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

    Static Equilibrium Door Problem

    Homework Statement A door made of a uniform piece of wood measures 1 m by 2 m and has a mass of 18kg. The door is entirely supported by two hinges, one at the bottom corner and one at the top corner. Find the force (magnitude and direction) that the door exerts on each hinge. Assume that...
  2. S

    Static Equilibrium: A 1380 N uniform boom of length ℓ is supported by a cable

    Homework Statement A 1380 N uniform boom of length ℓ is supported by a cable, as shown. The boom is pivoted at the bottom, the cable is attached a distance 3/4ℓ from the pivot, and a 3604N weight hangs from the boom’s top. Find the tension of the cable. here is a picture of the diagram...
  3. X

    What is the equation for solving static equilibrium questions?

    I do not understand how to solve static equilibrium questions. Like those: Or this one http://www.chegg.com/homework-help/questions-and-answers/a-uniform-120-lb-beam-is-supported-in-a-horizontal-positionby-a-pin-and-cable-as-shown-in--q701621 The second one with the pin is especially hard...
  4. D

    Static equilibrium mass and plank problem

    Homework Statement A plank having length L and mass M rests in equilibrium on two supports (1 and 2) that are separated by a distance D. The supports are located at equal distances from the enter of the plank. A mass m hangs from the right end of the plank. If L=6m and D=2m, which of the...
  5. H

    Static Equilibrium On a Beam Question

    Homework Statement A uniform beam of length L and mass m shown in the figure below is inclined at an angle of θ to the horizontal. Its upper end is connected to a wall by a rope, and its lower end rests on a rough horizontal surface. The coefficient of static friction between the beam and...
  6. P

    Static Equilibrium Problem Dealing with Torque

    Homework Statement The figure shows a model of a crane that may be mounted on a truck. A rigid uniform horizontal bar of mass = 90.00 kg and length = 5.200 m is supported by two vertical massless strings. String A is attached at a distance = 1.600 m from the left end of the bar and is...
  7. C

    Achieve a state of static equilibrium

    Homework Statement If a body is acted upon by clockwise moments of 75 N at 1.25 m And anticlockwise moments of 50 N at 1.3 m , Is it in a state of static equilibrium ? If not what is required to achieve a state of static equilibrium ? Homework Equations sum of all forces on all...
  8. P

    Static Equilibrium | 736g Beam & 5.25N Sphere | FBD & Tension Calc

    A 736g uniform mass beam is used to suspend a sphere that weighs 5.25N. it is supported by an ideal rope attached to the wall, and one third the length along the beam (from the wall). The angle between the rope ans the beam is 51.0 degrees. a) draw a free body diagram b) calculate the...
  9. S

    Rigid Body Static Equilibrium. Find force components

    Homework Statement Pin C joins members ABC and CDE Homework Equations Sum of moments at a point = 0 Sum of vertical forces = 0 Sum of horizontal forces = 0 Weight of triangle acts as a force at its centroid (1/3) its length according to this figure. The Attempt at a Solution...
  10. M

    How far can the remote control extend without tipping over?

    Homework Statement A .110-kg remote control 21.0cm long rests on a table, with a length L overhanging its edge. To operate the power button on this remote requires a force of .365N. How far can the remote control extend beyond the edge of the table and still not tip over when you press the...
  11. S

    Static Equilibrium Pulley and free body diagram

    Homework Statement Attached is the picture of the problem and my free body diagram. The system is in equilibrium. Homework Equations Fy = 0 Fx = 0 The Attempt at a Solution I'm having trouble solving the two equations that I arrive with... I use +x to the right, and +y up...
  12. D

    Static equilibrium for three point charges

    The result I got seemed sort of messy and I'm not sure I've gotten the basic idea correctly, so I thought I'd make it sure. I think this was the easiest problem we had to solve for charge distributions and point charges and whatnot, so I know for sure I'll have to practice more if I made any big...
  13. V

    Static Equilibrium and Torque Homework Question

    Homework Statement A hiker, who weighs 985 N is strolling through the woods and crosses a small horizontal bridge. the bridge is uniform, weighs 3610 N, and rests on two concrete supports, one at each end. he stops one - fifth of the way along the bridge. What is the magnitude of the force...
  14. M

    Finding tension in a wire in our static equilibrium unit

    This is the final question on a static equilibrium quiz i had today (physics 12). when comparing answers (as you tend to do after the quiz "did you get x for question y?"), half of my friends (all of equal ability in the course) got a different answer from me, and the other half the same. I am...
  15. M

    Where Should the Normal Reaction Be in a Static Equilibrium Problem?

