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.
These images have been taken from Goldstein, Classical Mechanics.
Why do we need Lagrangian formulation of mechanics when we already have Newtonian formulation of mechanics?
Newtonian formulation of mechanics demands us to solve the equation of motion given by equation 1. 19. for this we need...
I have been going through problems in my textbook and have a question.
The chapter is on gravitation and orbital mechanics. When answering the problems I seem to head towards different methods than what the book prescribes. My answers, primarily using known orbital equations, are close, but not...
Homework Statement
What will momentum measurement of a particle whose wave - function is given by ## \psi = e^{i3x} + 2e^{ix} ## yield?
Sketch the probability distribution of finding the particle between x = 0 to x = 2π.
Homework Equations
The Attempt at a Solution
The eigenfunctions of...
A mass m is tied to a string which is wrapped to a twig of a tree. How many minimum times should we wrap the string so that it doesn't fall?
Here is what i got...
1.There is friction between the twig (or fixed cylinder) and the string.
2. if the total friction between the string wrapped around...
Homework Statement
A mechanical servo-mechanism comprising of a movable piston-cylinder within a vertical cylinder operates based on a venturi contraction in a horizontal 350mm diameter pipe that delivers a fluid of relative density 0.95. The upper end of the 100mm diameter vertical cylinder is...
Hello! I got a bit confused about the fact that the whole the description of spin (and angular momentum) is done in the z direction. So, if we are told that a system of 2 particles is in a singlet state i.e. $$\frac{\uparrow \downarrow -\downarrow \uparrow }{2}$$ does this mean that measuring...
Rehashing this topic because I believe a clear misconception is stated in many threads. Classical mechanics is an incorrect ( by the definition of correct ) theory which is only an approximation that uses incorrect assumptions ie. Constant time but yet makes accurate predictions in its regime...
I’m a high school student reading through Young and Freedmans University Physics. The book has gotten my very interested in classical mechanics, and I wish to read more about it outside the textbooks.
However, I don’t know where I can read more about it. Sure, there are books that I can read...
I'm trying to think through a situation, and develop some confidence I've got it right.
The situation is a apartment building, about 60'/20m high, with a courtyard in the middle about 60'/20m square. In the middle of the courtyard, is an low exhaust stack, about 8' high and around 8' square...
Hello, this is my first question on PhysicsForum. I am primarily interested in statistics/machine learning. I have recently discovered that many of the ideas used in machine learning came from statistical physics/ statistical mechanics.
I am just wondering if it's a bad idea to attempt to learn...
Hello. I've been struggling for a day with the following problem on Quantum coherent states, so I was wondering if you could tell me if I'm going in the right direction (I've read the books of Sakurai and Weinberg but can't seem to find an answer)
1. Homework Statement
*Suppose a Schrödinger...
Homework Statement
Refer the given image. [Prob 2.9]
Homework Equations
F=ma
The Attempt at a Solution
I drew the normal vector perpendicular to the surface of the cone and resolved it as
##Nsin\theta=mg##
##Ncos\theta=\frac {mv_{0}^2} {r}## where ##v_{0}## and ##r## are the speed and radius...
Homework Statement
Two blocks with pulleys attached lie on a frictionless surface and are connected by a massless rope strung over the pulleys as shown at right. A force of magnitude F is applied to the second block. Draw a FBD for a system consisting of Block 1 and its pulley, and also a...
Hi everyone,
I have a real life fluids problem I am trying to solve theoretically.
During a commissioning exercise we needed to discharge fuel into a 100L steel drum to test flow rates for a new re-fuelling skid. To minimise turbulent flow and static build up a drop pipe was used for the hose...
Hi. I just received a copy of Ballentine's "Quantum Mechanics: A Modern Development" ordered from Amazon, after I heard well of it in this site. I'm wondering what edition I've bought: the one I've got has a white hardcover, and its ISBN is 9789810227074.
Does someone ever used this edition? Why...
