What is Conservative forces: Definition and 76 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. F

    I Conservative forces and internal and external forces

    Hello Everyone, This is not a completely new dilemma but I have been discussing it with several people and teachers and read different physics textbooks and continue to get different perspectives, sometimes overlapping sometimes not. Let me explain and summarize: Forces are interactions...
  2. K

    I Potentials of conservative forces

    Goldstein writes "only if ##V## is not an explicit function of time is the system conservative"That means ##V(r,\dot{r})## is a conservative potential, however I think that only potentials of the form ##V(r)## are conservative potentials. Could you please tell me where I'm going wrong. Thank you.
  3. F

    Conservative forces, Nonconservative forces and Potential Energy

    Hello, I would like to review and validate some concepts that I have been recently thinking about. Hope this is correct and useful to others that need to refresh these concepts. Forces can be classified as either conservative or nonconservative. Dissipative forces are always nonconservative...
  4. Like Tony Stark

    Conservative forces vs friction

    Hello I've written that homework statement as an example to illustrate my doubt: How can I tell if a force is conservative or not? I've read that, if the curl of the force is 0, it's conservative. But what about the friction force (##f=\mu N##)? Its curl is also zero, but it's not conservative...
  5. P

    B Conservative and Non Conservative Forces

    I was referring to the conservative and non conservative forces. When i was thinking about it for example when i apply force on an object on the table the object moves a distance and when i remove the force the object does not come back to original position. Can i assume that the force i apply...
  6. W

    I Are all conservative forces internal?

    Work done by conservative forces adds potential energy (by definition of conservative force), and potential energy can only be internal to a system. Thus, conservative forces must be internal to a system. Is this reasoning correct?
  7. When is Work done by Force Negative or Positive?

    When is Work done by Force Negative or Positive?

    Is it confusing to find when is Work done by a force negative or positive? It indeed can be. Learn in this chapter how the dot product of force and displacement can give you the value of work done by the force and also if it is negative or positive
  8. J

    B Conservative Forces: Internal or Not?

    Are conservative forces always taken as internal forces?
  9. 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...
  10. mamadou

    Conservative force for an elastic force?

    Hi , I wanted to know how elastic force could be a conservative force ?
  11. donaldparida

    Conservative forces and conservation of mechanical energy

    Why do conservative forces conserve mechanical energy while non conservative forces do not? According to me, What makes the conservative forces path independent is that for a particular case they always act in a fixed direction irrespective of the direction of motion of the object on which they...
  12. kuruman

    Acceleration at maximum displacement

    A common student misconception is that when a ball is thrown straight up in the air, at the point of maximum height, where the velocity is zero, the acceleration is also zero. This can easily be dispelled by observing that, if indeed the acceleration were zero when the velocity is zero, the...
  13. donaldparida

    How do conservative forces conserve mechanical energy?

    How do conservative forces exactly conserve mechanical energy while non conservative forces do not. Also why is potential energy defined only for conservative forces?
  14. S

    Why do conservative forces MUST depend on the position?

    ...Or do they? I read on a book a few years ago that you can spot a conservative force seeing if it depends on the position or not. That means a non conservative force doesn't depend on the position. What is the physical reason for the relationship between a force being conservative and the...
  15. 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...
  16. 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!
  17. hackhard

    B How to check if force is conservative?

    given a force F = f(x) i^ + g(y) j^ + h(z) k^ (x,y,z,are coordinates of body) how can i prove or disprove that the force is conservative ?
  18. A

    Nonconservative Force: Understanding Force of Friction

    I not understand because why if I have a (constant) force of friction and I apply the curl, I finding that this not is equal to zero, since this force is non conservative.
  19. AntoineCompagnie

    Potential energy variation = work of -(conservative forces)

    Homework Statement Why is potential energy variation between two points equals to the work of the opposite of conservative forces between these two points? Homework Equations If we call these forces $$\vec F_ext^C$$ \begin{equation} \Delta E_p=E_p(B)-E_p(A)=-\sum W_{A\rightarrow B}(\vec...
  20. Titan97

    Different cases of work done done by 3 conservative forces

    Homework Statement Homework Equations W=-ΔU for conservative force. The Attempt at a Solution Let all three forces be conservative. Since particle comes back to where it was, ΔU=0. Hence ΔUAB+ΔUBC+ΔUCA=0 Hence WCA=-WAB-WBC For case A, if both WAB, WBC>0, then WCA<0. Else its greater than...
  21. Hanyu Ye

    Is surface tension conservative?

