Classical mechanics Definition and 1000 Threads

Lagrangian mechanics is built upon calculus of variation. This means that we want to find out function which is a stationary point of particular function (functional) which in Lagrangian mechanics is called the action. To know what this function is, action needs to be defined first. Action is...

I was wondering how the second equation of motion produces negative displacements ##s= ut+\frac 12 at^2## . Is ##\frac12 at^2## kind of distance operator?

how does the first step use mean value theorem? I don't get it , can anyone explain , thanks.

The question I have is that if the aero plane is traveling in the same direction as the wind, would it not increase its velocity, as in with boats and streams? So, if by chance, ##w = v##, then the velocity of the aero plane would double. It feels weird as going by the same logic, if the speed...

A bullet with mass m, velocity v perfectly elastically, vertically collide with one end of a rod on a slippery plane and the bullet stops moving after the collision. Find the mass of the stick M the bullet stops moving after an elastic collision, so all energy is transformed to the rod. There...

I'm trying to understand Newton's third law in the context of collisions. Assume that one body has mass M kg and is traveling in the positive x direction with acceleration A m/s^2. Assume that the second body has mass m kg and is traveling in the negative x direction with acceleration a m/s^2...

I want to understand how the weight machines work that we use in homes and shops. I have been working on force and motion chapter and I was curious how this weight machine actually push up and how it applies force to the feet of the person being weighed? What reading is this that we see in...

This is a surface level question and I don't want to go into detail. Imagine an algorithm which when used with a sensor output gives the statistical moments of a variable in nature (for example mean and standard deviation of a variable). The sensor measures this once in a while (like once in a...

Assume that three boats, ##B_1##, ##B_2## and ##B_3## travel on a lake with a constant magnitude velocity equal to ##v##. ##B_1## always travels towards ##B_2##, which in turn travels towards ##B_3## which ultimately travels towards ##B_1##. Initially, the boats are at points on the water...

I mentioned answers above in the question.

Suppose there is one force gravitational force ##\vec{f_g}##. We can relate this downward force and downward acceleration with Newton sec law. This law can be written as ##F_{net,y}=ma_y## which becomes $$-F_g=m(-g)$$ or $$F_g=mg$$ $$\vec{F_g}=-F_g \hat j=-mg \hat j=m\vec g$$. Is it right...

x component of ##F_3## ##F_{3x}= m a_x- F_{1x}-F_{2x}## = ##ma\cos 50-F_1\cos(-150)-F_2\cos90## y component of ##F_3## ##F_{3y}= m a_y-F_{1y}-F_{2y}## =##ma\sin50-F_1\sin(-150)-F_2\sin90## And so on… My question how we can represent it in diagram ##F_1\sin(-150)##. I suppose...

Where exactly have I gone wrong? I think it is the part where I assume that the person gains the deceleration of the car, but I have no other way to proceed in this case. Also please only use the equations that I have posted below, and it would help if you would not use the equation for...

$$R=9.21 m$$ $$Difference = 9.21-8.95$$ $$D=0.26m$$ My question is when do we use the formula for R given above. Because we could have calculated the Rmax by ##R=(v0\cos(\theta))t## and then subtracted R from it to get the answer. Why the x and y component in the derivation of this (R)formula...

$$(y-y0)=ut-1/2gt^2$$ $$y= -1/2gt^2$$ $$t^2=-1/98$$ If I get t I will be able to solve for x=ut

I am stuck. Please ignore my handwriting. I am working on latex. All I am taking is x and y coordinates same of both particles. Yes they will meet at some time t.

I have attempted but I don’t get anywhere.

How the heck the bicycle reach from point A to point B with that velocity vector directions?

I don’t get where exactly the lengths start and end in figure.

Show that a point with acceleration given by: a=c*((dr/dt)×r)/|r|3 where c is a constant, moves on the surface of a cone. This is jut an example to illustrate my doubt. I don't know how to obtain the tracjectory given only the acceleration in this format. I realized that if i can show that...

“incidentally, to a good approximation we have another law, which says that the change in distance of a moving point is the velocity times the time interval, Deltas=vdeltat This statement is true only iF the Velocity is not changing during that time interval, and this condition is true only in...

I am currently reading some introductory physics. I am following resnik and Halliday. Can anyone suggest me some good general books on physics which would go comfortably with my resnik book. I need to read some general material not something technical. If possible on classical mechanics and...

How do you approach the problem as if you have never done it before?

If 150s is the time in which overtaking has to occur then why are they using this eqn: xp=x0+xs.

First I calculated the avg velocity with 1000m for both runners. It came 6.76m/s and 6.75m/s. It suggests that the velocities are same. This means yes that the L2 track is slightly longer than L1. Then why is it asking this question (…that runner 1 is faster)? Both are at equal speeds. I don’t...

The solution was done adding the two velocities of the car while finding the total time it took for the two cars to meet. I don’t really get the solution.

I was reading Motion chapter 8 in Vol 1 and I came across a line in speed topic which seemed confusing. So I checked with others and we concluded that its a mistake. Are there printing mistakes in this book? I will be surprised. Its pearson.

