What is Static equilibrium: Definition and 357 Discussions

In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. 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.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. 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. 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.

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  1. E

    Ladder in static equilibrium

    tried equating torques around the pivots of the ladder and equating them to zero but I'm not getting anywhere with that.
  2. YehiaMedhat

    Engineering Free body diagram for frame

    can you check if I sketched it correctly? And please if you know any good resources refrence it.
  3. tracker890 Source h

    Rotational balance problem

    Please help me to understand why it is wrong to take moment for point ## A’ ## , because I think static equilibrium should be static equilibrium for any point in space. Method 1: $$ \sum{M_A=0:} $$ $$ F\cdot R=\left( F_p \right) _x\cdot \left( R-y_p \right) +\left( F_p \right) _y\left( x_p...
  4. H

    Sign hanging from massless beam attached to hinge supported by string

    Attempted creating equations for zeros of torque and components of forces in x and y as seen in picture. Got lost with having only variables and the d & 2L for the length of the beam. Not sure how to do the question with two points of contact between the beam and the sign. Is the center center...
  5. S

    Tetrahedron with 3 points fixed, and force applied to 4th

    My approach to this problem is to recognize that the tetrahedron being still means that net torque is zero and net force is zero. Fd is given Fa + Fb + Fc = -Fd Fa X a + Fb X b + Fc X c = <0,0,0> This can be split up into a series of 6 equations, 2 for each component. However, this is where I...
  6. L

    Engineering Hand tool boundary conditions - Forces determination

    Hello, I' m trying to make a linear static analysis (Finite Element Analysis) on the following hand tool. I want to determine the boundary conditions. In order to do that I have decided to use a force couple to represent the forces that a bolt exerts on the jaws of this spanner. Despite using...
  7. NovatoOfPhysica

    Virtual Work and Static Equilibrium

    Hi there, this question has already been discussed in this forum, however I do not know how to proceed further and if my reasoning is correct. I start by imagining a downard displacement of the 1kg weight. As a consequence of this, block A moves upward and to the right. Also, block B moves...
  8. S

    Body forces in static equilibrium (FEM issue)

    Hi, I have an issue with understanding the body forces in the context of FEM simulations. I am using freefem to do the simulations. So I took a simple unit cube, fixed the displacements at side ##x=0## and prescribed a displacement ##u_x = 0.025## at ##x=1##. If required, the entire script is...
  9. L

    Is there any friction in this case?

    In the experiment, a cart on an inclined plane of 30 degrees is hooked with the force metre by a line. The line is tension T. It is also subjected to the force of gravity Fg. This makes the cart in static equilibrium. But since the cart is hooked with a line, it does not slide down. The net...
  10. C

    Calculate dimensions of floating laptop stand

    I am planning to build my own laptop stand with an acrylic sheet. The final product should look like the one in the attached image (bottom right) Material: most laptop stands are made with 6mm acrylic thickness, hence this is what I will use. Also I already have this material at home. I am...
  11. hedera

    Statics problem, suport reactions and pins, IDK where to go

    So far I got the simplified forces of 12, 48 and 36 kN, at 1, 5 and 9.5m (from A) respectively, but I'm confused as what to do next, can you help me?
  12. S

    Static Equilibrium Problem

    I have two questions regarding this problem 1. The following is my attempt to solve Fcy using the fact that the addition of torque = 0. I considered force mg and Fcy and their lever arms to set up the equilibrium. But this method seems not to work? Why? 2.At the bottom of the question, it...
  13. D

    Conceptual Problem - Static Equilibrium

    I am not sure whether I can prove like this, I am trying to explain it with the angle .
  14. R

    Trouble with Static Equilibrium

    My initial response to seeing the figure is what is ##F_{ua}## and where does it come from? How was i supposed to know it was there is they didn't give a picture? So for part a, ##F_{ua}## doesn't play a role because it exerts no torque, and apparently we are supposed to use the torque equation...
  15. J

    Static equilibrium: mass on beam

    A diagram of the physical situation is below: Choosing the positive ##y## direction to be upwards and the positive direction of rotation to be counterclockwise, Newton's linear second law gives: $$-m_D g + F_L + F_R = 0$$ where ##F_L## is the magnitude of the force exerted on the bar by the...
  16. archaic

    Static equilibrium problem: Finding tension

    The diagonal component of the boom's weight is ##R=w\cos\frac{\pi}{6}=\frac{\sqrt 3}{2}w##, and, considering ##R## as a "reaction", we have ##R_x=R\cos\frac{\pi}{3}=\frac{\sqrt 3}{4}w## and ##R_y=R\sin\frac{\pi}{3}=\frac 34w##. I will also have...
  17. archaic

    Static equilibrium: Placing a fulcrum

    I don't understand the question; they're telling me that the fulcrum is just under the center of gravity of the bar, but that I also need to find its position. In any case, I suppose that the fulcrum's position is ##x##. Let the weight at the left end be ##w_1##, at the right end be ##w_2##...
  18. archaic

