_2 - G_B = +m_B a$.

Now, since the cable is fully streched, $T_1 = T_2$.

Let's subtract eq. (2) from (1)

(5) $-(m_A + m_B)a = -(G_A - G_B)$

The net force that acts on the system, is the force that imposes an acceleration to the system. This force is $-(G_A - G_B)$, and the acceleration is

(6) $-a = -\frac {G_A - G_B}{(m_B + m_A)}$ .

Remember, the signs are here explicit.

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  • $\begingroup$ +1. Can you,please,explain in the light of a thermodynamics system? Thanks :) $\endgroup$
    – user36790
    Commented Dec 28, 2014 at 12:55
  • $\begingroup$ I will try, but please, later. For the moment I have to leave the computer for all sort of duties. $\endgroup$
    – Sofia
    Commented Dec 28, 2014 at 13:25
  • $\begingroup$ @user36790 : I am here. When you are in the SE please notify me. $\endgroup$
    – Sofia
    Commented Dec 28, 2014 at 19:53
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I think you missed out this :net moment about any point is zero. So for mechanical equilibrium you must have net force and net moment about any point equal to zero. Net Force can move a body but net moment can turn it about certain pivot point. It has same meaning in thermodynamics (if you are not asking about thermal equilibrium)

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In the absence of any unbalanced force within the system itself, and also between the system and surrounding system, the system is said to be in mechanical equilibrium.

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