Conservation Definition and 999 Threads

Does ##\frac{dq}{dt}=-\iint_S \vec{J}.d\vec{S} ## correspond to conservation of some quantity q in a region with boundary S whereas ##\frac{\partial q}{\partial t} = - \nabla . \vec{J}## means that for any point in space the quantity q is conserved? Since the divergence measures how much of q is...

My thinking is that because of the law of conservation of energy, the amount of energy needed to raise an object to a certain altitude has to be at least as much as the amount of energy released by the object if it were to be dropped from that altitude and hit the ground (and all that released...

I have tried the following. Firstly, we can write the law of conservation of impulse m1*v1 = m1*v'1 + m2*v'2, that is the first equation for the system. Then we can write the law of conservation of energy, like KE1 + KE2 = PE1 + KE'2, and then we can substitute formulas, but as far as I can see...

The answer from the textbook is: Use energy conservation ## \frac{1}{2}mv^2 + \frac{1}{2}I_{cyl}w^2 = mgh_{cyl} ## ## \frac{1}{2}mv^2 + \frac{1}{2}I_{sph}w^2 = mgh_{sph} ## Subtracting the two equations, eliminating the initial translational energy, we have: ## h_{cyl} = \frac{v^2}{g}...

I'm not quite sure how to apply conservation of string to this problem, so guidance would be appreciated. Normally as long as there isn't a "sub-pulley" I can do the problem fairly easily but this one tricks me up. Thanks

I initially thought about the different forms of energy present at each of the points: Total energy at starting point: PEA+ KEA= mgH at point D: KE_D = 1/2mv2f PED= mgD Energy at point D: PED+ KED D = mgD + 1/2 mv2f because EA= ED mgH = mgD = 1/2 mv2f mg(H-D) = 1/2 mv2f g(H-D) = 1/2...

Hello, I actually solved this problem using conservation of angular momentum, but I was wondering if linear momentum is conserved. Here's my thought process: (block + tile system) The block is going to hit the tile with some force ##\vec{F}##. Due to the Newton's third law, that force is also...

I used law of conservation of energy to calculate (d theta/ dt)^2 (from:mgasin theta=1/2m(d theta/dt.a)^2+1/2mu^2(u is the velocity of the C ring at time=t)), but wasnt able to find u(velocity of C).Is there any relationship between the tangential velocity of B(d theta/dt.a) and velocity of C(u)...

I don't quite understand the "subtle point" at the end of the author's solution. Ok, let's imagine for a second that the external forces have an impact on the internal forces. How does that change the mathematical result that the two forces are equal and opposite to each other? Even if...

My textbook says the correct answer for #79 is 1551 kg but I get 1600 kg. I just attempted to solve it using conservation of momentum. Can't see where the math is incorrect.

I tried to take angles and proceed by energy conservation But this doesn't seem to lead me anywhere . Here , the length of threads is ##l## each and ##2\theta## is the central angle. ##y_1## is the displacement of the charges attached at the extreme ends of the threads respectively while ##y##...

Hi Pfs, I would like to know if it would be possible for our known theories to derive conservation laws if space time was really granular. I think that entanglement is the only process which would succeed.

I am going to use this coordinate system: According to the answer of the book, I think no force is acting on this projectile: Let's say at top of it's trajectory its velocity is ##u##. Conservation of energy : $$2E_0=\frac 1 2 m_1 v_1^2+\frac 1 2 m_2 v_2^2$$ Conservation of momentum in...

I was watching this YouTube video by the channel The Action Lab: At one point it shows this capillary tube phenomenon: It got me immediately thinking: Conservation of energy much? What's stopping that second tube from being bent into draining into the leftmost tube, thus creating an...

Hi, so this is a lab in which we used an air track at an angle and a glider to gather some data through various trials, ultimately to calculate "g". L_glider = 10.15 cm x (photogate activation point) = 547.5 mm or 54.75 cm x_0 (release point) = 1800.0 mm or 180.00 cm (Δx)_midpoint = | x - x_0 |...

