Conservation of energy Definition and 1000 Threads

Reading again this Insight, I have a question regarding "I. Work done against friction" section. In that problem (billiard ball of radius ##R## initially spinning in the air then falling on a pool table) the system under analysis is "billiard ball". The work-energy theorem (which would be...

For the (a) portion of the problem, it asks to calculate the minimum speed a probe must be launched from earth to escape the solar system with residual speed of 10 ##mi \, s^{-1}## relative to the sun. To find the minimum speed, I assumed the gravitational force affecting the probe by the sun...

I get that the speed is 3.1 m/s, the forces in the rod are 38 N downward and 58 N upward, and that the force on the axis is 49 N.

I am attempting to derive equations of state for a flow loop that incorporates a magnetohydrodynamic (MHD) generator to extract energy from the working fluid, an ionized gas. I have been able to find the following equation to define the power output of the generator: (where K is load factor, σ...

I thought the initial elastic potential energy would be converted to the arrow's kinetic energy but it also appears that the bow has some velocity.

On the first attempt I used conservation of energy to get it down to a single equation involving theta and v (the speed when the angle is theta). But I had no idea how to find v. Now since the maximum speed is given, it is possible to find the maximum angular displacement, ##\alpha##. Then...

I've already solved this problem using another resource (just get the coordinate of the range of the center of mass and from there, get it for the larger mass ##R_{2}=(3v_{0}^{2})/(4g))##: Range CM: $$R_{(CM)} = \frac{v_{0}^2 sin{2\theta}}{2g}=\frac{v_{0}^{2}}{2}$$ then: $$ R_{(CM)}=...

I’ve been confused about the term static pressure for quite some time. Different sources use very different definitions. From the problems perspective, it’s usually some external pressure. For example we are having a pool with tiny hole on the bottom which makes water level decrease and it flows...

is conservation of energy present in our current theories of gravity? more specifically string theory and loop quantum gravity?

so I thought that when a system was measured there could be an interaction between the measurement device or environment and the system but overall energy was conserved, but I came across these 2 articles which seem to imply this is not the case...

Can someone please tell me where I am wrong? I tried to solve the problem using velocity equation; ##v_{f}^2= v_{i}^{2} + 2as## and got a= 50m/s^2, F= 50 000N and therefore F=kx -> k=50 000N/m because dx=1. But it's not correct. When I do it using conservation of energy I get 100 000N/m. Which...

From Wikipedia, I know that it is the case in GR that conservation of energy and other conservation laws are relegated to being local only I thought this wasn't the case in quantum field theory.

Is energy conserved in general relativity? I have read most of the posts here that address this. But it isn't clear to me, what most people say is that energy is conserved locally but it can't be defined globally, some people say this means that energy is not conserved in GE while others argue...

The gravitational potential leads to velocity in downward direction, but spring potential does in upward direction. So should these energies have different signs (plus and minus or vice-versa)?

Hi, What I understood about the principle of conservation of energy: Et = Ep + Ec = constant. For example: Et = 1/2mv^2 + mgh (h = height). Consider a car moving at speed v. For example: Et = 1/2mv^2 + E(gas + exhausts). Indeed, I include the exhausts, otherwise with the drop in the quantity...

Hi, I assumed I was supposed to find the amount of kinetic energy body 2 receives after contact, assuming the collision is central, body 1 will be at rest after the collision. I started by using the equation for conservation of momentum: \begin{align} m_1v_1 = m_1v_1' + m_2v_2' \\ 50 * 20 =...

Here is my attempt at the solution: a) The apparatus may only experience acceleration ##a > g## while in contact with the spring. Since the spring exerts the greatest force when it is the most compressed, the apparatus will undergo the greatest acceleration at that point. So Newton's second...

I know that we can answer it using conservation of energy or using N's 2nd law. Using N's 2nd Law: ##F = mv \frac {dv}{dx}## ##Fdx = mvdv## For spring we have : ##F=-kx## ##(mg-kx)dx=mvdv## We'll get same result using above equation. My question: Average spring force from 0 to x is ##-\frac...

The system of two material points of identical mass connected by a rigid rod of negligible mass and length ##L## is an example of a conservation of energy problem. The initial energy of the system is the sum of the kinetic energy of the two points and the potential energy of the rod, which is...

I am stuck on what to do to calculate the inertia of a flywheel using the method described. I am supposed to use conservation of energy equations to calculate the inertia. I have a picture of the experiment and also the measurements I have taken. It seems each method I try I get a different...

This is how I tried to do it, which is the most direct. The force that the mass exerts on the spring is mgsin(53). and I equated that to kx. and found x. but apparently, this is wrong and the teacher told me a different method. (ME)1=(ME)2 due to conservation of mechanical energy...

I was working on this problem but after getting to the answer I questioned the methods that I used for previous problems that I had solved. I understand that the total energy of the system remains constant and that we use the conservation of momentum to relate the two velocities. This gives two...

I've been working through Bernard Schutz's book on GR and have run into some confusion in chapter 4 problem 20 part b. In this chapter, the stress-energy tensor for a general fluid was introduced and was used to derive the general conservation law for energy/momentum, where we found that...

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 -...

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.

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, 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...

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...

Since the forces involved (gravity and electric force) are conservative we can use conservation of energy. The initial energy is ##E_i= k\frac{q_1q_2}{r_0}-G\frac{m^2}{r_0} ## and the final ##E_f=mv^2+k\frac{q_1q_2}{2r}-G\frac{m^2}{2r} ## so from ##E_i=E_f ## we get...

