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.
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
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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.
In the Aschcroft & Mermin solid state book there is a curve to compare F.D and M.B distribution. I can't understand the concept of M.B curve; what does mean exactlly when x =0? It means the probability of zero energy for particles is most or ...?
G'day.
I have a problem with my statics work, i understand its probably quite simple but I am having trouble in my understanding.
Essentially problems make more sense to me by using the component method, although in saying that i understand this problem would be quite a lot more simple were i to...
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The first part is easy, we have 2T= Mg
T= 0.5 Mg
Now for the second part where I'm having trouble understanding Morin's solution:
I take the normal force on a small circle arc to be N, we know that the y component of the normal force must be balance with Mg for the whole disk, therefore
Ny =...
Hello,
I have designed a gearbox that bolts on to a fixed engine and fixed pump. It is completely supported by them. The total mass of the gearbox and the components attaching it to the engine and pump is 7.7kg. Its centre of mass is 0.167m along the x-axis and 0.09m along the z-axis from the...
In Sommerfeld’s Lectures on Theoretical Physics, Vol II, Chapter 2, Section 6, Page 43 we derive an expression for the equilibrium of liquids as $$ grad ~p = \mathbf F$$ Where ##p## is the pressure and ##F## is the exertnal force. Then he writes,
[ The equation above ]includes a very remarkable...
Firstly I only consider one of the wheels. This wheel consists of a big wheel (black) with mass M and radius R and inside it a circular region with a negative mass (-m) and radius R/2. (I assume they have same mass density but with opposite signs. I do this because I don't know where the center...