What is Conservative force: Definition and 84 Discussions

A conservative force is a force with the property that the total work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the total work done (the sum of the force acting along the path multiplied by the displacement) by a conservative force is zero.A conservative force depends only on the position of the object. If a force is conservative, it is possible to assign a numerical value for the potential at any point and conversely, when an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken, contributing to the mechanical energy and the overall conservation of energy. If the force is not conservative, then defining a scalar potential is not possible, because taking different paths would lead to conflicting potential differences between the start and end points.
Gravitational force is an example of a conservative force, while frictional force is an example of a non-conservative force.
Other examples of conservative forces are: force in elastic spring, electrostatic force between two electric charges, and magnetic force between two magnetic poles. The last two forces are called central forces as they act along the line joining the centres of two charged/magnetized bodies. A central force is conservative if and only if it is spherically symmetric.

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  1. Z

    Understanding the generic nature of linearity in Physics

    Here is a link to the book. This question is about the section between the end of page 6 to the start of page 9. That section discusses the "generic nature of linearity". Let me go through the reasoning. Suppose there is a particle moving along the ##x##-axis with potential energy ##V(x)##...
  2. putongren

    B Exact differential and work done

    I was researching about conservative and non-conservative forces, and there is some information in a website that sates that the work done is independent of path if the infinitesimal work 𝐹⃗ ⋅𝑑𝑟⃗ is an exact differential. It further states that in 2 dimensions the condition for 𝐹⃗ ⋅𝑑𝑟⃗ = Fxdx...
  3. Stephen Bulking

    Can the Electric Field Outside a Conductor Have a Tangential Component?

    Here I am going to include the proof provided by my book. It is quite a splendid explanation, though there are a few key points I have yet to fully understand. If the electric force by the electric field on the charge at the surface of the conductor is conservative (which it is), then why is...
  4. Hamiltonian

    Work done by a conservative force using change in potential energy

    we know ##W_g = -\Delta U## but here to find ##\Delta U## we will need another equation won't it be wrong to write $$-\Delta U = -\int_1^{0.8}mgdy$$ as this equation is derived from ##W_g = -\Delta U## and as we have 2 unknowns we will need two equations. this is a rather easy problem but I am...
  5. Hajarmq

    I Conservative force pairs

    Let F_ki be the force applied by a point mass i on a point mass k. This force depends on the variables x_k and x_i which are the position vectors of respectively k and i (to simplify let´'s consider this in 1 dimension). Suppose this force is conservative. Then, according to my course and...
  6. E

    At what range does a conservative force contribute to the thermal U?

    Suppose we define our system to contain a few deformable bodies that exert gravitational forces on each other, and are consequently moving towards each other in some vague sense. We might want to express the total energy of the system as the sum of the mechanical energy and internal energy...
  7. Leo Liu

    Is Kinetic Friction a Conservative Force?

    If a block slides down an inclined surface under the presence of the kinetic friction, does that mean the total energy lost by the block is equal to the work done by the kinetic friction? Thanks in advance.
  8. JD_PM

    Particle moving in conservative force field

    I don't get why ##F \cdot dr = \frac{mv^2}{2}## I know this has to be really easy but don't see it. Thanks.
  9. Potential Energy of a Particle | Work done by Conservative Forces

    Potential Energy of a Particle | Work done by Conservative Forces

    What is a conservative force and how do you determine the work done by it. It is an interesting relation between the work done by such a force and the potential energy and kinetic energy of a particle.
  10. T

    Infinite time for an object to get K=0 conservative Force

    Homework Statement Think that we have only conservative force in this question and no nonconservative force like friction exists. Also## U ##means potential energy (eg Gravitational Potential Energy),##K## means Kinetic Energy (##1/2 mv^2##) and ##E = K + U = constant## We have a arbitrary...
  11. Arman777

    Potential energy and Conservative Force

    Homework Statement I have a force ##\vec{F} = a_x\vec{i}+2a_y\vec{j}+3a_z\vec{k}##. Find the potential Homework EquationsThe Attempt at a Solution Lets suppose And we know that ##\vec {F} = ∇U## In this case I said that ##U_x=-\int F_xdx## ##U_y=-\int F_ydy## ##U_z=-\int F_zdz## and then I...
  12. A

    Pressure gradient causes conservative force?

    Is the force that accelerates afluid betwen two points of different pressure conservative?
  13. L

    Why is/is-not energy conserved in these scenarios?

    Homework Statement PROBLEM A: A small cube of mass m slides down a circular path of radius R cut into a large block of mass M. M rests on a table, and both blocks move without friction. The blocks are initially at rest, and m starts from the top of the path. Find the velocity v of the cube as...
  14. Felipe Lincoln

    Conservative force in spherical coordinates

    Homework Statement Is ##F=(F_r, F_\theta, F_\varphi)## a conservative force? ##F_r=ar\sin\theta\sin\varphi## ##F_\theta=ar\cos\theta\sin\varphi## ##F_\varphi=ar\cos\varphi## Homework Equations ##\nabla\times F=0## The Attempt at a Solution In this case we have to use the curl for spherical...
  15. M

    I Why Is the Curl of a Conservative Force Field Zero?