    Static equilibrium and a diving board

    I take the left end as reference for torques: $$\sum\tau=F_\text{support}+\frac 32\times280+3\times500=0\Leftrightarrow F_\text{support}=-192.\times10^1\,N$$ It's facing up. I take the right end as reference for torques: $$\sum\tau=-192.\times10^1\times2+\frac 32\times280+3F=0\Leftrightarrow...
  19. S

    Static Equilibrium Problem (concept question)

    (figure)I was able to solve the problem and get the right answer. However, I solved it more with intuition, and I do not get how the force of the person pulling down on the rope makes the force to the left of the backpack equal to force to the right of the backpack.
  20. J

    Motion of 2 masses connected by a rod to a pendulum

    I am not sure which other forces I should consider besides those 3. I cannot consider tensions due to the massless rod on the masses since those will not add up to zero.
  21. benny1993

    Static Equilibrium and a beam

    I have been trying to work on this problem, but I keep getting the answer wrong. I would appreciate if someone could help me understand what I did wrong. Below is my answer and solution:
  22. penroseandpaper

    Ladder in static equilibrium

    Hi everyone, I'm studying an introductory physics course at college, but our teacher is off sick. On top of that, a planned strike means we won't be getting a new science tutor until the start of next month - instead, we've been told to read the textbook and answer the questions. I've got up...
  23. A

    Static equilibrium of a bar attached to a hinge

    item Fx Fy torque(z) rod 0 -mg -mg* (3/2) Fred 0 -Mg (-Mg) * (3/2) hinge -hx hy 0 wire F* cos(theta) F* sin(theta) 3*F* sin(theta) total 0 0 0 theta= tan^(-1) (2/3) = 33.7 degree 3*F* sin(theta) = (8*9.8)* (3/2) + (53*9.8) * (3/2) F= 538.7N tension is 538.7N
  24. M

    Engineering Calculate Static Equilibrium: SOH/CAH/TOA?

    When calculating static equilibrium, i know that you have to split for example, F1 into F1x and F1y. when using soh/cah/toa is it always SIN for the Y axis and always Cos for the X axis? I've been following this method and getting it wrong some times it's really stressing me out, Thanks for any...
  25. greenrichy

    Find the stretch of a steel wire in a static equilibrium problem.

    If I can determine the weight of that heavy object placed on the plank, I will be able to determine the stretch of that wire. But, when using the second condition for static equilibrium (torques of the system equal to 0), I always end up with two unknowns, no matter what point of rotation I...
  26. EEristavi

    Rotational Motion / Static Equilibrium - Mechanics

    I have a solution, However Cant understand 1 point.Now, This is the solution: ##N_2 l cos\theta + \frac 1 2 F_g l cos\theta - f_2 l sin\theta = 0## ## N_2(1 - \mu tan\theta) + \frac 1 2 F_g = 0## This is the the point that I don't like - yes it is less that 0, but it's even less that...
  27. N

    Static equilibrium force decomposition problem

    If you see the $\sum \tau_0 = L\cdot N_1 \cdot cos \theta - LF_1 sin \theta - L/2 \cdot G cos \theta$, all the trigonemetric parts are all opposite of what i can understand, given the angle as drawed in the Picture/url. Please help me :)https://pasteboard.co/IiXr8qA.png
  28. Lone Wolf

    Static equilibrium -- interpretation of forces

    I solved this question correctly, however I have a question regarding how I should work with the weight of the firefighter climbing the ladder. When drawing the force diagram for this problem, I should only include forces acting on the ladder, right? Which means I would represent the normal...
  29. E

    Show that a tilted free liquid surface undergoes shear stress

    i really can't understand the answer of this question, is the question 1.3 in fluid mechanics by Frank ,M White For the triangular element in Fig P1.3, show that a tilted free liquid surface, in contact with an atmosphere at pressure pa, must undergo shear stress and hence begin to flow. i...
  30. M

    Asymmetrical Static Equilibrium

    a) Answer that I found: 56.31 degrees b) Answer that I found: 121.71 Kg For b) not sure if I need to add the 20 N and 5 N to the total of the cargo mass.
  31. Susie

    Tension Force Problem: Solving for T1 with x and y components using trigonometry

    I know I have to find the x and y components of T1 using 400cos(55) and 400sin(55) and I know that the x-component of T1 will = the x-component of T2 but opposite sign to give 0. But idk how to get there and what do to for the y-component. I think I found the weight, I think it’s 32.42g but I’m...
  32. mmest

    Magnetic Field required to hold a loop in static equilibrium

    Homework Statement There is a square loop with mass of 4.0 kg and side length 4.5 m that is tilted upwards from the ground at a 25 degree angle with one side resting on the surface. The loop is a conductor that has 25 A of current going through it. The question asks to find the strength a...
  33. S

