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Is it true that potential energy of a particle always decreases in the direction of conservative force acting on it?

Pratik Aman
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1 Answers1

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Conservative forces are associated with potential energies, the relation between them is given by: enter image description here

F is the conservative force, U is the potential energy. That equation says that the conservative force acts in a direction of decreasing potential energy. So if a particle only experiences the force associated with the potential energy, it is true. It will move in the direction of decreasing potential energy

Gotaquestion
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  • ok take a inverse square force like A/r^2 always pointing towards origin. where 'A' is some constant and 'r' is distance from origin of force. then potential energy function for this is U= A/r + c . where c is arbitrary constant. then potential in this case increases in direction of force. – Pratik Aman Oct 03 '13 at 12:58
  • The force toward origin should be (A/r^2)*(-R) R capital being the unit vector in r direction. The potential energy is MINUS the integration of F which is U= -A/r+c. There are two minuses, one from the force and one from the relation above, so the function you integrate is positive, the result of the integral is negative. So at r=0 the potential is minus infinity while at infinity it is 0. Is it clear? – Gotaquestion Oct 03 '13 at 13:09