Equilibrium Definition and 1000 Threads

Hi guys. I have one problem from competition that I can't solve. I'll try to translate it. "rod of mass m and length l is lying on a ball of radius R in state of equilibrium. The rod makes angle θ with the horizontal. There is friction in every point of contact, and it's assumed that it is...

Homework Statement Determine the reaction at C. Homework Equations The Attempt at a Solution i know i have to take the moment about line DB and thus resulting in ƩM(DB)= λ(DA X F) + λ(DC X RC) =0 where λ = DB/ DB however the book solved it differently. they instead do...

Homework Statement Homework Equations The Attempt at a Solution The problem here is that it looks like having 2 equilibrium stages requires the same flow ratio as one equilibrium stage, according to my calculations. This seems strange to me, so I am wondering if I am wrong. I also am not sure...

Homework Statement If 5.00 mL of liquid carbon tetrachloride (CCl4, density = 1.587 g/mL) was injected into a sealed 5.00 L flask at 30.0°C, what volume (if any) of the CCl4 would remain as liquid after equilibrium is reached? (the vapor pressure of CCl4 at 30.0°C is 143.0 mmHg) Homework...

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Homework Statement An opening in a floor is covered by a 1×1.2-m sheet of plywood of mass 18 kg. The sheet is hinged at A and B and is maintained in a position slightly above the floor by a small block C. Determine the vertical component of the reaction (a) at A, (b) at B, (c) at C.Homework...

1. What is electrochemical equilibrium and what is chemical equilibrium? 2.What are the differences between the two above? 3. The difference between the two i think is electrochemical equilibrium is a state whereby the electrical charge in both compartments are equals. Wherease...

Homework Statement Suppose we take a 1 m long uniform bar and support it at the 22 cm mark. Hanging a 0.29 kg mass on the short end of the beam results in the system being in balance. Find the mass of the beam. Homework Equations \tau=F*r The Attempt at a Solution I set it up so that...

In reference to the graph at the bottom, my textbook has a statement '''..A process of vaporization or condensation at a constant temperature is illustrated by the lines G-H-I or I-H-G, respectively, in figure 16.3. Water would vaporize or condense at a constant temperature as the...

How is it that a solid can be in equilibrium below the triple point? Why can't liquid form? It seems odd to me that the molecules can go to a vapor, but not a liquid. It seems like the molecules can sublime more freely than they can melt. Can someone explain this from a molecular view point?

Homework Statement consider the following reaction: 2H2O(i) <-> 2H2(g) + O2(g) kc=7.3*10^-18 at 1000oC The initial concentration of water in a reaction vessel is 0.055 mol/L. What is the equilibrium concentration of H2(g) at 1000oC? Homework Equations h20 h2...

Why is the Fermi level a constant in thermal equilibrium? just like PN diode (P=material 1 ; N=material 2) the fermi levels are the same (Ef1=Ef2) in thermal equilibrium i confused that why there is no energy transfer so that can judge each energy E will obey rate from 1 to 2 ~...

Homework Statement http://imgur.com/yVOXkAT The two disks each have a mass of 18kg and are attached at their centers by an elastic cord that has a stiffness of k = 1.6kN/m . Determine the stretch of the cord when the system is in equilibrium and the angle θ of the cord. (Figure 1)...

Homework Statement An aqueous solution contains 0.84 g/L of an organic detergent. The osmotic pressure of this solution is 54.4 torr, at 25°C. What is the molar mass (in g/mol) of this detergent? Homework Equations ##pi=MRT## ##R=0.08206L*atm/(mol*K)## The Attempt at a Solution...

Can someone please help me with this one? I have found the equilibrium solutions,but I'm not sure what to do next. Consider dx/dt = x^3 - 4x Given a solution x(t) which satisfies the condition x(0) = 1, determine the limit(t -> infinity) of x(t). Thanks!

Homework Statement Find the equilibrium points of the system, determine their type and sketch the phase portrait. ##\frac{dx}{dt} = -3y + xy - 10, \frac{dy}{dt} = y^2 - x^2## The attempt at a solution Putting it together: ##\frac{dy}{dx} = \frac{y^2 - x^2}{-3y + xy - 10} \equiv...

Homework Statement H2+CO2=CO+H2O if 1.50 mol of each chemical species are placed in a 3.00l flask and allowed to achieve the equilibrium above, what mass of Co will be present at equilibrium? Homework Equations Keq= concentration of products each raised to the number of moles in...