I always think about entanglement as pure conservation of energy and conservation of angular momentum. In fact I see that only conservation of energy is non-local, and that quantum objects have nothing to do with non-locality, for example you can entangle 2 atoms that have never interacted with...
Greg Bernhardt submitted a new PF Insights post
Orbital Mechanics in Unity Game Engine for Augmented Reality
Continue reading the Original PF Insights Post.
I recently watched a video where Sean Carroll talked about QM and multiverses
1/ Could you please explain:
Where does all the energy come from to drive all these universes.
Surely this must take an enormous amount of energy to drive a multiverse
system (infinite).
Does each universe...
Homework Statement
A particle is moving parallel to x-axis in the positive direction with velocity v such that at all the instants the y -axis component of its position vector is constant and is equal to 'b'. Find angular velocity about origin.
Homework EquationsThe Attempt at a Solution
I...
They found an underground lake on Mars last week!
Given that the lake exists and is actually liquid (and has a surface), two obvious questions come to mind:
1. Will I be able to beet my earthly current record in bouncing a pebble there?
2. If I release a pebble from a given height here and...
Homework Statement
Homework Equations
orthogonality condition: that means that the point of ICR is orthogonal to the velocity Vb and Va
The Attempt at a Solution
the solution that i found with the problem is:
The ICR of the bar is at infinity. the motion of the bar is translational.
I think...
Homework Statement
A solid disk of mass M and radius R is on a vertical shaft. The shaft is attached to a coil spring that exerts a linear restoring torque of magnitude Cθ, where θ is the angle measured from the static equilibrium position and C is a constant. Neglect the mass of the shaft and...
I have been taking many online courses. In the prerequisites for many courses, it has been mentioned, "basic" quantum mechanics.
It has become important to define where the boundary of basic ends and the advanced level starts, though I believe that is not well defined. I have been studying QM...
Supposing the Many Worlds interpretation of QM is true... If a branching occurs during what we perceive is a wave function collapse, why would this be perceptible to us as probabilties? Wouldn't we just branch, leaving it just as imperceviable as the passage of time? That is, it just happens...
Homework Statement
A uniform cylinder of mass ##M## and radius ##R## is released from rest on a rough inclined surface of inclined surface of inclination ##\theta## with the horizontal as shown in the figure. As the cylinder rolls down the inclined surface, what is the maximum elongation in...
Homework Statement
A light uniform spring is tied between the ceiling and the floor keeping the spring vertical as shown in the figure. A bead of finite mass is glued at a distance l from the upper end and then allowed to go slowly down. The bead shifts a distance y.How does the y depend on...
Homework Statement
A car of mass 2000kg moves along a horizontal road against a constant resistance of manitude (P)N. The total work done by the engine in increasing its speed from 4ms^-1 to 5.5ms^-1 while it moves a distance of 60m is 30000J. Find P.
Homework Equations
ΔEk+WP=WE
The Attempt...
1. The problem: Two blocks of mass m=5kg and M= 10kg are connected by a string passing over a pulley B. Another string connects pulley B to the floor and passes over pulley A. An upward force F is applied at the centre of pulley A. Both pulleys are massless. Find acceleration of the blocks if F...
I lost my book on Quantum mechanics! It was published in the late 80s or early 90s in England. Title: Quantum Mechanics. The book used algebra with more advanced math in the appendices. If you know the author , please reply. Thanks!
At my school, you have to take Quantum mechanics at the same time as Statistical mechanics (co-requisites) in either junior or Senior year as a physics major; why is this?
What is the relationship between the 2?
ER=EPR, black hole complementary, firewalls, vacuum entanglement etc..
Where do I begin studying these new ideas? I have a solid understanding about Quantum Field Theory and the classical theory of gravity, but no knowledge of string theory. Are there some advice or book recommendations anyone...
I’m having a hard time, as I begin learning QM, knowing what it applies to, if I can put it that way.
Is QM the rules that describe how the particles of the Standard Model interact with each other? Or what is the best way to understand the relationship between what one studies when one studies...
