Static equilibrium Definition and 49 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. 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.
  2. 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...
  3. 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...
  4. 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...
  5. 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...
  6. 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...
  7. 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...
  8. 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?
  9. 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...
  10. 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.
  11. 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
  12. 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...
  13. 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...
  14. Susie

    Tension Force Problem

    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...
  15. S

    Static equilibrium -- A picture hanging on a wall

    Homework Statement 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...
  16. 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...
  17. 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...
  18. 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...
  19. 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...
  20. 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...
  21. 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...
  22. 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
  23. 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...
  24. E

    Unhinged -- Static Equilibrium for a Door

    Homework Statement Homework Equations Torque = r x F The Attempt at a Solution I expect the door to fall.
  25. A

    Spring angles at static equilibrium on application of force

    Homework Statement Two linear springs with stiffness Kh, Kv are attached to a single mass m at right angle to each other, i.e; one of the spring(Kh) is in the horizontal direction(x-axis) and the other(Kv) is in the vertical direction(y-axis). A constant force F is being applied to the mass...
  26. U

    Lifting a Beam with a uniform weight distribution

    Homework Statement Hi There, I'm having trouble understanding (what I guess should be) a simple concept and so I can't apply it to a project I'm working on (also kind of rusty on torques and mechanics problems) If I have a hinged beam (of uniform weight) and I lift it from one end and stay...
  27. person123

    Pulley System

    I was working on a pulley system as shown here: The mass on the right and left side is equivalent, and I am solving for when the system is in static equilibrium. Theta is the angle between the rope on either side of one of the pulleys. H and y are both measured from the original position of...
  28. W

    How to calculate the tension in a beam of a bridge?

    Homework Statement A bridge, constructed of 11 beams of equal length L and negligible mass, supports an object of mass M as shown in the picture. Assuming that the bridge segments are free to pivot at each intersection point, what is the tension T in the horizontal segment directly above the...
  29. Kevin de Oliveira

    Static Equilibrium

    I have a 3 pulley system statically balanced hanging weights at a determined relative angle (we are taking into account friction). If I change the position of one pulley, angles will remain the same. However, if I have a 4 pulley system, at the same conditions, changing one's position will...
  30. D

    Direction of force exerted by ground for the ladder problem

    This question pertains to the classic ladder-leaning-against frictionless wall scenario. The system is in static equilibrium. The ladder is thin and can be assumed to be made of a homogeneous material so that the center-of-mass lies at the geometric center. The forces in this scenario is...
  31. kamhogo

    What is the force exerted by each hinge on the door?

    1. Homework Statement The door has a mass of 30 kg, is 200 cm long and 90 cm wide. The hinges are installed at 25 cm from the bottom (R2) and 25 cm from the top (R1). What are is the magnitude of the force exerted by each hinge on the door? The door is in a state of static equilibrium...
  32. merricksdad

    Determining mass of a weight on a three spring scale setup

    Homework Statement Given three spring scale readings, positioned at unknown angles, find the mass of the weight hanging from all three scales without using trig, and without measuring the angles. You have only a yard stick. This is a static equilibrium problem. Homework Equations Not allowed...
  33. E

    I Proportion in 2D and 3D static equilibrium?

    If you were to look at a simple 2D or 3D static equilibrium diagram, where a mass is suspended by multiple ropes at different angles, my gut feeling is that there is a fairly simple proportion between the distance between the center of mass and the rope (the distance created opposite of the...
  34. A

    Static Equilibrium Problem involving Moments

    Equations: Net torque=0=Net force I believe this is a static equilibrium question but can't figure out how to do it

    Static Equilibrium of Board

    Homework Statement There is a diving board held up by two pillars A and B, and there is a diver standing on it's edge. What are the directions of the forces exerted at points A and B? Picture Below: Homework Equations F_NET = 0 T_NET =0 The Attempt at a Solution I thought both A and B were...
  36. S

    Static Equilibrium: holding a sign

    Homework Statement You are holding a sign as shown below. The sign (including the horizontal bar it hangs from) has a mass of 2.20 kg and is 40.5 cm wide. The sign is hanging from a 1.03 m tall, 4.46 kg vertical post. The sign is symmetric with a uniform mass distribution as implied by the...
  37. R