Background: I've derived the equation of motion of the bead shown in the picture below using the Lagrangian \omega^2Rsin(\theta)+r\ddot{\theta}=0 The equilibrium points are at θ=0 and π. I'm now to show that only one of these points is stable. Homework Statement Show that only one of the...

Homework Statement Derive the differential equilibrium equation in the tangential direction \theta Homework Equations \sum F_\theta = 0 V = 1/2(2r + \Delta r)\Delta r \Delta \theta Small angle approximation: \cos(\frac{\Delta \theta}{2}) = 1 \sin(\frac{\Delta \theta}{2})...

What is the physical meaning of an object to be in stable equilibrium? Would it make sense to say that the object wants to stay at that position and any movement will cause the restoring force to move the object back to equilibrium?

Homework Statement in the attached picture are all the information needed to solve the problem. The bent rod of a negligible weight is supported by a ball and a socket joint at A and a single journal bearing at B. End of D of the rod rests against a friction-less vertical surface. find...

Homework Statement Trying to find angle u of bars (symmetrical) with ground at equilibrium under load. Two bars, negligible weight of length .4m Spring at midpoint k = 3kN/m, unstretched when bars at 45 deg F = 150N, 5 deg W of block 10kg Slope of ground under block 5 deg coef friction...

Hello, I am wondering conceptually why the maximum conversion of products is made at chemical equilibrium? I was thinking if you use le chatelier to push towards products, the conversion will be higher. Sorry if this sounds too vague, my prof's lecture was called "Equilibrium: The ultimate...

Homework Statement The gas stream from a sulfur burner is composed of 15-mol% SO2, 20-mol% O2, and 65-mol% N2. This gas stream at 1 bar and 480 C enters a catalytic converter, where the SO2 is further oxidized to SO3. Find the equilibrium conversion of SO2. The equilibrium constant for...

Homework Statement http://puu.sh/4NWw9.PNG question 2.65** Homework Equations I've tried using the law of sine and law of cosine method with the triangle for equilibrium and I've tried the 600^2 = Fx^2 + Fy^2 The Attempt at a Solution Here is what I did using the F^2 = Fx^2 + Fy^2...

Homework Statement I need to find the tension T, γ and β in part 2 of this question. The question is attached. Homework Equations First of all, the frame is a right angle triangle because (3L)^2 + (4L)^2 = (5L)^2 take torque about the point O we got 2LF + mg(4Lcosγ) = Mg(3Lsinγ) from...

A cylinder has rigid, adiabatic and impermeable external walls. It is provided with a mobile internal ideal partition wall, dividing it in two volumes (A and B). Each volume is filled with an ideal monoatomic gas. Initially, the volume, pressure and temperature of A and B are identical...

Hi! I have problem with uderstanding of Liouville equation. Which sais that if we have a Hamiltonian system (energy is conserved), then the the volume of phase space is conserved, or equivalently the probability density is conserved (the total derivative of probability density per time is...

This problem is trying to find out how much weight can be placed in the middle of a system before the weights on the outside go over the pulleys. A diagram of the problem can be found here...

Homework Statement For the reaction 2 NO_{2}(g) \leftrightarrow N_{2}O_{4}(g) ΔH°_{rxn} = -57.2 kJ and ΔS°_{rxn} = -175.8 J/K A 1 L container is initially filled with 1 atm of NO_{2} at 298 K. Find the equilibrium pressures of NO_{2} and N_{2}O_{4} at 298 K if a. volume is held...

So in a given amount of solution, the equilibrium constant is the product of the concentrations of the ionic species present, raised to the power of the stoichiometric coefficient. Wouldn't it make more sense if it was the sum of the concentrations though,since basically the net number of ions...

My problem here is that I keep trying to make substitutions for the normal forces and cannot come up with the number for P. I saw 4.92 and don't understand how there is a range of force for which equilibrium can be maintained. The force I came up with for P is way too big, the answer is 0.955 lb

Homework Statement What are the bifurcation values for the equation: dy/dt = y^3 +ay^2 Homework Equations The Attempt at a Solution Equilibrium solutions: y^3 + ay^2 = 0 ==> y^2 (y + a) = 0 ==> y = 0 (double root), or y = -a. a = 0 is the sole bifurcation point, since...