Homework Statement
Freight car and hopper*
An empty freight car of mass M starts from rest under an applied force F. At the same time, sand begins to run into the car at steady rate b from a hopper at rest along the track.
Find the speed when a mass of sand m has been transferred.Homework...
:rolleyes: I would like to find a free online course, not too hard. I have minors in math and physics, but have been away for awhile. Maybe something on youtube. If someone knows of a decent course that I could educate myself with I would appreciate any info on it. Thanks in advance...
In Special/General Relativity invariance of a space-time interval is just so important. But in Quantum Mechanics, be it non-relativistic or QFT, there seems to be no such parallel. I have always noticed this.
I have some ideas about the reason:
1 - it's not part of the theory to have a...
Homework Statement
A polymer chain consist of a large number N>>1 segments of length d each. The temperature of the system is T. The segments can freely rotate relative to each other. A force f is applied at the ends of the chain. Find the mean distance ##\textbf{r}## between the ends...
Hi.
I bought Messiah's "Quantum Mechanics" because it was at an excelent price from Dover. But, even though it was considered a Bible of quantum mechanics until recently, people consider it outdated now. Is it no longer comprehensive? I intend to read on relativistic quantum mechanics and...
Homework Statement
A light rod ##AB## of length ##2a## has a particle ##P## of mass ##m## attached to ##B##. The rod is rotating in a vertical plane about a fixed smooth horizontal axis through ##A##. Given that the greatest tension in the rod is ##\frac {9mg}{8}##, find, to the nearest degree...
So, I've been trying to study Mechanics in my spare time - about an hour or two every day - for over two years now. I'm up at 4:00 am most mornings studying before work. Despite being able to speak French, Italian and Irish fluently, holding a few Masters Degrees, and being a teacher myself, I...
Homework Statement
Consider scattering of a particle of mass ##m## on the potential
$$U(r) = \begin{cases}
0, & r \geq b\\
W, & r < b \\
\end{cases}$$
Where ##W## is some arbitrary chosen constant, and the radius ##b## is considered a small parameter. Find the cross section ##\sigma## in the...
Homework Statement
The Attempt at a Solution
[/B]
Hi All,
I'm having trouble answering part (f) of the above question. I have managed parts (d) and (e) fine but am not sure how to proceed with part (f). I am pretty sure that the amplitude of the reflected wave in region 1 will be zero...
I am preparing for an exam which requires me to solve problems in electrodynamics and electrostatics problems along with classical mechanics and geometrical optics problems. The concern is that I do not have electrodynamics in my course in school so I have to study it completely on my own. I...
I’m studying large strain and deformation solid mechanics and I have a (seemingly) basic question on solution approaches. Is my interpretation below correct?
The governing equation of momentum for solid mechanics can be solved using a total or updated Lagrangian approach. The updated...
I'm working through Gregory's Classical Mechanics and came across his derivation of energy conservation for a system of N particles that is unconstrained. We get to assume all the external forces are conservative, so we can write them as the gradient of a potential energy. There's a step he...
Homework Statement
Water flows over a dam as depicted below. Across section 1 and 2 we have a hydrostatic pressure distribution. Calculate the force on the dam.
The Attempt at a Solution
My question is regarding control volume. The solution manual has given us this:
The two hydrostatic...
Homework Statement
A block of mass 20kg is on rest on a rough plane inclined at 60 degrees to the horizontal. A force P is applied to the block to "maintain equilibrium". P is parallel to the line of greatest slope of the inclined plane. The maximum value of P is twice the minimum value of P...
Hello, all. These are not the circumstances under which I would have preferred to have made my first post, but unfortunately, as the question suggests, this semester (second semester of freshman year), I earned a C in my calculus-based Intro to Classical Mechanics course. Not really for lack of...
Homework Statement
I have a situation as illustrated by the image above, where the red box illustrates the CV. The pressure on the left side of CV is P1, while the pressure on the right side of CV is P2. Here I´ve directed the pressure forces acting inwards on CV. The problem arises with Fk. I...