Equilibrium Definition and 1000 Threads

As shown in Figure Q1a, a frictionless, massless, piston, supported by two springs, A and B, is held by a pin in a vacuum inside a rigid-walled container. The properties of the springs are: spring constants kA = 3,859 and kB = 3,090 (in N/m), natural lengths LA0 = 0.03 and LB0 = 0.1 (in m). When...

As shown in Figure Q1a, a frictionless, massless, piston, supported by two springs, A and B, is held by a pin in a vacuum inside a rigid-walled container. The properties of the springs are: spring constants kA = 3,859 and kB = 3,090 (in N/m), natural lengths LA0 = 0.03 and LB0 = 0.1 (in m). When...

Homework Statement Here is the prompt/picture The hint given is a FBD of the bead is recommended to being this problem. Find the coordinates of B so that both the magnitude and orientation of the elastic cord force can be properly represented. Also, two mutually orthogonal normal force...

Homework Statement A gas is in an insulated box, which is divided into two portions by an insulated partition. There are n1 moles of the gas at temperature T1 in volume V1, and likewise n2 moles of the (same) gas at temperature T2 in volume V2. The partition is composed of two layers; one...

Homework Statement Suppose I've got a static mass on a downward plane. (For instance a car on a drive way). How would you set up this free body diagram? Homework Equations F = f1+f2...etc The Attempt at a Solution My preference is A, but I've seen it displayed in examples in my book as B...

Homework Statement Blocks A and B each weight 170 lb and rest on frictionless surfaces. They are connected to one another by cable AB. Determine the force P required to hold the blocks in the equilibrium position shown and the reactions between the blocks and surfaces. Hint given: This...

Homework Statement Two coplanar dipoles are oriented as shown below. If θ is fixed, what is the equilibrium angle θ' ? Homework Equations The torque exerted by dipole P on dipole P' is given by $$\vec{N'}=\vec{P'}\times\vec{E}$$ where vector E is the electric field. The Attempt at a...

Homework Statement A 10 000-N shark is supported by a rope attached to a 4.00-m rod that can pivot at the base. Calculate the tension in the cable between the rod and the wall, assuming the cable is holding the system in the position shown in Figure P12.49. Homework EquationsThe Attempt at...

Homework Statement Problem 6.2 from Magnetic Resonance Imaging: Physical Principles and Sequence Design. Show that M_o \approx \rho_o \frac{s(s+1)\gamma^2\hbar^2}{3kT}B_o Homework Equations M_o = \rho_o \gamma \hbar \frac{\sum m_s e^{m_s(\hbar w_o / kT)}}{\sum e^{m_s(\hbar w_o / kT)}} ...

Homework Statement The cords ABC and BD can each support a maximum load of 100 lb. Determine the weight of the crate, and the angle θ for equilibrium. Homework Equations ∑F= 0 ∑Fx=0 ΣFy=0 Setting derivative of an expression to zero To find critical point Second derivative test for determining...

Homework Statement A 1 200-N uniform boom at 65 degrees to the vertical is supported by a cable at an angle of 25 degrees to the horizontal . The boom is pivoted at the bottom, and an object of weight = 2 000 N hangs from its top. Find the tension in the support cable Homework EquationsThe...

Homework Statement SO3 decomposes on heating: 2SO2(g) 2SO2(g) + O2(g) A sample of pure SO3 was heated to a high temperature T. At equilibrium, the mole ratio of SO2 to SO3 was 0.152 and the total pressure was 2.73 atm. If the piston was pushed into cut the volume in half what is the new...

I know in case of unstable equilibrium of dipoles when dipole makes zero angle with electric field intensity ,But how we decide that this is unstable equilibrium I know in case of unstable equilibrium dipole returns to it's place after the small displacement ,I want to know why or how?why/how...

Homework Statement Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed (Fig. P12.19). Usually, the drawbridge is lowered to a horizontal position so that the end of the bridge rests on the stone ledge. Unfortunately, Lost-a-Lot’s squire didn’t lower the drawbridge far...

If H2A2+ is being titrated with NaOH, a buffer forms. The processes taking place are equilibrium between H2A2+ and HA+ ions, autoprotolysis of water and reaction of OH- ions with H2A2+ ions. As NaOH is added, the concentration of acid tends to decrease but because of the equilibrium ##H_2A^{2+}...

