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The work done by a conservative force in a closed loop is:
Positive
Negative
Zero
Infinite
Zero
A conservative force is defined by the property that the work done by it on an object moving between two points is independent of the path taken. Consequently, when an object returns to its starting point in a closed loop, the net displacement is zero, and the total work done by such a force is always zero.
A conservative force is defined by the property that the work done by it on an object moving between two points is independent of the path taken. Consequently, when an object returns to its starting point in a closed loop, the net displacement is zero, and the total work done by such a force is always zero.
Think of moving a ball up and down a hill; when you bring it back to its original height, the energy spent gaining potential energy is exactly returned as kinetic energy, resulting in no net change in the system's mechanical energy.
CON-ZERO: Conservative forces = Zero work in loops.
тИоCтАЛFconsтАЛтЛЕdr=0 тАФ Definition of work done in a closed loop
WABтАЛ=U(A)тИТU(B) тАФ Work done as the change in potential energy
The work done by a conservative force is derived from a scalar potential field, such that F=тИТтИЗU. By the fundamental theorem of calculus for line integrals, the integral тИоCтАЛFтЛЕdr=0 for any closed path C. This implies that energy is conserved within the system, as the force only stores energy in the potential field rather than dissipating it as heat.
Conservative forces include gravitational force, electrostatic force, and spring force.
Non-conservative forces, such as friction or air resistance, perform non-zero work in closed loops.
The energy stored by a conservative force is termed potential energy.
Enables the use of the principle of conservation of mechanical energy.
Calculation of satellite orbits in a gravitational field.
Designing circuit components that store charge in an electric field.
The path independence of conservative forces is a defining characteristic.
Option A and B are incorrect because they imply net energy gain or loss, which violates the law of conservation of mechanical energy for these specific fields.
C is correct тАФ The work done by a conservative force along a closed path is always zero because the net displacement is zero and the force is path-independent.
Always remember that if a force is path-dependent (like friction), it is non-conservative and its loop-work is never zero.