The answer is .32m. I set the elastic potential energy as equal to the work, but at first I put the force in the work equation as (F elastic - F kinetic friction) times distance and rearranged. 1/2kx^2 = (kx-Ff) d (0.5) (22) (0.035)^2 = (22 x 0.035-0.042) d 0.013475= 0.728 d 0.013475/0.728 = d...

I found this article* about the behavior of quasar outflows in cosmology and how they can create a magnetic field. In section 2.1.4., the authors say that when a quasar produces a "wave" or an outflow, the material will be emitted with energy coming from both the quasar itself and the Hubble...

What I have done is on my Ipad that I cant upload or at least don't know how to... :/ With hope of help DJ

I tried approaching this question like this: F_N - mgcos(theta) = -mR(theta_dot)^2 and theta_dot = v/R since R is constant F_N = m(gcos(theta) - (v - v_0)^2/R) (with v being final velocity and v_0 being the initial velocity from the impulse) and then using energy conservation: at t = 0: E =...

I'm thinking about how the energy is conserved when a E.M. wave pass through a conductor. If a E.M. pass through a conductor, the electrons must move "oscillated", thus the energy from the E.M. wave is converted to kinematic energy. Another way I see that is the E.M wave must generate a current...

I already know the solution to this, all you do is set the height of the top of the trampoline to 0 and solve for initial velocity so the equation for the conservation of energy $$mgh_0 + \frac{1}{2}mv_0^2 + \frac{1}{2}kx_0^2 = mgh_1 + \frac{1}{2}mv_1^2 + \frac{1}{2}kx_1^2$$ becomes...

Hello there, I have tried the problem but don't get a different of 6g's as I am supposed to. I am not sure whether I interpreted the problem in the correct way, but I would love some feedback/hints on what went wrong in my solution, thanks in advance. Solution: SITUATION DRAWINGS + FBDS so...

so I haven't looked at the solution yet, but I know that a 100% the velocity needs to be bigger, but analytically, I get a - sign instead of a + sign as you'll see at the final square root. So for the first 15meters of the motion all you should know is that ##v_1 = 10.458 m/s##. for the 2nd...

If we have a ball with mass m dropped from a height h down to the ground, how come we can't set the conservation of energy equation just as the velocity of the ball turns 0. mgh = 0 If instead the ball were moving with an initial velocity v, would the equation be ##mgh + \frac{1}{2}mv^2 = 0##...

I was able to calculate the correct answer (given by a solution sheet), V=5.364 m/s, using the momentum impulse equation, P0+J=Pf. If this value is correct, however, I don't understand how energy is being conserved. The speed increases after the person bounces off the trampoline while the mass...

Part A) So from a force diagram we can see that the only two forces acting in our system are the spring force(positive y axis) and the weight of the rocket(negative y axis), which means the spring force is equal and opposite to the weight force. The weight is simple enough ##12* 9.8=117.6N##...

Hey, I have a question about explosions and how kinetic energy works during them. I have outlined my question on the attached image. Please let me know if something is wrong or needs clarifying. Thank you.

Ei = 1/2 K (x)^ 2 K = .0152N/m x = .0375 m Ei = 1.06x10^-5 Ef= 1/2mv2 + mgh m = .164kg, v is unknown, h is .0375sin(8.3)=.00541, Ef set equal to Ei 1.06x10^-5=1/2(.164kg)(v^2)+ (.164kg)(9.8)(.00541) v = .3254m/s I have gotten this answer multiple times but it is not correct. I am going...

The household LPG burns with a blue flame. There's nothing to prove! But what if we attempt to do that? How do we go about it? I started with the assumption that it is a complete combustion of the LPG. A Google search tells me that the calorific value (the amount of heat a substance gives off...

I have a problem in understanding angular momentum equation (mrv), especially the part where radius is involved. imagine an elastic collision occurred between sphere of mass (M) attached to a string forming a circle of radius (R) and moving with velocity (V) and another stationary sphere having...

Hi all, I'm not a physics student (although I have a PhD in a different field) and so don't have the math, but I'm trying to interpret a key passage from Krauss' book 'A Universe from Nothing' where he is (trying?) to explain, in 'layman's terms', what Alan Guth termed 'the ultimate free lunch'...

I have used the work energy theorem like all source have shown me an have arrived at the right answer where work one by all the forces is the change in kinetic energy -1/2kx^2 - umgcosΘx +mgsinΘx = 0 is the equation which becomes -1/2kx -umgcosΘ+ mgsinΘ = 0 where k= spring constant u=...

It is known that constructive interference in one place must be compensated for by destructive interference in another. Take a simple Fabry Perot resonator for example. The interference occurring at both sides of the first mirror (assuming one incident electric field) compensate each other out...

Hi everyone! I regularly use the forum to learn but never registered to post anything, as I have nothing to teach really… But today I have a question regarding the law of conservation of energy that I can’t find the answer to, and maybe someone will help me understand: (I’ve attached a drawing)...

Quantum mechanically speaking when we split a wave in two the resulting waves must have a 90 degrees phase difference for energy to be conserved. Take the beamsplitter depicted in [1] for example. But the Fresnel equations state that the reflected wave should experience a phase shift of π when...

Two masses m and M are attached to a compressed spring. When the spring decompresses, the masses won't be pushed off the spring. What will happen to the masses and the entire system? By conservation of energy, the elastic potential energy of the spring will convert into kinetic energy, but which...