Homework Statement An amino acid H2N-CHR-COOH e its as a dipolar ion: +H3N-CHR-COO-. In strongly acidic medium, it takes H+ to form conjugate acid +H3N-CHR-COOH 50ml solution of conjugate acid required 30ml of 0.1M NaOH to completely convert into dipolar ion. The pH of solution during titration...

My teacher was teaching me salt hydrolysis today and I understood everything up to hydrolysis of salt of weak acid and weak base. Then he introduced amphiprotic anion in salt. He took NaHCO3 This is what he wrote: HCO3-+H2O ##\leftrightarrows## H2CO3+OH- H2CO3##\leftrightarrows##H++HCO3-...

1. Homework Statement Find forces P,F,and THomework Equations Fx = 0 Fy = 0 The Attempt at a Solution So far I only got force T from getting the moment from point b. Don't know how-to start getting force P and F since they're both at the same point. Any help will be much obliged thank you [/B]

I'm doing a lab where we use three strings connected to a ring, with each string attached to separate spring scales. What would be sources of error in this? And how does friction affect my results?

I need to find tensions in suspensions wires on the picture: I wrote 4 equilibrium equations for moments in A, B, C, D and equilibrium about y-axis, but i got matrix with rank two. \begin{pmatrix} 3 & 2 & 1 & 0 \\ 0 & 1 & 2 & 3 \\ -1 & 0 & 1 & 2 \\ -2 & -1 & 0 & 1 \\ 1 & 1 &...

Homework Statement The formation of cadmium complexes with Br- exhibits successive equilibrium constants such that log(k1)=1.56, log(k2)=0.54, log(k3)=0.05, log(k4)=0.37. Explain why k4 is greater than k3 Homework Equations $$K=e^{\frac{-\Delta H}{RT}}\cdot e^{\frac{\Delta S}{R}}$$ The...

If inert gases are added at constant volume to an equilibrium mixture, the total pressure increases. But the mole fraction of the gaseous reactants or products decrease. Partial pressure ##p=x\cdot P## where P is total pressure and ##x## is mole fraction. How can you say that ##p## remains...

Let's say I have a mass attached to an oscillating spring on a friction less horizontal surface. Why is it that the speed of the mass is greatest at equilibrium? I would have thought it would be greatest just before reaching the amplitudes due to maximum kinetic energy?

Hello everyone! Applying the Iterated Elimination of Strictly Dominated Strategies (IESDS) to a game resulted with the solution of the Nash Equilibrium. Actually that specific "quadrant" of the matrix is the: * Pareto optimal * Nash Equilibrium * Dominant strategies (through IESDS). This is...

Homework Statement 2. Homework Equations Net Force = 0 Net Torque = 0 The Attempt at a Solution I know how to deal with these problems. My question is: What the word 'minimum' means here? A zero normal force over the second support point?

Hi. Let's say we have two separate systems (containing gases), each with their own temperature, pressure and volume. Then these systems are brought together, with no walls in between. Of course, one might consider they are now technically the same system, but the distribution of pressure and...

Homework Statement Homework Equations principle of moments The Attempt at a Solution Okay so when resolving the forces horizontally and vertically, I get RA= T cosθ for horizontal component and RB= W + T sinθ for vertical component. To get my T, I chose to take moments about B, though I'm...

Homework Statement A uniform sphere of radius R is supported by a rope attached to a vertical wall,as shown in the figure. The point where the rope is attached to the sphere is located so a continuation of the tope would intersect a horizontal line through the sphere’s centre a distance R/2...

Homework Statement Homework Equations Net Force = 0 Net Torque = 0 3. The Attempt at a Solution At the support point , is there a horizontal force component?

Homework Statement A woman pedals her bicycle up a 8-percent grade on a slippery road at a steady speed. The woman and bicycle have a combined mass of 76 kg with mass center at G. If the rear wheel is on the verge of slipping, determine the coefficient of friction μs between the rear tire and...

Homework Statement The handheld press is useful for such tasks as squeezing rivets or punching holes. What force P is applied to the sheet metal at E for the 64-N forces applied to the handles? Homework EquationsThe Attempt at a Solution Not sure how to get this one started, i initially took...

Homework Statement Homework Equations sum of forces equal to zero. The Attempt at a Solution

Homework Statement Calculate the forces in members BC, BE, and EF. Solve for each force from an equilibrium equation which contains that force as the only unknown. The forces are positive if in tension, negative if in compression. Homework Equations Sum of forces and moments equal zero. The...