    I am working on this word problem, you can see from my attachment.. I want to make sure my body diagram is correct?
  16. G

    Static Equilibrium / Normal Forces / Braking Forces on tires

    Homework Statement In the figure below, the driver of a car on a horizontal road makes an emergency stop by applying the brakes so that all four wheels lock and skid along the road. The coefficient of kinetic friction between tires and road is 0.36. The separation between the front and rear...
  17. O

    Static equilibrium of a hanging, unbalanced beam.

    Homework Statement a. A uniform beam is hanging from a poing 1.00 m to the right of its center. The beam weights 140 N and makes an angle of 30° with the vertical. At the right-hand end of the beam, a 100-N weight is hung; an unknown weight w hangs at the left end. If the system is in...
  18. M

    Why Might Forces and Torques Not Sum to Zero in a Static Equilibrium Lab?

    In a static equililibrium lab, what are some reasons why the sums of the forces and/or torques may not be equal to zero. The forces in N are very close to zero (as my professor said they should be) and the torques in N-cm are not anywhere close to zero. I know the torques are greater than their...
  19. D

    Solving Static Equilibrium Problem

    Static Equilibrium Problem Homework Statement A uniform bar of length 16 m and mass 8 kg is attached to a wall with a hinge that exerts a horizontal force Hx and a vertical force Hy on the bar. The bar is held by a cord that makes a 90 degree angle with respect to the bar and 45 degree...
  20. K

    [static equilibrium] pin and link support type

    Hello every one I am confused between two support type: the pin, and the link On the textbook, it says, the pin prevents the object from translating vertically and horzontally, therefore, it provides fx and fy reaction forces. but another type of support is much identical to the pin...
  21. J

    Static equilibrium problem:A-shaped ladder

    Homework Statement A ladder is made in the shape of the letter A. Treat the two sides of the ladder as identical uniform rods, each weighing 455 N, with a length of 3.60 m. A frictionless hinge connects the two ends at the top, and a horizontal wire, 1.20 m long, connects them at a distance...
  22. M

    Time for Hydro System to Reach Static Equilibrium

    I was tasked with redesigning our system to hydrostatically test valves. I had to incorporate a drip test downstream of the valve that would be the determining factor whether the valve was leaking or not. The system I came up with has 3/8" ID tubing (app. 10 ft) running from the downstream of...
  23. T

    Static Equilibrium: Sliding and Tipping Bookcase

    Homework Statement See Picture: I am only stuck on Part (c) where it asks to calculate the force as the bookcase starts to tip. Homework Equations sigma Fx=0, sigma Fy=0, sigma tau=0 The Attempt at a Solution I am setting up the problem by picking an axis that runs through the...
  24. A

    Solving Static Equilibrium Problem in 3D: P=50N, Ay=108.8, Cy=58.1, By=32.4

    Been working on this problem http://www.flickr.com/photos/archiphoto77/6179533925 (SEE LINK FOR PHOTO OF PROBLEM) for quite some time now, and the components don't quite add up for me so I am just a tad exasperated... In the x-z projection, I see two forces acting along the x-axis---one...
  25. S

    Finding a length of a cable, in static equilibrium

    Homework Statement Find H as a function of L and XHomework Equations http://imageshack.us/photo/my-images/28/project1questoin.png/ http://imageshack.us/photo/my-images/28/project1questoin.png/ The Attempt at a Solution my answer came out to a ridiculous solution and I am not really sure if it...
  26. V

