Equilibrium Definition and 1000 Threads

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...

The solution says that when the effusion rate ratio is multiplied by the equilibrium mole ratio of H2 to CH3OH, the effused mixture will have 33.0 times as much H2 as CH3OH. I don't understand why. I just set the equilibrium mole ratio of H2 to CH3OH as equal to 33.0 times, Why is this...

6.2(9.8)=60.8 (incorrect) 46.2cos40.4= 35.2 (incorrect)

Summary:: I am doing my structural analysis homework and I can't seem to identify between pin joint and roller. Please take a look at the following exercises and help me understand: 1) In exercise 6.87, the joint at C is a pin joint whereas in exercise 5.63 the joints at the casters are...

Could I please ask for help regarding the following question: D, E and F are the midpoints of the sides QR, RP and PQ respectively of triangle PQR whose circumcenter is O. Forces of magnitude kQR, kRP and kPQ act at O in directions ##\overrightarrow{OD}##, ##\overrightarrow{OE}## and...

Components of gravitational force on M: normal force:M*g*cos(90-α)M*g*sin(α) Downhill force: M*g*sin(90-α)=M*g*cos(α) On m: normal force: m*g*cos(α) Downhill force: m*g*sin(α)

I would like to write a program to calculate the equilibrium concentrations of 10 or more chemical species at any axial location along a quasi 1D isentropic methane-liquid oxygen rocket nozzle. Is anyone aware of any good textbooks that cover this topic in depth, specifically dealing with large...

So I already know the normal force is 268.08 from a previous part of the question. I thought that the friction force must be less or equal to uFN for an object to stay in static equilibrium. So Tcos(angle)=uFN T=uFN/cos(angle)=116.49 But the answer is suppose to be 133.37.

I believe it is just an arithmetic medium, but I am not sure. Could someone explain to me?

See attached for work. I did notice that making the torque from the force of gravity negative I got the right answer, but don't understand what I did wrong (its positive in my solution). i hat cross negative k hat is a positive number after all.

See attached file. Answer is supposed to be 61.25 N, I get 20.09 N.

Hi everyone, I need help with this exercise becouse I don't know how to calculate the equilibrium points of a circuit. The original exersice is the following: Assume that the open loop dynamic response of the OVA-opamp gets captured by Fig. 1(a) and consider the circuit of Fig. 1(b). Consider...

Hi, I’m wondering if someone can help me understand this question. I can find a resultant force/vector when given an initial angle but I’m stuck here when the only information is the two magnitudes. I think I’m solving for the unknowns but a little lost on how or what equation I should be using...

The answer is 280N but I don't have any idea hoe to get to the anseer. Atleast a hint would help.

Help, this one is completely different, the weird pulley is making it hard for me and I don't even know what to do with it and where to start. The answer is 185N but I want to know how.

So for the first one on the left is it T= 2g*20=40Nm ? Our professor said it is clockwise I just don't understand how she gets that conclusion.

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

I seem completely lost at this. I barely know where to begin. I know that the forces will sum to 0 but the vectoral nature of the question is really confusing me. Best I have is that the distance between e and q2 has to be sqrt(2) times the distance between e and q1. I don't know where to go...

The principal equilibrium in a solution of NaHCO3 is HCO3-(aq) + HCO3-(aq) <-> H2CO3(aq) + CO32-(aq) Calculate the value of the equilibrium constant for this reaction. My solution: This overall reaction is the same as the sum of the following reactions: HCO3-(aq) <-> H2CO3(aq) + OH-(aq)...

I tried to solve it via equilibrium equations and I got 92N for block A

t is Torque I is the inertia moment P is the power c is the constant light speed r is the spot distance to the fiber p is the torsional constant theta is what we want In the equilibrium $$t = 0$$ $$ F\Delta T = \frac{E}{c} = \frac{P\Delta T}{c} => *F* = \frac{P}{c} (1) $$ This will be the...

Hello everyone, For this equation, I have found Ay as 0.677kN by using Ma = 1.5kN(7m)-Ay(15.5m). To find Cy, would I be using the sum of forces to find the answer? For example Fy = Ay - F2 - F1sin55 + Cy = 0 This would then get Cy answer as 2.05kN

The boom is supported by a ball-and-socket joint at AA and a guy wire at BB Hey guys, I am stuck with this question in find the Tension in B and the moments around A. I have done plenty of 2d Tension questions but not a 3D one.

I know what K does, what can change K, and I know about the equilibrium equation. I don't know how to use that to answer this problem. I'm not given any chemical reactions or their K values. How should I start this problem?

