Statics is the branch of mechanics that is concerned with the analysis of (force and torque, or "moment") acting on physical systems that do not experience an acceleration (a=0), but rather, are in static equilibrium with their environment. The application of Newton's second law to a system gives:
F
=
m
a
.
{\displaystyle {\textbf {F}}=m{\textbf {a}}\,.}
Where bold font indicates a vector that has magnitude and direction.
F
{\displaystyle {\textbf {F}}}
is the total of the forces acting on the system,
m
{\displaystyle m}
is the mass of the system and
a
{\displaystyle {\textbf {a}}}
is the acceleration of the system. The summation of forces will give the direction and the magnitude of the acceleration and will be inversely proportional to the mass. The assumption of static equilibrium of
a
{\displaystyle {\textbf {a}}}
= 0 leads to:
F
=
0
.
{\displaystyle {\textbf {F}}=0\,.}
The summation of forces, one of which might be unknown, allows that unknown to be found. So when in static equilibrium, the acceleration of the system is zero and the system is either at rest, or its center of mass moves at constant velocity. Likewise the application of the assumption of zero acceleration to the summation of moments acting on the system leads to:
M
=
I
α
=
0
.
{\displaystyle {\textbf {M}}=I\alpha =0\,.}
Here,
M
{\displaystyle {\textbf {M}}}
is the summation of all moments acting on the system,
I
{\displaystyle I}
is the moment of inertia of the mass and
α
{\displaystyle \alpha }
= 0 the angular acceleration of the system, which when assumed to be zero leads to:
M
=
0
.
{\displaystyle {\textbf {M}}=0\,.}
The summation of moments, one of which might be unknown, allows that unknown to be found.
These two equations together, can be applied to solve for as many as two loads (forces and moments) acting on the system.
From Newton's first law, this implies that the net force and net torque on every part of the system is zero. The net forces equaling zero is known as the first condition for equilibrium, and the net torque equaling zero is known as the second condition for equilibrium. See statically indeterminate.
A physicist who does research in statics is called a statician.
Hi, I'm currently looking to improve my understanding (mostly conceptually) on Dynamics (such as colllisions)and Statics of Bodies that aren't perfectly rigid, while considering mass, density, thickness, shape , kinetic energy, momentum and material stiffness/strength/toughness.
In the picture you can see what I'm talking about. This is a simple problem to do if you can use moments, but alas my education system seems to have something against those.
##AB## is the uniform rod/ladder, G is its centre of mass, BE is the horizontal x axis, AD is the wall, BD is the smooth...
I'm having problem in drawing the distributed load (weight per foot) for the inclined beam as it shows.
should it be rectangular? if so shouldn't the distributed load be vertical down as the resultant weight at the centroid (W)
please help me understand how to draw the free body diagram for this...
I would like to understand the topic discussed in this thread more. https://www.physicsforums.com/threads/tipping-over-a-table-how-much-overhang.1012197/post-6598527
As I understand it, I can find the load required to tip the table can be calculated by this formula. L<W a/x
This is illustrated...
The problem is from Hibeller's book, Mechanics: Statics and attached below is the picture of the problem:
My question about this problem is about the FBD of the reactions. Here is how I drew it:
But when I tried checking the solution for the problem, they have this as their FBD:
My...
The figure and formulas is shown above. My strategy of cutting the areas/shapes is shown below:
Area 1 = Area of Triangle
Area 2 = Area of the square - Area of the quarter circle
Area 3 = Area of the larger quarter circle - Area of the smaller quarter circle
Computing for the areas, I got...
The figure is shown below:
Here is my FBD for the figure with assign +x and +y directions
I started off by summing up the forces in the x-direction:
Next is the summing up of the forces in the y-direction:
After this, I solved for the moment at point A: assuming that counter-clockwise is +...
If it was about beams, I would usually do clockwise and anti-clockwise first, taking moments on A/B, clockwise forces times distance = anti-clockwise forces times distance, since its in equilibrium.
What I did was split the problem into two seperate summations based on x & y coordinates:
Tcos(25) - Tcos(55) - Px = 0
Tsin(25+Tsin(55) +Py - Q = 0,
Where Q = 1860
I initially got an answer of 2391N, but it keeps marking me wrong for said answer.
