What is Mechanics: Definition and 999 Discussions

Mechanics (Greek: μηχανική) is the area of physics concerned with the motions of physical objects, more specifically the relationships among force, matter, and motion. Forces applied to objects result in displacements, or changes of an object's position relative to its environment.
This branch of physics has its origins in Ancient Greece with the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo, Kepler, and Newton laid the foundation for what is now known as classical mechanics.
It is a branch of classical physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light.
It can also be defined as a branch of science which deals with the motion of and forces on bodies not in the quantum realm. The field is today less widely understood in terms of quantum theory.

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  1. BookWei

    Velocity is a vector in Newtonian mechanics

    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##...
  2. W

    Position mean in momentum-space (QM)

    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 |...
  3. TaylorLL

    Rocket subject to linear resistive force -- two methods

    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 =...
  4. Maria

    Simple closed force system -- Mechanics

    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...
  5. Q

    Independence of Position and Velocity in Lagrangian Mechanics

    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...
  6. W

    I Accuracy of Relativity vs Quantum Mechanics Measurement

    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?
  7. FQVBSina

    Orbital Mechanics Angular Momentum

    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...
  8. kolleamm

    Randomness of quantum mechanics and Pi

    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...
  9. FQVBSina

    Orbital Mechanics Vis Viva Equation Question

    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...
  10. R

    I Building intuition for Quantum Mechanics

    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...
  11. Soffie

    The period of oscillation of a bob in an accelerating frame

    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...
  12. jybe

    Work/energy to find horizontal displacement

    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...
  13. A

    B The Impact and Relevance of Quantum Mechanics: An Interview with an Expert

    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...
  14. J

    Finding Tension Force in a Metal Stick Connected to the Ceiling

    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...
  15. K

    Find the force as a function of radius to pull a ribbon

    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...
  16. P

    B What are the physics behind fishing rods?

    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...
  17. EF17xx

    Understanding Static Friction on a Ramp: Why is the Object Stationary?

    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...
  18. E

    Difficult version of boatman problem

    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...
  19. K

    Given a uniform chain on an incline, find the work done by friction

    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...
  20. Fia Ismi Nur Alfiah

    Newtonian Mechanics : Rectillinear Motion of a Particle

    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...
  21. AntSC

    Moments - Support forces acting on a rod

    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...
  22. binbagsss

    Taking classical limit question (statistical mechanics )

    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...
  23. NFuller

    Statistical Mechanics Part II: The Ideal Gas - Comments

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

    Obtaining the equation of motion using analytical mechanics

    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?
  25. Alexander350

    Calculating the angle of a bus driving off a cliff

    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...
  26. Muthumanimaran

    Charged pendulum in magnetic field

    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...
  27. Derek P

    A Is non-linear quantum mechanics (even) plausible?

    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...
  28. C

    Finding the Mass of a Hanging Rope (Wave Problem)

    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...
  29. jamalkoiyess

    Studying How to recover in a Quantum mechanics course

    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...
  30. J

    Need help with mechanics exercise - Vertical motion of 3 balls

    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 =...
  31. Brilli

    An equilibrium problem -- Spinning a hinged rod and a ball

    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...
  32. qttv

    A Classical Mechanics: Continuous or Discrete universe

    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...
  33. Gene Naden

    Classical Undergrad Classical Mechanics with Hamiltonian formulation

    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!
  34. Manolisjam

    3 balls in a moving mechanics problem

    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...
  35. Manolisjam

    Classical Mechanics Problem with balls

    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...
  36. S

    Why does ENGR Mechanics: Statics cover *hinged* trusses?

    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...
  37. Robert Shaw

    I Does the concept of an "object" belong in Quantum Mechanics?

    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)...
  38. Robert Shaw

    I Quantum Mechanics: The Debate Over "State

    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...
  39. N

    Fluid Mechanics: Choosing a fuel line diameter for a required pressure drop

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

    Programs Cosmology and quantum mechanics as a joint degree?

    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.
  41. T

    How Does the Feynman Paradox Apply to Solenoid Flux Calculations?

    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...
  42. F

    Mechanics of materials: Statically Indeterminate member

    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 =...
  43. A

    Other Senior Quantum Mechanics Research Project

    I am going to be doing a high school senior research project on how Quantum Physics will change the world in the future. Basically my current idea is to describe what quantum mechanics is, and then give examples that I explain and I state how they will change the world and the estimated time...
  44. D

    Deflection of Tapered Beam with Elliptic Cross Section

    I am working on deriving expression for deflection of a tapered beam with an elliptic cross-section. Hence, area moment of inertia is a linear function of the beam length. The beam is fixed at one end, and a concentrated force F is applied on its tip at the free end. I am using the known...
  45. T

    Mechanics II: Hamiltonian and Lagrangian of a relativistic free particle

    Homework Statement I am given the Hamiltonian of the relativistic free particle. H(q,p)=sqrt(p^2c^2+m^2c^4) Assume c=1 1: Find Ham-1 and Ham-2 for m=0 2: Show L(q,q(dot))=-msqrt(1-(q(dot))^2/c^2) 3: Consider m=0, what does it mean? Homework Equations Ham-1: q(dot)=dH/dp Ham-2: p(dot)=-dH/dq...
  46. W

    QM: Formalism of 2-state systems

    Homework Statement Hi all, I'm working on the following problem and would like some help. Many thanks in advance! The Figure below presents the Mach-Zehnder interferometer with an additional phase shift element in the upper path. $$\left( \begin{array}{cc} e^{i\phi} & 0 \\ 0 & 1 \end{array}...
  47. Elizabeth Chick

    Homework Question about Statistical Mechanics

    Homework Statement Consider the system of two large, identical Einstein solids, each with oscillators, in thermal contact with each other. Suppose the total energy of the system is 2 units of the energy quanta, i.e., =2ℏ, (i) how many MACRO-states (e.g., one macro-state corresponds to one...
  48. W

    Mach-Zehnder Interferometer interpretation

    Hi all, I have a problem trying to interpret the mathematics of this experiment and would like some help. I think it's best I write out all my ideas (and misconceptions) so that I can be corrected. An illustration of the setup is below. Thanks in advance for any assistance! Let the following...
  49. Boltzman Oscillation

    Finding Lagrangian for Overhanging String on Frictionless Table

    Homework Statement B is 10kg C is 20kg can I find a lagrangian for this system? If so how? Diagram: http://imgur.com/j811rzw Homework Equations L=T-V Kinetic = .5mv^2 Potential = mgh The Attempt at a Solution I know the kinetic energy must be 0 right? How could I find the potential?
  50. SemM

    A How does one "design" a PDE from a physical phenomenon?

    Hi, I have read some on the PDEs for fluids, and particularly for rogue waves, where for instance the extended Dysthe equation and the NLSE look rather intimidating: Take for instance the Non-linear Schrödinger eqn: \begin{equation} \frac{\partial^2 u}{dx^2}-i\frac{\partial d...
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