Homework Statement A 30 kg neon sign is suspended by two cables, as shown. Three neighbourhood cats (5.0 kg each) find the sign a comfortable place. Calculate the tension in each cable when the cats are in the positions shown. Ft1 = tension in left cable Ft2 = tension in right cable...

Homework Statement Homework Equations ΣF=0 ΣM=0 The Attempt at a Solution I think i correctly identified two 2 force members at A and B. But would the system be a 3 force member? If it is i don't quite know how to solve for the missing angles. Is the problem asking for the sum of the...

Homework Statement The smooth homogeneous sphere rests in the 132° groove and bears against the end plate, which is normal to the direction of the groove. Determine the angle θ, measured from the horizontal, for which the reaction on each side of the groove equals the force supported by the end...

I was receiving help for the following problem... The 2.0 kg wood box in the figureslides down a vertical wood wall while you push on it at a 45 ∘ angle. The coefficient of kinetic friction of wood on wood is μk = 0.200. What magnitude of force should you apply to cause the box to slide down at...

Homework Statement The vertical and horizontal poles at the traffic-light assembly are erected first. Determine the additional force and moment reactions at the base O caused by the addition of the three 100-lb traffic signals B, C, and D. Report your answers as a force magnitude and a moment...

Homework Statement Determine the minimum cylinder mass m1 required to cause loss of contact at A. Homework Equations ΣF=0, ΣM=0 The Attempt at a Solution Im not sure where to go with this one. the solution would be in terms of mass(m)

Take for example a canonical ensemble, to use the derived distributions and probabilities, the considered system has to be in thermal equilibrium with the heat bath. Where in the derivation of the probabilities and distributions do we usually assume this? There is a point that I can identify...

Homework Statement What weight WB will cause the system to be in equilibrium? Neglect all friction, and state any other assumptions. Homework Equations ΣF=0 The Attempt at a Solution I can't figure out what I am doing wrong with these pully problems, I tried putting in resultant forces at...

Homework Statement A former student of mechanics wishes to weigh himself but has access only to a scale A with capacity limited to 120 lbs and a small 20-lb spring dynamometer B. With the rig shown he discovers that when he exerts a pull on the rope so that B registers 19 lb, the scale A reads...

All particle species are in equilibrium at early times of the universe. But I didn't find any book that makes the difference of kinetic and chemical equilibrium clear. I have some of my own opinions and I hope to get your comments: (1) kinetic equilibrium means the distribution function obeys...

It is well known that the ideal gas law applies only to an ideal gas, one consisting of particles infinitesimal in size and exhibits no interactions between the particles. Considering an ideal gas, is the ideal gas law valid under non-equilibrium conditions? For example, does the ideal gas law...

I am trying to resolve for the forces in the attached diagram. In order for this object to be in rotational equilibrium, the torques of the normal force and the garvitational force would have to be equal. However, this would imply that normal force produced by the fulcrum would be far greater...

Hello, What "path" do objects take to reach thermal equilibrium? Does heat from a hot part sitting in room temperature air like to travel through the most thermally conductive portions? My thought is that it is similar to current in a circuit taking the path of least resistance (where the most...

Homework Statement A marble that is rolling without slipping approaches a hill at 8.5 m/s. How high vertically will the marble go under these circumstances: If the hill is rough enough to prevent any slipping? If the hill is perfectly smooth? Why does the marble rise to different heights when...

In Dodelson's "Introduction to Modern Cosmology" at p. 61 he introduces a non- equilibrium number density $$n_i = g_i e^{\mu_i/T} \int \frac{d^3p}{(2\pi)^3} e^{-E_i/T}$$ and an equilibrium number density $$n_i^{(0)} = g_i \int \frac{d^3p}{(2\pi)^3} e^{-E_i/T},$$ from which it follows that the...

four charges each equal -Q placed at the four edges of a square and a charge q is placed at the centre. if system is in equilibrium the value of q is, the answer is q = Q/4 * ( 1 + 2(√2) can anyone please solve this, would be great

Homework Statement The landing gear of an aircraft is composed of a main leg OA (with a weight including the wheel is 1000N to G) and two secondary links BC and 50cm long each CD. The DC link forms an angle θ of 30 degrees with the vertical. a) Add the rotational equilibrium equation with...