This is the free body diagram, (the previous...
I am new to statistics and recently learned about ISO guidelines for Accuracy & Precision and Uncertainty & Error. But there are some graphs of probability distribution I found on internet which I am not able to grasp.
image Source
Q. In this graph(above) if...
TL;DR Summary: I am taking the Statics course next semester (in a month) and it seems very difficult as people told me, I couldn't find someone who did great in it to seek advice. so if you did great in statics please provide me with tips and advices, thanks in advance.
By the way I am...
In some problems, there is a dependency between the reactions at the supports and the displacements due to the deformations. In such cases, typical tools from statics and resistance of materials cannot be used. I believe that is because one of the main assumptions is that only very small...
So for this problem I have already solved for the Y forces: Dy = 171.43 N, Cy = 228.57 N, and By = -428.57 N. For the X forces I split up the frame and took the moment of DE.
Me = 1.5(300) + 3.5(300) - 5(Dx), Dx = 300
For CD Dx = -Cx fo I got Cx = 300, as when you forces are two member Dx =...
My textbook introduces this angle concept really early on and I still don't understand it. It just shows that a normal to a line and some other random angle shown is the same. I don't see any transversal angles or anything. Where did they get the secondary line to form theta for the normal line?
Hello, I am studying probability and came across this theorem, it's the law of total probability with extra conditioning, I tried to work out a proof but couldn't ,does anyone know the proof for this :
thanks!
Hi!
For this fluid statics problem,
One of the answers is:
However, why did they assume the pressure at the top was zero? I thought the pressure at the top would be 1 atm?
So tried to take atmospheric pressure into account putting 1 atm at the top,
Do you please know how to get P_0A/2 so...
Figure:
My attempt at a solution:
For the calculation of ##F_{DB}## we consider the equilibrium in the whole machine.
$$\left. \begin{array}{r}
h\rightarrow h=6\cdot \sin \theta +3=6,44\, \textrm{ft} \\
d\rightarrow d=6\cos \theta -1,5=3,41\, \textrm{ft}
\end{array}\right\} \,\, \alpha =\arctan...
Statement : Here is the statement from the text that I paste to the right. Diagram : Does anyone have a diagram (image) as to how does the situation look?
Normal Reaction : When a rod rests against a smooth wall, we know that the direction of the reaction is normal to the wall. I understand...
Attempting to draw the FBD for this problem but was wondering what to do about the cable, especially when I determine the internal loadings at E. At C, do I only draw one force arrow (CB), or draw both on the left and right side?
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...
I drew out a small diagram to illustrate my attempt. I interpreted 280 degrees from the vertical as 10 degrees from the horizontal. Using trig I solved for the h, which I get an obviously incorrect answer. The actual answer in the book is 2.3m,
hello, i have a question in this topic of frames in mechanic engineering, if i have a problem with 3 or 4 members that connected and a moment of couple is applied at specific frame,a moment of couple is general and is applied at any given point of the body. so when i dismember the frame and draw...
I'm designing a table and need to know how much overhang I can have. Assuming the table is completely rigid, is symmetric, and has weight W acting on the CG, how much overhang x can I have? For instance, I know that zero overhang could have L = ∞ (if completely rigid) as the load wouldn't be...
I am trying to figure out why the two approaches do not match in solving this statics problem. This involves the image below.
The first thing to do is to find the reactions at A and E. This is easy enough, with the results being that E only has a vertical component equal to 400 N and A has Ax...
Part of a project I am working on (part #3…see description below) is asking us to find the internal loads (shear and moment) and draw the corresponding shear/moment diagrams of the control arm shown below. It’s a little tricky to me, because all of the members associated with these type of...
So, for the link "AB"...they didn't directly list the pin reactions from pin "A" here, but I want to be sure that I understand what those reactions are. So, from what I see in this image, the member is pushing at the pin "A" (red arrow) because otherwise, the bucket would want to rotate...
I can't seem to find the arclength between A and B.
I tried using L = integral (0.6 to 0.4) of sqrt (1+ (dz/dx)^2) to no avail.
