Mechanics Definition and 999 Threads

Bathe (reference below) outlines the updated Lagrangian (UL) and total Lagrangian (TL) approaches using the second Piola Kirchhoff (PK2) stress. Others (i.e., Ji, et al. and Abaqus) define the UL and TL formulations in terms of the Kirchhoff or the Cauchy stress in rate form. This form requires...

Homework Statement The attached image. Homework Equations Momentum conservation Conservation of mechanical energy The Attempt at a Solution I tried conserving momentum, ##P=mv_{1} + Mv_{2}## and then conserving M.E., P^2/(2m)=1/2##mv_1{1}^2## + 1/2##Mv_{2}^2## After that I can't seem to...

Just found this forum--hope there isn't a max post limit haha. I have been a bit stumped on this, but when doing problems about deflection and axial loadings, I am confused when to use which equation. I think I know that axial member need to be 2 force members, loaded only at the ends, and...

In general when one talks about an idealized gas, should/could one assume it is non-relativistic? (s.t E=p^2/2m will hold) many thanks

Homework Statement A small disk A is placed on an inclined plane forming an angle (alpha) with horizontal and is imparted an initial velocity v. Given coefficient of friction =k and ant initial moment angle of velocity =90 degrees. Find out how long it takes to come ro rest and give the...

Hey, I am interesting in analyzing a bicycle's frame statically from a vertical fall of x metres, this after using the energy principle i get that the force F = mv^2/r, where v = sqrt(2*g*h), r is the deformation of the bicycle at its contact point and m is total mass from the cycle and cyclist...

Hi all. Where can I find some good introductory sources teaching the use of statistical mechanics to study things like tornado formation or climate in general? I took P. Chem., a while ago now but I'm reviewing the material independently. We used one of Moore's texts, 80's - ish, and in it he...

Hi everyone, I just created this account because it was actually the first time I wanted to ask a question myself, but this forum has helped me a lot in the past with my Physics and Maths related courses. So thank you for that. Going back to the topic...Now that I've completed some of the...

I studied the vector analysis in Arfken and Weber's textbook : Mathematical Methods for Physicists 5th edition. In this book they give the definition of vectors in N dimensions as the following: The set of ##N## quantities ##V_{j}## is said to be the components of an N-dimensional vector ##V##...

Homework Statement Find ##\langle x \rangle## in the momentum representation I am having trouble understanding some of the steps needed to get to the expression, assistance is greatly appreciated! Homework Equations 3. The Attempt at a Solution [/B] $$\langle x \rangle = \langle \psi | x |...

Homework Statement Consider a rocket subject to a linear resistive force, $$f = -bv$$, but no other external forces. Use Equation (3.29) in Problem 3.11 to show that if the rocket starts from rest and ejects mass at a constant rate $$k = -\dot{m}$$, then its speed is given by: $$v =...

Homework Statement There is a system of 4 points located along a circle of radius R. Points are connected by undeformable ropes (pink on the picture). There is a force applied to each point. Scheme: https://we.tl/MsCEViCQdB I need to find resulting force in the system. The Attempt at a...

In Lagrangian mechanics, both q(t) and dq/dt are treated as independent parameters. Similarly, in Hamiltonian mechanics q and p are treated as independent. How is this justified, considering you can derive the generalized velocity from the q(t) by just taking a time derivative. Does it have...

Just for a bit of fun, which theory , relativity or quantum mechanics has the most accurate ( i.e to how many decimal places confirmation between theory and experiment) measurement ever made?

Hello all, I have a question regarding the precise definition of angular momentum in orbital motion. I see one definition says angular momentum h, position, r, and radial velocity, r_dot, are related as follows: h = r x r_dot. However, I also see one definition that says h is related to r and...

Just a thought I had one day, but the general idea I've heard is that quantum mechanics has a random property to it. The number Pi is apparently a number without any sort of apparent pattern to it either, seemingly random? Could these two things somehow be related? For example somehow...