    Static equilibrium -- A picture hanging on a wall

    Homework Statement https://imgur.com/v13K6sE a uniform rod of mass m is placed as shown, with one of its end resting on a smooth wall while 1/4 of the rod's length is sticking out of a rough table. Find the net force the table exert on the rod at the corner. Homework Equations i drew the free...
  34. Arman777

    Spring static equilibrium Problem

    Homework Statement a) If the distances ##s_1## and ##s_2## are the amounts the springs are streched while in static equilibirum, Write down the static equilibirum equations. b) When the system is distrubed from its equilibirum state, both mases move vertically. Let ##y_1(t)## and ##y_2(t)##...
  35. G

    Question about Normal Force and Torque

    Homework Statement A block of uniform density experiences a force F to the right, applied 5/3 m from the bottom of the block. The block is 2 m high and 1 m wide. Take the pivot point to be the point at the bottom right of the block. Find the value of the force that is just able to tip the box...
  36. S

    Static equilibrium: Find the tension in a support cable

    Homework Statement Homework Equations Σtorque = 0 Σfx=0 Σfy=0 torque= F r sinθ (θ is the angle between the r and the F)The Attempt at a Solution OKay, now i know how to solve this, but it's like i asked myself, how to know if this is a question that i am supposed to use Σfx=0 and Σfy=0...
  37. F

    Statics and equilibrium - asking for some guidance

    Hi, I'm not used to communicate physics in English, so my language may be a bit off. This task is fairly simplistic. It's a figure which is held up in points A and B (both having an x and y force exerted on them), and the figure has a joint C. It is depicted in attached files. The answers...
  38. S

    B Maximum Overhang in Static Equilibrium

    Hi, i am trying to trying to solve this question as this question is slightly different from the usual type of overhanging question. Please advice on the approach. Thank you I have to find the maximum overhang possible, l, before the whole blocks falls apart
  39. I

    Force Calculation -- Hydraulic cylinder and a rotating arm

    Hi There, Long time reader, first time poster.. I hope someone out there can help me. I'm designing an add-on to an existing piece of equipment and I'm unsure of how to calculate the resultant force output from a hydraulic cylinder. On a straight push, the chosen hydraulic cylinder has an...
  40. Zack K

    Weight of an object in static equilibrium

    Homework Statement An object is suspended on a frictionless slope inclined plane by a rope parallel to the incline. If the angle of the incline is 25° and the tension on the rope is 5000 N, what is the weight of the object Homework Equations ∑F=0 The Attempt at a Solution So in my eyes, you...
  41. A

    Quick Question about Torque and Tension

    Homework Statement A meter stick with a mass of 260 g is supported horizontally by two vertical strings, one at the 0-cm mark and the other at the 90-cm mark A) What is the tension in the string at 0 cm B) What is the tension in the string at 90 cm C) The string at the 90-cm mark is cut. What...
  42. Zack K

    Mass of a picture in static equilibrium

    Homework Statement An artist must push with a minimum of 75N at an angle of 45° to a picture to hold it in equilibrium. The coefficient of friction between the wall and the picture frame is 0.30. What is the mass of the picture? Homework Equations ΣF=0 Ffr=μFN F=ma The Attempt at a Solution I...
  43. Emanuel0406

    Static Equilibrium Problem Help Needed

    Hello! I was wondering if anyone could give me a hand with the following problem. I am stuck and I don't know how to solve it. You can see attached the problem and my work so far. Thank you very much for your help.
  44. Emanuel0406

    Solve Static Equilibrium Problem: Get Help Now

    1. The problem statement, all variabHello. I uploaded a picture with the problem that concerns me. As you can see from my work so far...I have tried to solve the problem but I'm stuck. I have tried a few times and I'm starting to question myself if the problem is correct or not. Please give me a...
  45. jalalapeno

    Finding Tension and theta in a pulley system

    What I've attempted to do is resolve vertically and horizontally: T1sin(30)+T2sinΘ+T2=9g T2cosΘ=T1cos30 After that... I'm completely stuck. Any help would be appreciated, I've spent so long on this I bet I'm just missing one simple thing. Thanks in advance
  46. C

    MHB Static equilibrium for boom

    The uniform boom shown below weighs 668 N, and the object hanging from its right end weighs 386 N. The boom is supported by a light cable and by a hinge at the wall. Calculate the tension in the cable and the force by the hinge on the boom (both in N). (Enter the magnitudes.) Tension in the...
  47. S

    Find the mass in static equilibrium problem involving a spring

    Homework Statement Consider a rigid 2.60-m-long beam (see figure) that is supported by a fixed 1.30-m-high post through its center and pivots on a frictionless bearing at its center atop the vertical 1.30-m-high post. One end of the beam is connected to the floor by a spring that has a force...
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