    Are these torques correct for a simple balancing/fulcrum exp

    Homework Statement For my physics lab, they had us do a simple static equilibrium experiment where we rested a ruler on a fulcrum (at its center of mass) and then attached varying amounts of weight on either end at different distances from the fulcrum. This screenshot is the data we recorded...
  38. K

    Angles in a Static Equilibrium

    Homework Statement I have 3 masses (Fα, Fβ & Fg) with 2 pulleys, and a wind variable which is in static equilibrium. I have already calculated the appropriate forces for the 3 masses by multiplying it with 9.81m/s² (gravity). Fwind = 60N Fα = 313.9N Fβ = 619N Fg = 882.9N I'm required to find...
  39. C

    Magnetic Force/Field, Current, Inclined Plane Problem

    Hello! I just need someone to check my work here. I already turned in the homework with my hunch, but now I just want to check my work because it is killing me not knowing 100% :) I am having strong conflicting thoughts on particular parts and thought I'd post it here for clarification. I will...
  40. T

    Chain on a cone

    Homework Statement A loop of flexible chain, of total weight W, rests on a smooth, frictionless right circular cone of base radius r and height h. The chain rests in a horizontal circle on the cone, whose axis is vertical. Find the tension in the chain. Homework Equations Virtual work, but...
  41. O

    Easy statics problem -- Block being hoisted by a pulley and rope

    I drew a FBD about point A and came up with the two equations: ∑Fx=0 20sinθ - T-ab(cos70)=0 ΣFy =0 -20cosθ + T-ab(sin70) -20=0 My answer is not coming out so I either messed up on the FBD or the equations, some help would be appreciated. I'm on 3-10 by the way.
  42. A

    Tension force and a board fixed to a flat surface

    A heavy board is fixed to another flat surface along its entire upper edge and not moving. How can I find the tension force that is acting on the board? Is it the same as if the board would be fixed to a string in the middle of the upper edge and hung and then the tension would be T=mg?
  43. Curieuse

    Static equilibrium of a wheel

    1. Problem statement In figure, what magnitude of (constant) force F applied horizontally at the axle of the wheel is necessary to raise the wheel over an obstacle of height h=3.00cm ? The wheel's radius is r=6.00cm , and it's mass is m=0.800 kg. Homework Equations Balance of forces: Fnet=0...
  44. C

    How is the torque shared between two points?

    Figure: 1. Homework Statement We know system is in equilibrium and we are given the mass m, and the distances d, r1, and r2. We assume that the rotational inertia of the bar is negligible. What are the forces at points a and b? Homework Equations Torque = radius × Force Force = mass *...
  45. P

    Static Equilibrium - trick question?

    Homework Statement A man stands on a board of negligible mass with a length of 10m is supported by 2 cables, one on the left on one on the right, with a tension of 300N and 200N respectively. How much does the man weigh in Newtons? Homework Equations F=ma Torque= F*lever arm The Attempt at...
  46. 1

    Static Equilibrium Question

    Q: Why does the pin have a vertical force in this diagram (Static equilibrium)? The diagram depicts as follows: A mass (M) sits a a distance (d) away from the end of a board of length L. The board has a mass of m and is held to a wall by a pin and string. The string has a tension (T) and is at...
  47. A

    Moment in different dimensions in 2 D

    Homework Statement This isn't exactly a HW question, it's a question in my statics midterm today, he wants the reactions at the supports B and C, which is easy but the problem is this 60 N.m moment, all my friends were like :" let's just sum the moments around B ( due to the 50 N and the...
  48. V

    KT of Gases and static equilibrium

    In a recent class, my instructor covered the Kinetic Theory of gases. My question is in regard to the theory which states 1) The size of the individual molecues in a gas are so small that their volumes can be considered negligible. The instructor then mentioned that the paticles in the gas can...
  49. Aristotle

    Need assistance in Physics question relevant to Torque & Static equlibrium

    Homework Statement Homework Equations Static equilibrium: Net force & net torque = 0 The Attempt at a Solution Am i doing this correctly for part a? [/B]