    Why the curl of a conservative force field is zero everywhere?
  16. SciencyBoi

    How to differentiate b/w a conservative/non-conservative force?

    Homework Statement How do we determine a specific force mentioned in a question to be conservative or non-conservative? 2. Relevant data Conservative force is a force whose work done does not depend on the path that is taken while doing it. Examples include electrostatic force, gravitational...
  17. kmm

    I Understanding Conservative and Velocity Dependent Forces in Physics

    I actually have a few things I'm thinking about here. I'm curious as to whether a velocity dependent force field absolutely cannot be a conservative force field, in principle. I have at times come across statements in physics that I found out had mathematical exceptions for, but we don't...
  18. EastWindBreaks

    A car traveling upward on inclined plane

    Homework Statement consider a 3300 lb car whose speed is increased by 35 mph over a distance of 200 ft while traveling up a rectilinear incline with a 15% grade. model the car as a particle, assume the tires do not slip, neglect all sources of frictional losses and drag. find the work done by...
  19. E

    Does Compressing a Spring Decrease Its Potential Energy?

    I have just read chapter 7.4 FORCE AND POTENTIAL ENERGY in Sears and Zemansky's university physics 14th edition. There they show that a conservative force always acts to push the system toward lower potential energy in a one-dimensional motion with the equation Fx(x) = - dU(x)/dx. As I...
  20. mamadou

    Conservative force for an elastic force?

    Hi , I wanted to know how elastic force could be a conservative force ?
  21. Summer95

    Figuring Out if A Force Field is Conservative or Not

    Homework Statement There is a collection of different force fields, for example: $$F_{x}=ln z$$ $$F_{y}=-ze^{-y}$$ $$F_{z}=e^{-y}+\frac{x}{z}$$ We are supposed to indicate whether they are conservative and find the potential energy function. Homework Equations See Above The Attempt at a...
  22. J

    Why is change in potential energy is always negative?

    I'm studying relation between conservative force and potential energy,and getting a big question on change in potential energy is always negative. For gravitational PE ,when an object is lifting up, it's work done is negative(opposite direction). so the change in work done is negative. On the...
  23. P

    I Question about the formal definition of conservative force

    So, I was reading the mathematical description of a conservative force o wikipedia : https://en.m.wikipedia.org/wiki/Conservative_force and at the line "Many forces (particularly those that depend on velocity) are not force fields. In these cases, the above three conditions are not...
  24. S

    I Is internal battery "emf" a conservative force?

    First, the electric/Coulomb force set up by a battery across its terminal is conservative, and its potential is given by the well-known V. I also understand the conventional usage of emf is as a voltage potential. However, a battery does more than just set up the electric field and its...
  25. O

    Why is a spring a conservative force?

    Let's say you are holding a bowling ball in the air, and there is a spring on the ground directly below it. You drop the bowling ball and it lands on the spring, compressing it, and then the bowling ball rolls off the spring onto a point P right next to the spring. Wouldn't this do a different...
  26. S

    Why do conservative forces try to reduce potential energy?

    I do not understand the reason why a conservative force always "tries" to reduce the potential energy of a system at its minimum (forgive me if I said it in a wrong way). The explanation I gave me is: since for a conservative force, from the definition of potential energy, W=-\Delta U that...
  27. E

    Work function of conservative forces

    Could anyone help me with the following questions? - Why is the work done by conservative forces equivalent to the potential energy? - Why is the variation of the potential energy in such cases equals to the variation of the work function? Thanks!
  28. H

    Conservative force in a time-dependent potential

    A conservative force is one that is derivable from a potential energy function ##V##. If ##V## is time-dependent, is it still possible to have a conservative force or work done such that the work done is only dependent on the initial state ##(x_i, y_i, z_i, t_i)## and final state ##(x_f, y_f...
  29. Z

    Work done by a non conservative force

    The work done by a conservative force on a closed curve is zero but why it isn't true for the non conservative force?
  30. gracy

    Work done by conservative force

    I know work done by conservative forces= - ##ΔU##=##ΔK.E## But I have a question.Does it mean work done by all the conservative forces present (in a particular physics problem)= - ##ΔU##=##ΔK.E## or just work done by a conservative force= - ##ΔU##=##ΔK.E## I mean let's say a problem in physics...
  31. R

    Single conservative force acting on a particle

    Homework Statement Homework Equations U(final)(x)= (-) Integral F dx + U(initial) Integration from (x-initial to x-final)The Attempt at a Solution U(final)(x)= (-) integral (-Ax+Bx^2)dx Not sure on limits of integration
  32. Calpalned

    Why is work considered a conservative force?

