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In the case of a conservative force, the potential energy _______.
can be defined for any configuration of the system
depends on the work done by friction
is zero
is path dependent
can be defined for any configuration of the system
Potential energy is a scalar quantity defined only for conservative forces, where the work done depends solely on the initial and final positions of the object. Since the work done is independent of the path taken, the potential energy U can be uniquely defined for any configuration (x,y,z) in the system's field.
Potential energy is a scalar quantity defined only for conservative forces, where the work done depends solely on the initial and final positions of the object. Since the work done is independent of the path taken, the potential energy U can be uniquely defined for any configuration (x,y,z) in the system's field.
Think of potential energy like the altitude on a topographic map; no matter how you hike up a mountain, your potential energy change depends only on your starting and ending elevations.
C-P-I: Conservative forces have Potential energy that is Independent of path.
W=тИТ╬ФU тАФ Relation between work and change in potential energy
F=тИТтИЗU тАФ Conservative force as the negative gradient of potential energy
For a conservative force F, the work done W is the negative change in potential energy, expressed as W=тИТ╬ФU. Mathematically, this exists if the curl of the force field is zero, i.e., тИЗ├ЧF=0. This allows for a path-independent potential function U(r) such that F=тИТтИЗU.
Conservative forces are path-independent.
Non-conservative forces (like friction) dissipate energy as heat and cannot be represented by a simple scalar potential energy function.
The total mechanical energy E=K+U is conserved in systems involving only conservative forces.
Simplifies calculations in dynamics.
Allows for the law of conservation of mechanical energy.
Not applicable to non-conservative forces like kinetic friction or air drag.
Gravitational field problems
Electrostatic potential energy calculations
Option B is wrong because friction is a non-conservative force.
Option C is wrong because potential energy is relative and defined by a reference point, not necessarily zero.
Option D is wrong because conservative forces are path-independent, not path-dependent.
A is correct тАФ Potential energy is a well-defined scalar function of position for conservative force fields, independent of the path taken to reach that configuration.
In competitive physics, always check if the force is conservative (like gravity or spring force) before applying the conservation of mechanical energy.
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