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Equilibrium

A body is said to be in equilibrium when the net forces acting on the body is balanced, net torque acting along the body is balanced and the temperature of the body is the same as that of the system it is a part of or its temperature it the same as the bodies in which it is in contact with. When a system is at equilibrium, nothing is changing. The sum of the forces and the sum or the torques is equal to zero.

∑F=0

∑τ= 0

Equilibrium is a state in which opposing forces or influences are balanced. There are many different types of equilibrium in physics. These include hydrostatic equilibrium, hyperbolic equilibrium point, mechanical equilibrium, radiative equilibrium, secular equilibrium and thermal equilibrium. Each specific type of equilibrium a different approach, however, the basic principle remains the same; all forces are balanced. 

Rotating frame of reference

A coin stands upright at an arbitrary point on a rotating turntable, and spins (without slipping) at the required angular speed to make its center remain motionless in the lab frame. In the frame of the turntable, the coin rolls around in a circle with the same frequency as that of the turntable. In the frame of the turntabl

Equilibrium Principle of Moments

Can you please explain me some more problems on principle of moments, balancing see saw and forces acting on a bridge. Would like to understand in such examples which forces are downward (CG)and upward.

Canonical Transformation

The motion of an object of mass m in two dimensions, in the presence of a gravitational field may be determined from the Lagrangian: (look at attached for better formula representation) L = 1/2m (x^2+y^2) - mgy Consider the transformation give by: x' = x + alpha + beta(t) y' = y Where alpha and beta are constants. For

Christoffel Symbols and Geodesic

In cylindrical coordinates (ds)^2=(dp)^2+p^2(d(thi))+(dz)^2. Find the non-zero Christoffel symbol and the equations of the geodesic for the two dimensional case of movement on the surface of the cylinder of radius p=R.

hamilton's equation

A system with one degree of freedom has a Hamiltonian see attached where A and B are certain functions of the coordinate q and p is the momentum conjugate to q. a) Find the velocity q(dot) b) Find the Lagrangian L(q q(dot)) (note variables)

Lagrangian of a Rotating Mass, Spring and Hanging Weight

The mass m1 moves on a smooth horizontal plane, m2 moves vertically under the force of gravity and the spring. Using polar coordinates r, theta for m1, l for m2 and taking b for the total length of the string plus the unstretched length of the spring, find: (diagram attached in file) a. the Langrangian of the system b. the equ

Small oscillations of rhombus figure

Four massless rods of length L are hinged together at their ends to form a rhombus. a particle of mass M is attached at each joint. the opposite corners of the rhombus are joined by springs, each with a spring constant k. In the equilibrium (square) configuration, the springs are unstretched. The motion is confined to a plane, a

Position probability distribution for a pendulum

Please help me with these problems. Thank you. Position probability distribution for a pendulum. Consider the classical motion of a pendulum bob which, for small amplitudes of oscillation, moves effectively as a harmonic oscillator along a horizontal axis according to the equation. x(t) = Asinwt The probability that the b

The Boiling Temperature of water as a function of pressure

At 100 degrees C, the specific volume of water and steam are 1.043 cm^3/g and 1673 cm^3/g, respectively. The latent heat of vaporization is 2257 J/g. a) Calculate dP/dT b) The pressure on the top of the mountain Everest is about 0.35 atm. Calculate the boiling temperature of water at this location.

Harmonic Frequencies and spring problems

1. If the second harmonic of a guitar string is at a frequency of 640 Hz, what is the frequency of the third harmonic? 2. A clarinet is an instrument which acts like an "open-closed" tube. Suppose you play a note which is the fundamental of the instrument (with all holes closed) which is at 415 Hz. What is the frequency of th

Mass attached to a vertical spring

A mass m is attached to a vertical spring (with a spring constant k). Any source of friction is neglected. The equation of motion of the mass is given by m(d^2x/dt^2) = mg - kx where g is the constant of gravitation and x refers to the vertical position of the mass. Solve this equation to find the function x(t), assumin

Calculate the normal force exerted

The flat circular disc rotates about a vertical axis through O with a constant angular velocity of 240rpm. Prior to rotation, each of the 0.5kg sliding blocks has the position x=25mm with no force in its attached spring. Each spring has a stiffness of 400N/m. Neglect any friction between the blocks and the slots, and neglect

Gas Pressure in A Cylinder

A 30cm diameter vertical cylinder is sealed at the top by a frictionless 17kg piston. The piston is 86cm above the bottom when the gas temperature is 308oC. The air above the piston is at 1.00 atm pressure. What is the gas pressure in the cylinder using 4 significant figures? p_o = __________________________________

Static Equilibrium Question

A 646 N window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 390 N and is 4.76 m long. Assume the window washer stands 1.03 m from the left end. What is the tension in the rope on the right? Answer in units of N

Equilibrium of Moments Problem

A uniform meter stick is supported by a knife edge at the 50-cm mark. It has masses of 0.40 kg at the 10 cm mark and a 0.60 kg mass at the 80 cm mark. At what mark should a third mass of 0.30 kg be to keep the stick balanced?