    Static equilibrium pulley problem

    Homework Statement http://img849.imageshack.us/img849/3716/staticeqpulley.jpg Hopefully the image showed up. If not, here's the link: [PLAIN]http://img707.imageshack.us/img707/3716/staticeqpulley.jpg" Sorry for the low quality pictures. Hopefully it will do though. The question is: Relate...
  27. D

    Calculators Troubleshooting Simultaneous Equations with Trigonometric Functions on TI-89

    Homework Statement My problem is getting the SOLVE() function to work correctly. I have used it plenty of times in the past, but when I put in these 4 equations to solve simultaneously, it gives me the wrong answers. My Professor said that TI-89's sometimes have problems when having to solve...
  28. N

    Static equilibrium: Elastic rope with load

    Homework Statement It's not possible for me to solve this problem. Maybe work/energy relations is required ? Homework Equations I've ended up with polynomiums of 3. and 4. degree, trying to find the roots. But finding the...
  29. S

    How Do You Calculate the Third Force in Static Equilibrium?

    Homework Statement I have been given two forces and have to calculate the magnitude and direction of the third force that will result in equilibrium. The two forces I have been given are: F1 = 2.156N at 48 degrees F2 = 4.508N at 203 degreesHomework Equations I used both the cosine law (c^2...
  30. P

    Bridge truss Static Equilibrium

    Homework Statement A bridge truss extends x = 214 m across a river (Fig. P12.68) where θ = 35°. The structure is free to slide horizontally to permit thermal expansion. The structural components are connected by pin joints, and the masses of the bars are small compared with the mass of a 1270...
  31. H

    Static equilibrium ladder question

    Homework Statement A nonuniform fire escape ladder is 6.0 long when extended to the icy alley below. It is held at the top by a frictionless pivot, and there is negligible frictional force from the icy surface at the bottom. The ladder weighs 250 , and its center of gravity is 2.0 along the...
  32. N

    How Does the Angle θ Relate to Φ in Static Equilibrium of a Tilted Rod?

    Homework Statement The uniform rod in the figure is supported by two strings. The string attached to the wall is horizontal, and the string attached to the ceiling makes an angle of ϕ with respect to the vertical. The rod itself is tilted from the vertical by an angle θ. If ϕ = 29.9°...
  33. P

    Calculating Tension and Mass in Static Equilibrium: Are My Methods Correct?

    1. A gymnast of weight 720 N is holding himself in the cross position on the high rings. He is quite still. A free-body force diagram for the gymnast shows the two upward pulls of the rings on the hands, each, size 380 N. Calculate the angle between the wires supporting the rings and the...
  34. S

    Another static equilibrium question

    Homework Statement Homework Equations M=fd M= r x F The Attempt at a Solution this question really loses me. I'm not sure what exactly it is asking for, much less how to solve it. I am assuming it want's the force on A and E? I suppose I need to find the moment about each...
  35. Femme_physics

    Brakes, static equilibrium problem is my Free Body Diagram correct?

    Homework Statement Calculate minimal force P of the brakes during the stopping of the wheel. http://img823.imageshack.us/img823/6017/problemzy.jpg Solution is P=34.3 [N] Homework Equations (Written on scan above) The Attempt at a Solution...
  36. Femme_physics

    Stuck in another static equilibrium problem

    Homework Statement At what distance "d", from point "A", the board with the person will slide whereas http://img267.imageshack.us/img267/6139/skkkkkkk.jpg Uploaded with ImageShack.us Homework Equations Weight of board = 50 [kg] Weight of person = 100[kg] Frictional coefficient...
  37. Femme_physics

    Is this static equilibrium problem even solvable?