When is Hamilton's principle##\delta \int L d t=0## valid ? Is it only valid for monogenic and holonomic systems? What about monogenic and non holonomic systems? (I'm asking this because I got confused because I've found that Goldstein has got something wrong related to this in his 3rd edition)

Wikipedia article under generalized forces says Also we know that the generalized forces are defined as How can I derive the first equation from the second for a monogenic system ?

I'm trying to find the quality factor of a damped system. I know 3 points from the graph, ##(t,x): (\frac{\pi}{120},0.5), (\frac{\pi}{80},0), (\frac{\pi}{16},0)## From this I found that ##T = \frac{\pi}{20}## ##\omega_d = \frac{2\pi}{T} = 40 rad## Then, from the solution ##x(t) = A_0...

Found a question on another website, I have the exact same question. Please help me Goldstein says : I do not understand how (2.34) shows that the virtual work done by forces of constraint is zero. How does the fact that "the same Hamilton's principle holds for both holonomic and...

I want to learn about the non holonomic case in lagrangian and Hamiltonian mechanics. I've seen that many people say that Goldstein 3rd ed is wrong there. Where should I go to learn it. My mathematics level is at the level Goldstein uses. Please help

It is my second "energy state diagram problem" and I would want to know if I am thinking correctly. First I have done some function analysis to get a glimpse of the plot: - no roots but ##\lim\limits_{x\to-\infty}U(x)=\lim\limits_{x\to+\infty}U(x)=0## - y interception: ##U(0)=-U_0## - even...

Goldstein 3rd ed says "First consider holonomic constraints. When we derive Lagrange's equation from either Hamilton's or D'Alembert's principle, the holonomic constraint appear in the last step when the variations in the ##q_i## were considered independent of each other. However, the virtual...

(This is not about independence of ##q##, ##\dot q##) A system has some holonomic constraints. Using them we can have a set of coordinates ##{q_i}##. Since any values for these coordinates is possible we say that these are independent coordinates. However the system will trace a path in the...

(I drew motion in the opposite direction so the object would rotate trigonometrically but it should be the same thing) I have just finished the Kinetic Energy and Work chapter in my course and this is the last problem from the problem set. I have not worked many problems with the Work-Kinetic...

$$\overrightarrow{p_i}=\overrightarrow{0},~\overrightarrow{p_f}=m_c\overrightarrow{v_f}$$ $$\overrightarrow{p_f}-\overrightarrow{p_i}=\int\limits_{t_i}^{t_f}\overrightarrow{F}dt$$ $$t_i=0,~t_f=\frac{m_s}{b}$$ $$m_c\overrightarrow{v_f}=\overrightarrow{F}\frac{m_s}{b}\Rightarrow...

Firstly, There is something I want to clarify. When the system starts moving, parts of the chain that still lies on the table, which have mass ## \frac {(L- y_0)M} {L}##, will be pulled by the force that the hanging chain's weight exert,right? If yes, then : As far as I know, the formula ##F=...

Hi all, Consider a system of ##N## noninteracting, identical electric point dipoles (dipole moment ##\vec{\mu}##) subjected to an external field ##\vec{E}=E\hat{z}##. The Lagrangian for this system is...

I don't attempt solving a problem until I fully understand it, conceptually. After the hit (when maximum velocity is reached) the person starts losing momentum, having a constant upwards acceleration. The forces acting on the person are gravity and the normal to the ground. $$N - mg = ma$$...

Books that teaches classical mechanics through a discourse method ie asking interesting questions and answering them maybe a similar one to Understanding Basic Chemistry Through Problem Solving: The Learner's Approach Book by Jeanne Tan and Kim Seng Chan. Not exactly asking numerical questions...

(a) ##u_{min}=\big(1+\frac{m_2}{m_1}\big)\sqrt{2\mu_k g d}## (b) ##x_f=\sqrt{\frac{2h}{g}\Big(\big(\frac{m_1}{m_1+m_2}u\big)^2-2\mu_k g d\Big)}## Can someone check please?

Someone pls solve this. I've done it but I'm not sure if it's correct. Thanks!

Hello, I have posted a similar thread on this question before, but I'd like to get some help to simplify the answers I've got so far in order to match the solutions provided. If anyone could help me, I would really appreciate it. Since (c) is quite similar to (b), I'll leave here what I've done...

Hello, I'm having some trouble understanding this solution provided in Landau's book on mechanics. I'd like to understand how they arrived at the infinitesimal displacement for the particles m1. I appreciate any kind of help regarding this problem, thank you!

So I've been studying classical mechanics and have come across a small doubt with the solution provided to the problem in question from Landau's book. My question is: why are the coordinates for the particle given as they are in the solution? I imagine it has something to do with the harmonic...

Image above is the question. Below image depicts solution. if F1 is removed then the acceleration of that mass must be sum of accelerations of remaining forces. Right?? But answer says that acceleration of that mass is equal to acceleration of F1. I don't understand it. Can someone explain it??