Forces and Moments Effects

Problem: Problem: a. what is the force acting through (F) required to hold the lever in static equilibrium? Indicate clearly the Force and resistance vectors due to the weight, the force moment arm and the resistance moment arm, as well as the axis. Note that the weight is 40 kg and gravity is g=9.81 m/s2. b. What would be

Charged Pendulum in an Electric Field

A small 6.3g plastic ball is suspended by a 28cm long string in a uniform electric field of 4400N/C in the +x direction. If the ball is in equilibrium when the string makes a 25.9 angle with the vertical, what is the net charge on the ball?

Mechanics - Static Equilibrium

A load of 100 kN is supported by a crane as shown in the figure attached. DAE is the cable which passes over a smooth pulley at A. Draw a free-body diagram of the pulley A and hence find the forces in the cable, the tie AC and the jib AB of the crane. Assume that the diameter of the pulley and the weight of the jib are both negl

Determining the Tensions Developed in Wires

Determine the tensions developed in wires CD, CB and BA and the angle theta required for equilibrium of the 25 lb cylinder E and the 0.2225 kN cylinder F. (1 lb = 4.4482 N). Please refer to the attached image for more information.

Mechanical physics: Fluid pressure and string tension

Please provide direction for the following questions: A) A 2.8-N force is applies to the plunger of a hypodermic needle. If the diameter of the plunger is 1.3 cm and that of the needle 0.20mm, (a) with what force does the fluid leave the needle? (b) What force on the plunger would be needed to push fluid into a vein where

Mechanics: Statics

(Please see the attachment for the figure) A uniform rod AB of length 2a and weight W is inclined at 30 degrees to the horizontal with its lower end A on a rough horizontal ground, the angle of friction being 30 degrees. The rod rests in contact with a smooth peg C (AC < AB). Calculate the height of the peg above the groun

Analysis of Motion of a Simple Pendulum

?What is the effective force constant for a simple pendulum of mass .6 kg and length 2.27 meters? If released from a position .1362 meters from equilibrium what will be its velocity when it is halfway to its equilibrium point, and what will be its velocity at equilibrium.

Harmonic Oscillator Problem

A simple harmonic oscillator is subjected to a net restoring force F = - 3000 N/m * x at displacement x from equilibrium. It is observed to undergo simple harmonic motion with a frequency of 1.3 cycles / second. What is its mass?

Pendulum velocity at equilbrium, period of motion

A pendulum is released from rest at a displacement of .31 meters from its equilibrium position. It is stopped abruptly and uniformly at its equilibrium position and it is observed that a loose bit of metal slides without resistance off the pendulum and falls to the floor .95 meters below. If the projectile started off with

Harmonic oscillators

If i had two spring coupled to one mass with each end of the springs fixed. |---spring---{mass}--spring----| neglecting friction and gravity, if the mass is displaced horizontally. would it oscillate forever? if not how can u get the maximum amplitude of oscillation for a given period of time before it

Physics

Please provide step-by-step solutions to the following problems: 1. Two different forces, acting on the same object, are measured. One force is 2.0031 N and the other force, in the same direction, is 3.12 N. These are the only forces acting on the object. Find the total force on the object using the correct number of signific

Physics: Equilibrium, balance point

Please view the attached file for the diagram. 1. A shop sign weighing 215 N is supported by a uniform 135-N beam shown in the figure below. Find the tension in the guy wire and the horizontal and the vertical forces exerted by the pin on the beam. 2. A beam balances 30.0 cm from one end. When a 0.75 kg mass is hung from

Hydraulic lift, Hollow spherical ball, Objects submerged in water

1. The small piston of a hydraulic lift has a cross-sectional area of 3.00 cm^2 and its large piston has a cross-sectional area of 200 cm^2. What force must be applied to the small piston for the lift to raise a load of 15.0 kN? (In service stations, this force is usually exerted by compressed air.) 2. Small piston of a hydra

Mechanics: Equilibrium of forces

A meter stick is pivoted at its 50 cm mark but does not balance due to nonuniformities in its material that cause the center of gravity to be displaced from its geometric center. However when weights of 150 and 200g are placed at the 10 cm and 75 cm marks respectively balance is obtained. The weights are then interchanged and ba