    My textbook says that work done by a conservative force is independent of the path taken. This tells me that ##\int_{a}^{b} \vec{f} \vec{dl} ## only needs displacement (not distance) between points a and b. Conservative, according to my book, means that there is no friction. I have difficulty...
  33. Titan97

    Work done by a conservative force

    Homework Statement The potential energy ##U## of a particle of mass 1kg moving in x-y plane obeys the law ##U=3x+4y##. x and y are in meters. If the particle is at rest at (6,8) at time t=0, then find the work done by conservative force on the particle from initial position to the instant when...
  34. brianeyes88677

    Calculating Work and Determining Conservativity for a Force F=(xy)i+(2*y^2)j

    Homework Statement A force F=(xy)i+(2*y^2)j,an object (mass=m) is move from (0,0) to (1,3) along y=3x , how much work does F do? Is F a conservative force? Homework Equations 3. The Attempt at a Solution [/B] Can I do it on the two axes?I mean ∫Fdx+∫Fdy , and because the work differ from the...
  35. johann1301

    Conservative Force: Is F Dependent on Velocity?

    If F is a force acting on a atom and is dependent on the velocity of the atom. Is the force conservative?
  36. Z

    Understanding Conservative Force & Its Potential

    they say that a conservative force can be associated to a potential .. Why is that ? and what does it mean that a force has a potential ?
  37. S

    One dimension conservative force and potential energy

    Homework Statement Given a conservative force, how can we obtain the change in potential energy? Given a potential energy function, how can we determine the associated conservative force? One dimensional.Homework Equations Fx = -du/dx ΔU = -∫ F dx The Attempt at a Solution I know I can...
  38. C

    Conservative force and potential energy

    Problem: A conservative force F is acting on a particle that moves vertically. F can be expressed as (3y-6) j head N, y is in m and j head is a unit vector along vertical direction. a) Calculate the potential energy associated with F, with the potential energy set to zero at y=0. b) At what...
  39. Greg Bernhardt

    What is the conservative force

    Definition/Summary A force is conservative (the following definitions are all equivalent): if it complies with the work-energy theorem: work done equals change in mechanical energy if the work done is path-independent if the work done on a closed path is zero: \oint_C \mathbf{F}...
  40. AwesomeTrains

    Is the Force Field \vec{F}=f(r)\vec{r} Conservative?

    Homework Statement Show that the force field \vec{F}=f(r)\vec{r} is conservative. f(r) is a scalar field. r=|\vec{r}| Homework Equations curl(\vec{F})=0 The Attempt at a Solution I tried calculating the cross product, in cartesian coordinates, but how do i treat f(r) when doing the...
  41. J

    A particle moving under a conservative force

    Homework Statement From, Classical mechanics 5th edition, Tom W.B. Kibble, Frank H. Berkshire Chapter 2, problem 30 A particle moving under a conservative force oscillates between x11 and x2. Show that the period of oscillation is τ =...
  42. T

    Potential of a conservative force

    Homework Statement Hello everybody, i have the following problem: The following force vector is given: \vec{F}(x, y, z) = (2x + 3y)*\vec{e}_x + (z*cos(y*z))*\vec{e}_y + (y*cos(y*z))*\vec{e}_z Is it possible to find a potential for this given force? If it is possible, find it...
  43. T

    Getting the Potential Energy from a Conservative Force

    Homework Statement The problem basically asked me to check if a given force was conservative and if it was conservative, also find the potential energy. F = k(x,2y,3z) Homework Equations (\nabla X F) = Curl of F U = Integral of F 3. attempt So the force is clearly conservative as the curl...
  44. D

    Proving Work is Same for All Paths of a Conservative Force

    So for a force to be conservative it can only depend on position and the work as to be the same for all paths. The force mass time gravity is conservative but how do I show the all paths are the same?
  45. S

    Conservative Force: Properties & Definition

    what are the properties of conservative force?
  46. M

    Conservative Forces: The Relationship Between Work and Energy Conservation

    My question is can work be the transformation of potential energy to kinetic energy ( assuming no energy is lost)? I understand that work is energy transferred to and from the system with a change in the energy of the system. However, if there is no change of energy in the system, how can work...
  47. orlan2r

    The upward buoyant is a conservative force?

    If the upward buoyant is a conservative force, then it is possible to assign a numerical value for the potential at any point. See this please (altought this is in spanish): http://cpreuni.blogspot.com/2012/03/energia-potencial-hidrostatica.html...
  48. B

    Potential Function of a Conservative Force

    Homework Statement Given a conservative force with the Force given as F=y^2(i)+2xy(j), what is the potential function related to it. Homework Equations -dU/dx = FThe Attempt at a Solution I know I have to integrate the components but I don't know how... since the (i) direction was...
  49. D

    Conservative Force: Work Done and Potential Energy Calculation

    Homework Statement Find the work done by a force F = ix^2y^3 + jx^3y^2 Show that this is a conservative force and find the potential energy U(x, y). Homework Equations A force F is conservative when : dFx/dy = dFy/dx The Attempt at a Solution dFx/dy = d(x^2y^3)/dy =...
  50. sankalpmittal

    Confused regarding conservative and non conservative force

    Confused regarding conservative and non conservative force... Ok , so here is my explanation : Suppose I take a box at a height 5m from a reference point upwards. Work done by gravity on the block is -mg(5) J. Upwards is taken as positive and downwards as negative. Then I again take that box...