    Okay, me and my friend have been working on this problem for a while and it just been a headache catalyst for us...your help is called upon, people of the internet. Homework Statement A system of weights is in equilibrium. Calculate the distance "s" where WD = 5[N] WF = 5 [N] WE =...
  38. Femme_physics

    Simple Static Equilibrium question

    Homework Statement Two workers carry a beam at the length of 3 meters. One worker holds the beam at the edge and carries 0.4 of the beam's weight. At what distance (x) from the other edge holds the second worker? Homework Equations None. The Attempt at a Solution The solution is...
  39. P

    Static Equilibrium between 2 known points and 1 unknown

    Homework Statement A charge -q and a charge 4/9q are located at coordinates x = 0 and x = a, respectively. If you place a third charge so that all three are in static equilibrium, justify that its position and its charge,respectively, can only be x=3a Q=-4q Homework Equations...
  40. Femme_physics

    Static Equilibrium don't understand something

    Static Equilibrium...don't understand something http://img135.imageshack.us/img135/4664/helpo.jpg Look at the equation at "sum of all forces on y axis" and please tell me: How the heck did 0.4Na -mg = 0 turn into Na = 2.5m g?
  41. I

    Problem involving static equilibrium

    Hi I have posted the picture of the problem. I have already done the problem but I have some questions. Here the trailer is accelerating due to the applied force P. I used an inertial frame of reference at some distance to the left of the car.And then did the torque calculations with...
  42. N

    Static Equilibrium of a 10m Rod with a Hanging Weight at 1.46m Distance

    one end of a uniform 10 meter long rod weighing 50 Newtons is supported by a cable at an angel of 53 deg with the rod the other end rests against the wall where is is held by a friction us=2 . determine the minimum distance x from the left end of the rod at which a block weighing 20 Newtons can...
  43. R

    Length of bar needed to lift a crate(Torque, static equilibrium problem)

    Homework Statement A large crate weighing 4520 N rests on four 12-cm-high blocks on a horizontal surface (figure below). The crate is 2.0 m long, 1.2 m high, and 1.2 m deep. You are asked to lift one end of the crate using a long steel pry bar. The fulcrum on the pry bar is 11 cm from the end...
  44. E

    Why Don't We Need to Consider Net Force in Rotational Static Equilibrium?

    Homework Statement I have a question about rotational static equilibrium. When we consider the static equilibrium of a system, I realized that most people only consider the net torque acting on the system. Why don't we need to consider the net force acting on the system? For instance: A...
  45. P

    How is the Torque Equation Set Up for a Leaning Ladder in Static Equilibrium?

    Homework Statement A uniform ladder of mass m and length l leans at an angle theta against a frictionless wall. If the coefficient of static friction between the ladder and the ground is mu, determine a formula for the minimum angle at which the ladder will not slip. Homework Equations...
  46. D

    Static Equilibrium and Moment of Inertia problems

    Homework Statement Please help me do these : [PLAIN]http://broadcastsol.com/321.JPG Prob1 The mechanical system of massless members is shown in the figure. Determine the relationship between two forces P1 and P2 to keep the system in equilibrium at position as showing in the...
  47. D

    Static Equilibrium and Structure problems

    Homework Statement [PLAIN]http://broadcastsol.com/123.JPG Prob. 1. The structure of massless members is shown in the figure. Determine the reaction forces at the supports C, and forces in the rod EF and DG. Givens: P, a, b, c. Prob. 2. The structure of massless members is shown...
  48. A

    Theory type Question of Static Equilibrium

    Hi everyone! I just have a quick question about the theory behind a concept in statics. Problem: I was given a question that states that a sign is attached to a pin joint and also to a spring. The other end of the spring is attached to a spring joint as well. They hang there in static...
  49. N

    How Do Two People Balance a Uniform Beam at Different Distances?

    a uniform beam of length l and mass m is caried by two people one is distance d1 from the left end the other is distance d2 from the right end determine the force each person exerts on the beam. I have yet to encounter a rotational problem such as this with 2 axi
  50. B

    Static equilibrium of diving board

    Homework Statement A uniform diving board of mass=27kg and length x=4.3m is supported by two beams. beam A at x=0m and beam B at x=1.1m. A 68kg diver stands at the other side of the board. A. Find force on support A. B. Find force on support B. Homework Equations Net force = 0 Net...
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