IIUC, entanglement sometimes plays a role in conserving come quantity like momentum or spin: the quantities measured for two particles must be correlated in order to get a certain total value. But is this always the case? For example, what, if anything, is conserved in the Hong-Ou-Mandel...

Hello, this question may seem weird but I really need help on this. To bring the formula for the height h of the triangle above, I have to create a relation between potential and kinetic energies of the black ball with mass m (I can't find any other methods than this). For a sphere falling...

I've had this question for a while now and I wonder if anyone can make sense of it. It's about two scenarios where the difference between them seems to contradict conservation of energy: Scenario 1: In a vacuum chamber, there is a robotic arm, a box, a lower platform and a higher platform. At...

Start by finding the equilibrium position, so we have {4mgx}/{a} = mg giving us x = a/4, therefore the spring's length is 5a/4. Now the loss in EPE (and therefore gain in energy of the particle) between the bottom and the equilibrium position is clearly 4mg((a/4 + d)^2 , and then from the...

Hi. If I drop an inelastic body, its potential energy first gets converted to kinetic, then to deformation energy. We use conservation of energy without taking into account the kinetic energy gain of the earth during the fall. However, at first sight conservation of momentum seems to be...

We all know we need to apply conservation of angular momentum here. This necessarily leads to a difference in mechanical energy. Since initial rotational inertial is less than final rotational inertia, there is a loss of mechanical energy. However, I have not been able to convince myself what's...

I tried using conservation of energy, and using the equations for circular motion, but I can't seem to find a solution. Any help?

Hello, As far I know, in a closed system both, linear and angular monentums, are conserved. İmagine such a scenario: everything is motionless, both momentums zero initially, then from a disk are fired (compressed spring push) two equal mass balls at same speed but opposite direction. Now balls...

There appears to be a conservation of charge momentum (qv) analogous to that for mass (mv) although in the case of charge it is more potential in nature. A change in the flow of charge (or current) produces changing magnetic and electrics fields according to Maxwell's equations. These in...

Why is (1/2)(mv0)^2 = 1/2(M+m0)gh not a valid equation for conservation of energy? Isn't the energy from when the dart is shot the same as when the two masses move at speed v?

I have often wondered why Inertia , Newton's 1st Law, is not simply called Conservation of Velocity Can anyone give me a reason why it should NOT be called Conservation of Velocity ??? Conservation of Energy is valid in the absence of External Forces. Conservation of Momentum is valid in the...

TL;DR Summary: . An electrone moves in a magnetic field ##B(\vec r)=g \frac {\vec r}{|\vec r|^3}##. Why does the conservation of the quantity $$\vec J=\vec r \times\vec p +eg\frac {\vec r}{|\vec r|}$$ mean that the motion is on the surface of a cone?

For this problem, The reason why I am not sure whether it is a valid assumption whether momentum is conserved because during the collision if we consider the two masses to be the system, then there will be a uniform gravitational field acting on both masses, and a spring force that is acting...

Here is question + drawing.

I understand that conservation of motion comes from the action and reaction pairs of newton's third law. When it is triggered, two forces appear that cancel when analyzed as a system. My question is how is it that momentum is conserved if before the shot there was no force in the system and...

Hi. Question as in the summary. Spin has no obvious classical interpretation but it is often a conserved quantity and considered as some sort of angular momentum. What do you need to establish that spin is a conserved quantity? I'm finding references to situations where spin is not a...

Hi guys, i’m always looking to conserve at best my motorcycle and car, i’m here to understand the correct way to do it

So, I cannot for the life of me write a conservation of energy statement, when an object is lifted up by a force. So in my example there is a box on the floor with v = 0, and then a force of magnitude F, where F > mg, acts on the ball, now the net force is F-mg, and hence the work done is (F -...

