# Conservative and Non Conservative Forces

by saiaspire
Tags: conservative, forces
 P: 16 Hi, i have a simple question.. What exactly are conservative and non - conservative forces? and why are some forces conservative and other are not? Thank you..
 HW Helper P: 2,274 If the force produces the same work regardless of its trajectory between two points then is conservative, if not the is non-conservative. This is usually represented by $$\oint \vec{F} \cdot \vec{ds} = 0$$
 PF Patron HW Helper P: 2,688 To expand on Cyclovenom's response, an example of a conservative force, or one which does the same amount of work regardless of the path it works over is gravity. You gain the same amount of kinetic energy whether you fall straight down 4 meters or slide down a frictionless slope until your vertical height decreased by four meters. Friction is an example of a nonconservative force. The longer the path, the more work it does. Does this help?
P: 16

## Conservative and Non Conservative Forces

the terms u have given are pretty much the same as my textbook...

i want some better explanation so that i can understand what it really means..
 HW Helper P: 2,274 What isn't clear? You have 2 points, and if you move a particle from A to B, by following different trajectories and you still get the same WORK, then the force is CONSERVATIVE. When the work is trajectory dependent the force is NON-CONSERVATIVE. Remember the formal definition of work is $$W = \int_{c} \vec{F} \cdot d \vec{r}$$ Work depends on the trajectory.
 Mentor P: 10,699 Here's my loose qualitative definition: If you can do work against a force, and then "get that work back" later, then the force is conservative. For example, when you lift an object a distance h against gravity, you have to do work F.d = mgh. If you then let the object fall, you get that work back, either in the form of the object's kinetic energy at the bottom, or you can attach the object to a string or pulley and let it do work on something else as it falls. On the other hand, if you can't "get that work back" later, then the force is non-conservative. For example, if you push a book across a table top, doing work F.d against friction, then let go, the book just stays there. You've effectively "lost" the work you did, and you can't get it back again as kinetic energy of the book, or work done on something else. "Frictional heat" doesn't count here, because you can't convert the thermal energy completely back to mechanical energy of the object.
 P: 5 conservative forces are defined as: 1.work done by the force on a particle moving between any two points is independent of the path taken by the particle;2. and the work done is 0 when moving through ay closed path.(intial position=final position
 P: 30 Also using the above mentioned properties the work done by the force may be written as the difference in some potential energy function for that force. Then the work-energy theorem may be restated as a conservation of mechanical energy principle with the given potential energy function. This conservation of mechanical energy may be used to fully exploit the concept of a conservative force because under their action, mechanical energy is "conserved" (hence conservative).
 P: 2 Conservative Forces: As you saw when lifting a book, the work that you do "against gravity" in lifting is stored (somewhere... Physicists say that it is stored "in the gravitational field" or stored "in the Earth/book system".) and is available for kinetic energy of the book once you let go. Forces that store energy in this way are called conservative forces. Gravity is a conservative force, and there are many others. Elastic (Hooke's Law) forces, electric forces, etc. are conservative forces. Nonconservative Forces: As you say when pushing a book, the work that you do "against friction" is apparently lost - it is certainly not available to the book as kinetic energy! Forces that do not store energy are called nonconservative or dissipative forces. Friction is a nonconservative force, and there are others. Any friction-type force, like air resistance, is a nonconservative force. The energy that it removes from the system is no longer available to the system for kinetic energy. Of course, if energy is a "real thing," the energy taken away by a nonconservative force can't just disappear! I wonder where it goes....

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