Hello, I want to make certain of my understanding of equilibrium solutions. Are equilibrium solutions the value(s) of y such that \frac{dy}{dt} = 0? So, suppose y = y0 is one of those solutions. Graphically, does this mean that one the horizontal line y = y0, little slope lines are too...

Homework Statement Sum of downward forces exerted at A and B is 41lbs by the leg, what is the weight attached? Homework Equations None, really... The Attempt at a Solution Tension (T) throughout the system must be constant and equal to the weight (W). I first assumed that the leg...

Problem Statement: As shown in the figure below, a uniform beam is supported by a cable at one end and the force of friction at the other end. The cable makes an angle of θ = 30°, the length of the beam is L = 1.50 m, the coefficient of static friction between the wall and the beam is μs =...

SOLVED Homework Statement A 23 kg child goes down a straight slide inclined 38∘ above horizontal. The child is acted on by his weight, the normal force from the slide, and kinetic friction. Find the magnitude of the normal force. Homework Equations cos(theta)=adjacent/hypotenuse The...

I have a problem. Lets say there were two pulleys put at equal height. You have a metal ring and attach three wires to it. At the end of each wire, have three weights of mass w. One weight hangs down, one weight goes over one pulley and the other over the other pulley. The system goes to...

Homework Statement A sample of Mo-101, initially pure at time zero, beta decays to Tc-101 which then beta decays to Ru-101 (stable). The half-lives of Mo-101 and Tc-101 are nearly the same and for this problem are assumed equal (14.4 min). After a decay period of one half-life how many atoms...

It seems to me that change in permeability should not shift the equilibrium of entering and exiting ions, except how fast equilibrium is reached. Consider this: two compartments are separated by a membrane. 1st compartment holds 1mM Na+ and 10mM K+ and 2nd one holds 10mM Na+ and 1mM K+. Let's...

So with this problem, I have been thinking about it. Since it is in equilibrium, I know the sum of forces and torques will be equal to zero. However, I'm not sure how the height, h, fits into this. I know the weights have a force and are a distance away from that fulcrum, d and 2d, so I could...

Homework Statement transverse loads are applied to the beam in the figure at A, C, and E, and a concentrated couple 3Pa is applied to the beam at E. Determine expressions for (a) the transverse shear force Vc and bending moment Mc at a section just to the left of the load at C, and (b) shear...

Hello, I am a first time poster and I need some help with a basic statics problem. I drew a free body diagram to help illustrate. An object with a mass 'M' is resting on a rotating disc that is spinning with constant velocity 'V'. The mass is continuously being pushed into a static wall due...

Law of cooling states that the rate of loss of heat by a body is directly proportional to the excess temperature of the body above that of its surroundings. The equation of determining temperature in time T(t)=Ta+(T0-Ta)*e^kt (Ta-ambient temperature, T0-initial temperature, k-heat transfer...

Homework Statement As indicated in the diagram, consider a rail inclined at an angle θ relative to the horizontal axis. A sphere (A) with a charge +q is fixed at the bottom of the rail. A second sphere (B) with a charge +2q and a mass (m) is free to move along the rail. The sphere (C)...

I have a complicated 3d nonlinear differential system which I solve algebraically using maple's solve command. I aim to find the equilibrium points of the system using MAPLE and then plot these equilibrium points as a function of the 3 parameters alpha,beta,gamma(a.k.a.bifurcation diagram). The...

Hi guys wondering if anyone can help me with this question that I am stuck on just not sure were to start.

Homework Statement Write the charge balance for a solution containing H(+), OH(-), Ca^(2+). HCO3(-). CO3^(2-) , Ca(HCO3)+, Ca(OH)+, K+, and CIO4(-).Homework Equations Also, I am having a trouble understanding the concepts of mass balance and charge balance. The Attempt at a Solution The...

If I want to calculate the number of moles ratio of reactants which, in a reversible reaction of equilibrium constant K, will give me a certain yield 'f', what is the mathematical definition of the yield in this case? For instance, in the reaction A + B ⇔ C + D, let's say we can denote extent...

Homework Statement A conductor (wire) is folded into a square loop with each side having a length of a. Total charge of Q is transferred onto the conductor. Describe the line charge density of the square loop in equilibrium. (If I am interpreting this correctly what is required is...