In the case of a satellite orbiting the Earth. Would the relative velocity calculated by the Vis Viva equation the same as the orbital speed of the satellite? If the satellite is in an ellipse, would Vis Viva give the circular tangential velocity Vt=rω, or would it give the orbital velocity...

I've been reading about self teaching physics (mainly because the college curriculum is too slow to get me to any meaningful level of understanding at the end of four years), and an issue was brought up about lack of intuition in quantum mechanics/GR, and depending too much on the math. I was...

If a suspended pendulum bob is accelerated (in a car, for example), if you're in the accelerating frame of reference, you will observe the fictitious force which appears to act on the bob (as you're in the accelerating frame, the bob is not 'moving' so to speak, so to establish equilibrium you...

Homework Statement A block slides down a frictionless incline (30 degrees above horizontal) for L=1.4m until it meets a horizontal surface with coefficient of kinetic friction 0.3 before coming to rest. Use work and energy to find the distance that the block slides on the horizontal surface...

Hello everyone! I am working on a quantum mechanics research paper and I need to interview one person. It can be electronically or even in a place like this. I just need one person to answer a few simple questions and to describe their qualifications that prove they are a reliable source for...

Homework Statement There is a metal stick that is connected to the ceiling with another one. The angle between them is 60°. Calculate the tension force of the bottom one. Homework Equations T = f N or actually none, except trygonometry The Attempt at a Solution [/B] I tried using this...

Homework Statement A disc is free to rotate about an axis passing through its center and perpendicular to its plane. The moment of inertia of the disc about its center is I. A light ribbon is tightly wrapped over it in multiple layers. The end of the ribbon is pulled out at a constant velocity...

Hi everyone, First post here. Been out of school for a while and quite rusty, but always had an interest in physics, and was pretty good back in the day. Can anyone help me understand the physics of fishing rods? How to look at a fishing rod in terms of physics and mechanics? (i.e. is it a...

Hi , The Static Friction force of an object on a ramp(inclined plane) making an angle with the horizontal is greater than the weight component down the ramp. My textbook says that this means that the object on the ramp is stationary as the frictional force is greater than the weight component...

1. Problem A boatman crosses a river of width ##D## from a point ##O##, looking to get to point ##A## on the opposite riverbank. Suppose that the flowrate is uniform with velocity of magnitude ##v_0##. The boat has a velocity ##\vec{v_1}## relative to the water, with constant magnitude, and it...

Homework Statement A uniform chain of mass 'm' and length 'l' rests on a rough incline (inclination is angle 'Q') with its part hanging vertically. The chain (inclined) starts moving up the incline (and the vertical part moving down) provided the hanging (vertical) part equals to 'n' times...

Homework Statement Find the velocity ± and the position x as functions of the time t for a particle of mass m, which starts from rest at x =0 and t =0, subject to the following force functions: (a) Fx = F0 + Ct (b) Fx = F0 sin Ct Ct (c) Fx = F0e^ct where F0 and c are positive constants...

Homework Statement This is more of a question of applying the correct principles to a range of problems involving a horizontal rod hinged to a wall that is then supported by another rod. The support rod is also attached to the wall from above or below and then attached to the horizontal rod, so...

1. Homework Statement Question attached. I am looking at the second line limit ##\beta (h/2\pi) \omega << 1 ## 2. Homework Equations above 3. The Attempt at a Solution Q1)In general in an expansion we neglect terms when we expand about some the variable taking small values of the...

Greg Bernhardt submitted a new PF Insights post Statistical Mechanics Part II: The Ideal Gas Continue reading the Original PF Insights Post.

Let's consider a particle moving along x – axis, its position at t = 1s is 1m and speed is 1 m/s. How can one calculate acceleration on the basis of this information?

Homework Statement Homework Equations Moment of inertia Torque Angular momentum The Attempt at a Solution I think I can understand the physics of the situation. There will be a torque on the bus due to gravity while the back of it remains in contact with the cliff and it will start to rotate...

