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System in which the forces acting on a body do work which is independent of the path followed by the body.

For example, when gravity is the only force acting on a body the system is conservative. However, this is no longer the case if friction is acting on the body.

In a conservative system it can be shown that the forces acting on a body are equal to spatial derivative of the potential energy. The potential energy (V) due to gravity is mgh where m is the mass of the body, g is the acceleration due to gravity and h is the height of the body above the ground. In this case, the force is given by,

F=dV/dh=mg

If a ball is thrown vertically in the air and reaches a height h or if it is thrown at any other angle to reach the same height, the potential energy of the ball will be mgh regardless of the path taken.

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