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Conservative Forces: A force is conservative if the work it does on a particle moving between any two points is independent of the path followed by the particle. The work done by a conservative force around a closed path is zero. A conservative force always conserves mechanical energy. A force is called conservative if it meets any of these conditions:
1) The curl of F is zero:
2) The work done, W, on a particle by a conservative force moving through a simple closed path is zero:
3) The force can be written as the gradient of a potential, Φ:
The gravitational force is an example of conservative force. Similarly, the force exerted by a spring on an object attached to it, is also an example of conservative force. Potential energy can be associated with the conservative forces. The work done on an object by a conservative force is equal to the initial value of potential energy minus the final value of the potential energy:
Potential Energy:
The energy possessed by a particle or system of particles due to the position is called potential energy. As the arrangement of a system of particles or objects changes, the potential energy of the system changes. It can be thought of as energy stored within a physical system. This energy can be released or converted into other forms of energy, including kinetic energy.
1) The gravitational potential energy (PE) of an object of mass m is the energy possessed by it due to its position from the ground (at a height h from the ground) at that point. It is given as follows:
2) The gravitational potential energy (PE) of a mass m1 at a distance R from another mass m2 is given by:
3) Electrostatic potential energy when electrical charges q1 and q2 are at distance d away from each other is given by:
where k is a constant of proportionality.
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Newtonian Mechanics