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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

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

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

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

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

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

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

Newtons law

Question 3 What force is required to give mass m = 40 kg acceleration a = 2 m/c2 ? Answer 60 N 80 N 40 N 20 N Question 4 What force is required to keep mass m = 20 kg moving with a constant speed along straight line? Answer 100 N 80 N 60 N

Thermodynamics of the Carnot Cycle

1. An ideal gas operates in a Carnot cycle so. that it produces a net positive work of 400joules per cycle. The maximum temperature during the cycle is 300 °C and the heat lost to a low temperature bath is 600 joules per cycle. a) What must be the temperature of the low temperature bath? b) What is the change in entropy of t

5 Multiple Choice Problems on Simple Harmonic Motion (SHM) and Hooke's Law

1. A 300-g mass at the end of a spring oscillates with an amplitude of 7.0 cm and a frequency of 1.80 Hz. (a) Find its maximum speed and maximum acceleration. (b) What is its speed when it is 3.0 cm from its equilibrium position? A) 8.96 m/s, 8.9 m/s2 (b) 0.45 m/s B) 79.2 m/s, 895 m/s2 (b) 0.512 m/s C) 0.79 m/s, 8

Elasticity: Stress, Strain and Compression

1. The figure below shows the forces acting on a tibia when a person stands on the ball of one foot in equilibrium. As shown, the force of the tibia on the ankle joint for a person (of weight 750 N) standing this way is 2800 N. The tibia has a length of 0.4 m, an average inner diameter of 1.3 cm, and an average outer diameter

Torque, Equilibrium and Harmonic Motion

1. A uniform meterstick pivoted at its center has a 100 g mass suspended at the 25 cm position. (a) At what position should a 75 g mass be suspended to put the system in equilibrium? (b) What mass would have to be suspended at the 90 cm position for the system to be in equilibrium? 2. An organic pipe that is closed at one end

Friction: Pushing a file cabinet

You are pushing a filing cabinet across a rough floor (mk = 0.33) in a straight line at a constant speed. Which of the following statements about the magnitudes of the forces acting on the filing cabinet are correct? 1. true false if you exerted twice the force, the cabinet would accelerate across the floor. 2. true false

Tension in Pulley Systems

A winch is used to raise a 500 kg crate at a constant velocity (a = 0 m/s2). Determine the tension in the support arm and the angle theta. Note: the cable that runs from the motor, over the pulley, and to the 500 kg crate is continuous. The picture consists of a motor that has a cable running up to a pulley (which has the 500

Buoyant Force, Projectile Range

A block of wood is held in water, totally immersed, by a string attached to a pont in the base of the tank. Calculation of range of jet stream flowing out of a tank. Please see the attachment.

A bead of mass m slides without friction on a ring

A bead of mass m slides without friction on a ring. The ring rotates with constant angular velocity w about a rotational axis that is aligned with a ring diameter, as shown in Figure 1. Find the Lagrange equations of motion, and the Hamiltonian for the bead. Is the Hamiltonian a constant of motion? Does it coincide with the ener

Three problems: Motion and equilibrium, Force, acceleration

16. The average speed of nitrogen molecule in air is about 6.70x10^2m/s, and its mass is 4.68x10^(-26) kg a) If it takes 3.00x10^-13s for a nitrogen molecule to hit a wall and rebound with the same speed but opposite direction, what is the average acceleration of the molecule during this time interval b)What average force do

Electrostatics: Equilibrium due to two point charges.

Need help with this problem: Consider a positive point charge. i) Give an example of how you might place two other point charges so that the net force on the initial charge is zero. ii) If the net force on the charge is zero then this charge is in equilibrium. The equilibrium will be stable if, when the charge is displace

Inclined Plane Calculations

1. A weight of 30lb rests on an inclined plane 3 ft high and 5 ft long. a force F making an angle of 30° with the plane pulls the body upward. If the coefficient of friction is 0.20, how much force is necessary to maintain uniform motion upward? 2. A board is 8 ft long. how high will one end be raised so that a block on it w

Determine the tension in the wires

Please see the attachment and answer problem 3 only. A uniform circular plate of radius 300 mm and mass 26 kg is supported by three vertical wires that are equally spaced arround its edge (see the attachment). A small 3 kg block E is placed on the plate at D and is then slowly moved along the diameter CD until it reaches C.

Two small blocks are stuck together and suspended at the end of a spring. To determine the extension in the spring and potential energy of the spring. One of the blocks gets detached. To determine the equation of oscillations of the block.

(Please see the attached file) Two small blocks, A and B , of masses 0.8 kg and 1.2 kg respectively, are stuck together. A spring has natural length 0.5 metres and stiffness of 98 N/m. One end of the spring is attached to the top of the block A and the other end of the spring is attached to a fixed point O. (a) The system