Homework Statement The question is in the attached document Homework Equations Newton's second law states that F=ma Charged particle in magnetic field experiences F=Q ( v X B) The Attempt at a Solution Since the charge 'Q' is constrained to move along a path in xy-plane in such a way that the...

The question is prompted by a claim raised in another thread that "There is good reason (theoretically) to believe that linearity fails at high enough energies." I've put this with an A prefix because it is going to be about some damned difficult maths, I know. But please try to avoid the...

Homework Statement "...you were presented with a geologist at the bottom of a mineshaft next to a box suspended from a vertical rope. The geologist sent signals to his colleague at the top by initiating a wave pulse at the bottom of the rope that would travel to the top of the rope. The mass of...

Hello PF, I am currently taking a course on quantum mechanics that is following Griffiths' textbook (page by page). The first exam in the course coincided with two other courses (analysis and probability theory) and so I did lack a bit of training while doing it (the required material was from...

Homework Statement So I've been stuck on this exercise for a few hours now, maybe you can help out: 3 balls meet at the same height hm. Ball 1 is accelerated straight up into the air for 1s from height 0. When the acceleration stops, ball 2 is launched straight up from height 0 with v2 =...

Homework Statement This is a practice olympiad problem A light rod with length l is hinged in such a way that the hinge folds in one plane only. The hinge is spun with angular speed ω around a vertical axis. A small ball is fixed to the other end of the rod. (a) Find the angular speeds for...

Good morning. The question of the "continuous" or "discrete" nature of the universe is the subject of diatribe among the greatest physicists in the world. I would like to discuss the same topic, but asking a question about the aspect of continuum in classical mechanics. The use of mathematical...

I am looking for an undergraduate textbook on Classical Mechanics that includes Hamiltonian and Lagrangian formulations. One reason for this is that I am interested in quantization and second quantization. It should include treatment of harmonics oscillators. Thanks!

Homework Statement Consider 2 balls A,B on the same line . and they are connected to a third one G with a rope L. AG, AB. now the system monves in the effect of the mass of G and its projection to the line AB is in the middle. No friction. mass of A=mass of B=m and mass of G=2m .FInd the time...

Homework Statement Consider 2 balls A,B on the same line . and they are connected to a third one G with a rope L. AG, AB. now the system monves in the effect of the mass of G and its projection to the line AB is in the middle. No friction. mass of A=mass of B=m and mass of G=2m .FInd the time...

Something that has always been off for me is the canonical pedagogical treatment of analysis of trusses in the course typically called "Engineering Mechanics: Statics". Certainly, every cantilever bridge I see has completely attached joints, although lately I have seen some airy, open...

Consider the following examples: 1) combine a spin 1/2 state (with 2D Hilbert space and three spin 0 states (each with 1D Hilbert space). The resultant state is in 3D Hilbert space. 2) combine the same spin 1/2 state (with 2D Hilbert space and one spin 0 state. The states in (1) and (2)...

The term "state" in quantum mechanics is not generally agreed across the physics community. Some physicists consider it to be synonymous with "state preparation procedure". Others find this too restrictive, as it would exclude states not prepared in a laboratory. For example my nose is not...

Homework Statement [/B] Homework Equations - The pressure drop equation. [/B]The Attempt at a Solution

Is it possible for me to do cosmology and quantum mechanics as a joint degree at uni? If so where and does it cost extra? I’ve been wondering for a whole and I’m not sure where to look.

I am currently going through a friend's Mechanics II notes and homework before I take the course at a different university next semester. I have a few problems that I am having trouble understanding and am posting here for help. 1. Homework Statement 1. A solenoid is on, Flux is Φ. 2. The...

Homework Statement Find reactions at ends and deflection at C Homework Equations RA + RE = 115kN ##\delta##Total = ##\sum## (PiLi)/(AiEi) The Attempt at a Solution RA + RE = 115kN Then apply superposition: (Get rid of RE) divide whole member into 4 elements and add. ##\delta##Total =...