    Hello, everybody. Is surface tension a conservative force? I think so, because it is related to surface energy. But I am not 100% sure. Thanks a lot.
  22. gracy

    Work done by conservative forces

    amount of work done by conservative force =amount of decrement in potential energy Is this correct?I think yes Because I have been told that Work done by non-conservative forces + work done by conservative forces = change in kinetic energy but Work done by non-conservative forces = change in...
  23. P

    Conservative Forces: Position, Velocity & Calculus

    When we say that conservative forces don't vary with time, we are talking about a specific position, right? Because if the position is allowed to vary with time, then the force varies with time. In general, the (net) force on a body may be written (in one dimension) as ##F = m\ddot{x} = mv...
  24. H

    Circular motion and work done by non conservative forces

    Homework Statement A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion.(Figure 1) Assume that the ball travels freely in this vertical circle with negligible loss of total...
  25. G

    Conservative Forces - Maths of Force & Energy

    Homework Statement A particle of mass m moves in a horizontal plane along the parabola ##y = x^2##. At t=0, it is at the point (1,1) with speed v0. Aside from the force of constraint holding it to the path, it is acted upon by the following external forces: A radial force: ##\vec F_a = -A...
  26. Z

    Force of tension of spring and rope

    why is the tension force of spring conservative and tension force of rope not conservative ??
  27. 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 ?
  28. P

    Block Sliding Down a Ramp that is Free to Slide

    Homework Statement A block with mass m rests on a smooth, frictionless ramp with mass M and height h. The ramp itself sits on a frictionless horizontal surface in which it is free to slide. The block slides smoothly down the ramp from rest. We want to find the speed of the block after it has...
  29. A

    Gravity: Conservative or Non-Conservative?

    We generally take the force of gravity to be conservative, but what if the source of gravity is moving through space? Then the force would only be conservative relative to the source, correct? As another example, consider someone in a balloon ascending with constant speed relative to earth...
  30. C

    Potential energy of a particle in a system

    1. A single conservative force acting on a particle within a system varies as = (− Ax + Bx6)ihat N, where A and B are constants, is in Newtons, and x is in meters. (a) Calculate the potential energy function U(x) associated with this force, taking U = 0 at x = 0. (b) Find the change in...
  31. H

    Internal Forces in System of Particles

    I am following along with Goldstien's Classical Mechanics Book and I am on page 11. The text is breaking down the total potential energy of a system into two parts: the external conservative forces and the internal conservative forces. My question pertains to the internal forces. Writing the...
  32. D

    Energy conservation, and conservative forces?

    What is the relationship of conservative & non-conservative forces to the conservation of energy? What differs with the two? Energy in each case...?
  33. C

    HW ?: Conservative Forces and Potential Energy

    A mass m = 6.2 kg hangs on the end of a massless rope L = 1.96 m long. The pendulum is held horizontal and released from rest. 1) How fast is the mass moving at the bottom of its path? I calculated this to be 6.201 m/s using the equation v=√(2gh) (correct) 2) What is the magnitude of the...
  34. M

    Work-energy principle and conservative forces

    Hi, all there are equation in the pic but I can't understand them. I know work-energy principle which is W= F * X (work equals force times way) but I think they are special forms. What concepts and topics should I study to understand them?
  35. A

    Checkpoint: Conservative Forces And Potential Energy

    Homework Statement Consider two identical objects released from rest high above the surface of the Earth (neglect air resistance for this question). In Case 1 we release an object from a height above the surface of the Earth equal to 1 Earth radius, and we measure its kinetic energy just...
  36. andyrk