I've already solved the orbital speed by equating the kinetic and potential energy in the circle orbit case. $$\frac{1}{2}mv^2 = \frac{1}{2}ka^2.$$And so $$v^2 = \frac{k}{m}a^2$$Now when the impulse is added, the particle will obviously change course. If we set our reference point in time just...

mgh=(1/2)(m)(v^2) gh=(1/2)v^2 sqrt(2gh)=v Should have the same v, but this is not the case based on the answer and real-life experiments.

Consider a fluid flow with density ##\rho=\rho(t,x)## and velocity vector ##v=v(t,x)##. Assume it satisfies the continuity equation $$ \partial_t \rho + \nabla \cdot (\rho v) = 0. $$ We now that, by Reynolds Transport Theorem (RTT), this implies that the total mass is conserved $$...

After trying to kinda get a picture of the field of play in quantum physics according to the standard model, a question came up. I tried to formulate the known bosons each as a particle transferring some property. 1. Photons transfer electric charge: the electromagnetic force gives attraction...

In Chapter 5.3, Ballentine uses geometrical arguments to obtain the initial magnitude of a hydrogen atom's bound electron momentum. How does equation (5.13) obtain? I tried to naively compute $$p_e^2 \equiv \textbf{p}_e\cdot \textbf{p}_e = p_a^2+p_b^2+p_o^2 + 2\textbf{p}_a\cdot \textbf{p}_b -...

Question: With maximum do they mean that the speed of the pions is the same as the proton and an antiproton? Otherwise there will be two unknowns, and if I use both relativistic-energy and momentum conservation equations I get difficult equations.

For this problem, How can energy be conserved if the bit highlighted in orange is true?Many thanks!

The statement of the problem is: Consider a taut string that has a mass per unit length ##\mu_1## carrying transverse wave pulses of the form ##y = f(x - v_1 t)## that are incident upon a point P where the string connects to a second string with mass per unit length ##\mu_2##. Derive $$1 = r^2...

I was wondering why energy of capacitor does not equal change in kinetic energy PLUS change in potential energy where potential energy is the change in the potential energy of the charges. I believe that should be so because energy conservation = change in kinetic energy plus change in potential...

In Dirac's "General Theory of Relativity", at the end of Ch. 25 (p. 47), right after deriving the full Einstein equation ##R^{\mu\nu} - \frac{1}{2}g^{\mu\nu}R = -8\pi\rho v^\mu v^\nu = -8\pi T^{\mu\nu}##, he makes a reference to the conservation of mass (Eq. 25.3): $$0 = (\rho v^\mu)_{:\mu} =...

For this problem, Why for part (a) the solution is, Is the bit circled in red zero because since the putty is released at a very small distance above the rod it velocity is negligible? Also for part (d) the solution is I did a computation of the initial and finial kinetic energies of the...

The charge of an isolated system is conserved. This implies the charge of the universe is constant. This implies that charge can neither be created nor destroyed. This implies that the net positive charge and the net negative charge of the universe are conserved. Is this right?

For this problem, Is the length vector into or out of the page and how do you tell? EDIT: Why must we use conservation of energy for this problem? I tried solving it like this: ##IdB\sin90 = ma ## ##IdB = ma ## ##v_f = (2aL)^{1/2} ## ##v_f = (\frac {2dIBL} {m})^{1/2} ## Which is incorrect...

For this problem I was very confused whether conservation of angular momentum should be applied to the person, the swing or the person-swing system. It seems to me that there is no net torque on any of the three systems I listed above. However, it seems that the angular momentums of the three...

In the derivation of the conservation law of the conservation of mass, the flux on one side enters and the flux on the other side leaves the control volume. I presume this is due to the assumption that the volume is infinitesimally small and hence v(x,y,z,t) will not change directions...

Assume you have a two particle system, A, which has a mass and gravitational pull of g, and B, an object with low mass, The system starts at time 0 with the distance between A and B being 0, A being at rest and B having enough kinetic energy to move it a distance r away from A, until time t all...

The rotating ball should push the vehicle first to the right and once it hits the airbag - to the left?? Even if this works, how are you going to automate it and repeat it?