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.
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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$$
where ##F_L## is the magnitude of the force exerted on the bar by the...
The diagonal component of the boom's weight is ##R=w\cos\frac{\pi}{6}=\frac{\sqrt 3}{2}w##, and, considering ##R## as a "reaction", we have ##R_x=R\cos\frac{\pi}{3}=\frac{\sqrt 3}{4}w## and ##R_y=R\sin\frac{\pi}{3}=\frac 34w##.
I will also have...
I don't understand the question; they're telling me that the fulcrum is just under the center of gravity of the bar, but that I also need to find its position.
In any case, I suppose that the fulcrum's position is ##x##.
Let the weight at the left end be ##w_1##, at the right end be ##w_2##...
I take the left end as reference for torques:
$$\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...
(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.
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.
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:
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...
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...
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...
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...
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
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...
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...
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.
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...
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...
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...
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)##...
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...
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...
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...
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
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...
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...
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...
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...
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.
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...
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
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...
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...