    Non Conservative Forces

    Can you tell me more about Non Conservative Forces? In non conservative forces like friction work done is dependent on the path that we take to reach one position to the other position but how? And why does potential energy have a meaning only for conservative force field and not...
  37. K

    Nabla calculus and conservative forces

    1. The problem statement I'm trying to show that the magnetic force is only conservative if dB/dt=0 Homework Equations F=q[E+(v\timesB)] Conservative if ∇\timesF=0 ∇\times(A\timesB)=A(∇\cdotB)-B(∇\cdotA)+(B\cdot∇)A-(A\cdot∇)B Maxwells equation: ∇\timesE=-∂B/∂t The Attempt at a Solution...
  38. P

    Distinguish Between Conservative & Non-Conservative Forces

    I have a general understanding of what a conservative force is. I am wondering if its possible to confuse a non conservative force with a conservative one. for example, speaking hypothetically, if you were measuring a force in an referance frame that was moving with constant acceleration...
  39. M

    Concept of Work and Conservative Forces

    Can work also be the transformation of energy? For instance, an object in free fall goes from an initial height (that has potential energy) to a final height where there is kinetic energy. If energy is conserved then how is work being done?
  40. A

    Conservative forces and systems

    I read in a book that if the constraint forces do work, the system is conservative, else it's nonconservative. In that case, consider a system of two bodies moving in an elliptical path under gravitational attraction. Since the gravitational force is continuously doing work on the particles, by...
  41. J

    Kibble book exercise about conservative forces

    Homework Statement Kibble book exercise 1, chapter 3. It is the following: Find which of the following forces are conservative, and, for those that are conservative, determine the corresponding potential energy function (a and b are constants, and a is a constant vector) ii) Fx= a*y...
  42. B

    Conservative Forces and Fg Questions

    Im SOOOO Confused. Im studying Work, Energy and Society and I'm really darn confused. I have the highest mark in the course, and If I'm confused, I'm wondering how others are feeling. Whenever I have multiple questions, and they may sound stupid but please help me out: 1. Does Fg do...
  43. B

    Conservative forces and Mechanical Energy

    1. A 750-kg automobile is moving at 20.0 m/s at a height of 5.0 m above the bottom of a hill when it runs out of gasoline. The car coasts down the hill and then continues coasting up the other side until it comes to rest. Ignoring frictional forces and air resistance, what is the value of...
  44. N

    Exam question about Conservative Forces

    Homework Statement (This was a problem in an examination test of physics) Problem: point 1) Make an example of conservative force; point 2) Write the vectorial expression point 3) Choose a coordinate system and find the expression of the potential energy in a generic point in the space...
  45. S

    Having trouble thinking about conservative forces

    I'm having trouble with the concept of conservative forces. I've been studying things of that nature for awhile now and can make most calculations on my own, but there are a few specific details that confuse me. It's easiest to explain my confusion with two simple examples. First Example...
  46. H

    Solving a problem using energy and conservative forces concepts

    Homework Statement It asks me to work out the work done by force P and it tells me that the ball m has a CONSTANT speed during its displacement. That diagram is taken from a book which has already solved the excercise without using the concepts of energy and conservative forces. It used a...
  47. S

    Conservative/ Non conservative forces problem

    Im kind of struggling with some conservative/nonconservative force problems. Someone please help me. Homework Statement A 1.8 kg rock is released from rest at the surface of a pond 1.8 m deep. As the rock falls, a constant upward force of 4.3 N is exerted on it by water resistance. Let...
  48. S

    Conservative Forces: Friction a Non-Conservative Force?

    Why is friction a non-conservative force ? It arises to Electric interactions which is a conservative force(field).
  49. S

    Total Mech Energy and Conservative forces

    I've managed to really confuse myself on the conservation of energy in a system. I guess the basic question boils down to why is the total mechanical energy of a system a meaningful quantity. I understand E for a point particle in a conservative field is constant. I understand E for CoM...
  50. M

    Conservative Forces (gravity/voltage)

    In both voltage and gravity, I know that the work done in moving a particle between two points is independent of the path taken. For my problem, it states "what if the path did make a difference?" I'm suppose to design a device/machine that will move a particle or object repeatedly between...