When I use the concept of activity to express the equilibrium constant expression, for either equilibrium pressures or concentrations, the units cancel and the value of K has no units (which is how K is customarily reported). But because of the difference in reference states (the reference...

The following are my works for the problems: I put squares on my final answers! Thank you!

Hi all Knowing that ##kp## is: ##k_p=\frac{pO_2.(pNO)^2}{(pNO_2)^2}## And knowing these relationships between the partial pressures, I obtained: At 700 K: ##pNO = 0.872.pNO2## ##k_p=pO_2.(0.872)^2## At 800 K: ##pNO = 2.5.pNO2## ##k_p=pO_2.(2.5)^2## Furthermore it is known that ##pNO + pNO +...

Suppose you have a container of water at a given temperature T (say normal room temperature) with a vacuum above it. Presumably water will evaporate until there is sufficient vapor that the pressure of it above the water is the SVP for that temperature. Now suppose that there is air above the...

Summary:: I need some help with moment when using equations of equilibrium Edit: Sorry I forgot to say what the question was! The question was to solve the value of R based on the diagram below alone. I was solving the question below and I tried to resolve R into a force that is perpendicular...

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...

Suppose you have a non-uniformly doped piece of semiconductor (without an applied bias) such that the acceptor dopant concentration Na(x) decreases from left to right (as x increases). In this case, the equilibrium hole distribution p(x) will not be uniform since then there would be a net drift...

$$Q_{(\alpha, \beta)} = \sum_{N=0}^{\infty} e^{\alpha N} Z_{N}(\alpha, \beta) \hspace{1cm} (3.127)$$ Where ##Q## is the grand partition function, ##Z_N## is the canonical partition function and: $$\beta = \frac{1}{kT} \hspace{1cm} \alpha = \frac{\mu}{kT} \hspace{1cm} (3.128)$$ In the case of an...

"The displacements of the blocks from equilibrium are both measured to the right. Block 1 has a mass of 15 grams and block 2 a mass of 10 grams. The spring constants of the springs are shown in dynes/cm." I don't know if i understood very well the notation, but i interpreted as F(t) acting only...

It is desired to remove the molecular hydrogen present in a flask. What will be better to introduce, ##Cl_2## or ##Br_2##? Why? ##2 HCl <-> H_2 + Cl_2## (1) ##k = 3,2.10^{-14}## ##H_2 + Br_2 <->2 HBr## (2) ##k = 2.10^9## I thought about turning equation (1) to make the...

Please help to see whether I did correct or wrong, thank you.

I am not sure whether I can prove like this, I am trying to explain it with the angle .

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...

According to the book "Principles of Statistical Mechanics" by Amnon Katz, page 123, ##\alpha## must be such that ##\exp ( -\alpha N ) ## can be expanded in powers of ##\alpha## with only the first order term kept. Is this the necessary and sufficient condition for small deviations from...

Not really sure how to start this one.

When a ball is thrown upward it becomes at rest at maximum height, at this it is not in equilibrium although it is at rest. It is not at equilibrium because force of gravity is acting on it? Still I cannot find good explanation from exam point of view.I also cannot find the figure/diagram.

I know the acceleration of the rock is equal to g, but why. If we neglect air resistance, what is actually making the rock fall? Wouldn't it be that g overcomes the acceleration of the y plane at some point so the rock starts coming down or in this case accelerate more by throwing below 0 degrees?

So I have always been thinking that equilibrium means that an object is not moving or having constant acceleration. On a webside they said: " A rigid body is in equilibrium when it is not undergoing a change in rotational or translational motion. " To me it sounds like the object then must not...

So here are two problems I have been working with lately: I have solved both, so I don't need the help to find the answers. The thing that confusses me is which object one should choose to apply the equations above. When it comes to the first problem, we apply the equations to the pole, but...

So I have this problem The soultion to the problem gives me this drawing But I don't understand what ##F_h## and ##F_v## is

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...

Abs Pressure: Gauge press: 1 bar G = 100,000 Pa = 0.987 atm 0.1 bar G = 0.0987 atm Atm press = 101.3 kPa = 1 atm Hydrostatic press: average CO2 occurs 2.5m up the vessel (9.81 ms-2)(1010kgm-3)(5/2) = 24,770.25 Pa 1 Pa = 9.869x10^-6 atm 24,770.25 Pa = 0.2445 atm Abs press= 0.0987 atm + 1 atm...

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...