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plzzzz.... explain meaning of conservative force feilds with an example

6 years ago

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Answers : (2)

										

conservative force is the force, work done by which is independent of the path followed but depends just on the initial and the final points.


 Example is gravitational force.


Explanation: suppose a body reaches a height H by first stairs, then by lift, and finally via an inclined plane. In all the cases net displacement is the same, <mind it not the distance>


So the magnitude of work done will also be the same which is weight of the body*displacement.


So the work done against gravitational force will be same.


DO APPROVE IF YOU LIKE


DEEKSHA


.


.


.

6 years ago
										

 


Dear Kedar


A conservative force is a force with the property that the 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 net work done  by a conservative force is zero


Suppose that a non-uniform force-field ${\bf f}({\bf r})$ acts upon an object which moves along a curved trajectory, labeled path 1, from point $A$ to point $B$. See Fig.. the work $W_1$ performed by the force-field on the object can be written as a line-integral along this trajectory:










\begin{displaymath} W_1 = \int_{A\rightarrow B: {\rm path} 1} {\bf f}\!\cdot\!d{\bf r}. \end{displaymath} (1)


Suppose that the same object moves along a different trajectory, labeled path 2, between the same two points. In this case, the work $W_2$ performed by the force-field is










\begin{displaymath} W_2 = \int_{A\rightarrow B:{\rm path} 2} {\bf f}\!\cdot\!d{\bf r}. \end{displaymath} (2)


Basically, there are two possibilities. Firstly, the line-integrals (1) and (2) might depend on the end points, $A$ and $B$, but not on the path taken between them, in which case $W_1=W_2$. Secondly, the line-integrals (1) and (2) might depend both on the end points, $A$ and $B$, and the path taken between them, in which case $W_1\neq W_2$ (in general). The first possibility corresponds to what physicists term a conservative force-field, whereas the second possibility corresponds to a non-conservative force-field.


 










Figure : Two alternative paths between points $A$ and $B$

\begin{figure} \epsfysize =2.5in \centerline{\epsffile{line.eps}} \end{figure}


 


 


Informally, a conservative force can be thought of as a force that conserves mechanical energy


The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces (in both cases, the energy is converted to heat and cannot be retrieved)


 


All the best.


AKASH GOYAL


AskiitiansExpert-IITD


 


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6 years ago

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