Would it be roughly similar to 400 km (the length from A to B) since the change in elevation could be considered negligible? Furthermore, how might I go about...
This isn’t a HW problem per say, but it’s an example shown in my statics textbook that is used to try an explain that you need to add a couple moment to move a force to a point not on the line of action, and I’m just not seeing how the direction of the couple moment is correct. See the image...
Can someone please tell me why I get two different result of the value of Cy (please see attached image for more detail)?
Am I doing a mistake?
If yes, what is my mistake?
I need help with the following question please.
I understand that the person carries on in straight line while is jumping. This is because there is no horizontal force acting on him so based on Newton's first law of motion he continues with the previous speed.
I know he should land on A or B...
Do you guys have techniques in solving for the Force in hydraulic IJ? I've been stucked for a while now and I can't seem to find the answer.The question says the answer should be = 11, 051.9516 N (T).
My two questions:
The author claims that ##T_1=T_2## and ##\alpha = \beta##, and this is supposed to be clear the force triangle. Why is this so?
Is it possible to use calculus of variation to find the lowest point C? That is, by maximizing the triangle ABC (Area of ABC = ##\frac{1}{2}(line...
So basically, I got close to a zero for my solution to this problem. I'm guessing based on the posted solutions that I wasn't able to get partial credit
due to the fact that my coordinate axis was aligned with the slender bar and not in its usual perpendicular position.
This resulted in...
I already have a degree in physics. Is there a book that describes the applications for a person who knows the underlying physics? Poking around, I can only found 1000 page tomes that are also teaching the underlying physics.
In the back of my head I am thinking about
1) Systems of wheels...
I am installing a garden gate at the back of my house.
The length (L) of the gate is 1.7m and the mass is 62.6kg, there are 2 hinges positioned 1.3m apart.
The gate has an inherent sag, such that, the bottom corner on the unhinged side is 5cm lower than the corner on the hinged side.
What...
I have problem on this question on how to draw free body diagram. Can you please show me on how to draw free body diagram on this question ?
The calculation part I think I do not have a problem with it.
Thank you in advance ! I am really struggle with this question.
Problem illustration:
The possible answers are:
I don't understand why it says Mc if it is asking for the moment at A, not C. But maybe I am getting something wrong.
So with the formulas I posted above, I have this:
Wich The Program (Software) Using To Draw Statics And Dynamics Mechanichal Same This 100% When Create This below Which Program Using ?
And set Dimensions
Thanks For All
I have to apologize if the diagram is awful: I drew it for the sake of asking... I am analyzing the rope that is hanging the pulleys. From the diagram, the pulley at the left (let's call it L), has two objects with mass M at both ends. The pulley at the right (let's call it R), has an object...
A force P is exerted on two articulated rods that are connected to two small blocks A and B. Both blocks have the same weight G. The magnitude of the force P = 1.26 G. The static friction coefficient between the blocks and the ground is 0.3. The mass of the rods may be neglected.
It can be...
I get the correct answer if I use the COM as the axis of rotation for torque calculations. Shouldn't I be able to use any point as the axis of rotation for torque calculations, e.g. where the front wheels make contact with the ground?
For this problem (see image), I get the correct answer for the normal force at point E if I:
1) divide the frame into members AB and CB,
2) solve for the x and y components of the reaction force at point B,
3) make a free body diagram with the cut at point E forming member EB and setting the sum...
I approached this question with a free body diagram.
my Verticle length of BA is y-2
AC= 15-AB
Horizontal length of AC= a; Horizontal length of BA=10-a
I have too many unknowns in this problem and I don't know any directions(angle).
I know that I should start at the weight and try to resolve the...
I was reading about Nikola Tesla in his autobiography where he constantly talks about "static". Do you know what that is? He also talks about solving statics.
Here's a quote from the book, "Its introduction for telegraphic, telephonic and similar uses will automatically cut out the statics and...
so i was wondering what assumptions needed to make this solvable and ' support at both thrust collars can totally support the moments of 400 Nm before they slip' means which axis of moment
could not understand why it is partial constraints. Also, I don't understand how link works. Below here is what I am thinking i think it is totally wrong can someone explain what's wrong with my idea here.