The work done by non-conservative forces in a closed loop is ______.

Question

Examoogle · Accepted Answer

The correct answer is Option C: dependent on the path. Non-conservative forces are forces where the work done depends on the path taken between two points, rather than just the initial and final positions. Consequently, the net work done by these forces over a closed loop is generally non-zero and path-dependent.

Step-by-Step Solution & Concepts:
Non-conservative forces are forces where the work done depends on the path taken between two points, rather than just the initial and final positions. Consequently, the net work done by these forces over a closed loop is generally non-zero and path-dependent.

Working Principle: In a non-conservative system, such as friction or air resistance, energy is dissipated as heat, sound, or deformation. Because this energy loss is cumulative and proportional to the distance traveled, the work done $W = \int \vec{F} \cdot d\vec{r}$ over a closed path $\oint \vec{F} \cdot d\vec{r}$ results in a non-zero value, typically negative representing energy loss.

Key Formulas: $\oint_{C} \vec{F}_{nc} \cdot d\vec{r} 
eq 0$ — Representation of non-zero work done by non-conservative forces in a closed loop.; $W_{dissipated} = \Delta E_{thermal}$ — Relation between non-conservative work and energy dissipation.

Key Points: Conservative forces (like gravity or electrostatic forces) have a closed-loop work of zero.; Non-conservative forces always dissipate energy into the environment.; Work done by non-conservative forces is path-dependent because it depends on the total distance or contact duration.; Friction, air resistance, and viscosity are primary examples of non-conservative forces.

Advantages: Useful for modeling energy dissipation and real-world system losses.

Disadvantages: Makes calculation of total energy conservation more complex as it is not a state function.

Applications: Mechanical braking systems in vehicles.; Aerodynamic drag calculations for aircraft design.

Additional Info: In a conservative field, $
abla 	imes \vec{F} = 0$, whereas for non-conservative fields, the curl is non-zero.. Option A is incorrect because it describes conservative forces. Option B is incorrect as it is the definition of a conservative force field property.

Answer: C is correct — The work done by non-conservative forces depends on the path, and thus the total work in a closed loop is not zero.

Exam Tip: Remember that if the work is independent of the path, the force is conservative and its curl is zero; always check if energy is conserved in the problem statement.

Examoogle · Answer

Option A: always zero

Examoogle · Answer

Option B: independent of the path

Examoogle · Answer

Option D: negative

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