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Question #42165

Difficulty: 8/10 | 🟢 Free

The Question

A non-ideal rubber cord is slowly stretched from its natural length $x = 0$ to an extension $x = 0.1 \text{ m}$ and then slowly relaxed back to $x = 0$ . The magnitude of the restoring force exerted by the cord is $F_{s}(x) = kx + \alpha x^2$ during stretching and $F_{r}(x) = kx - \alpha x^2$ during relaxation, where $k = 100 \text{ N/m}$ and $\alpha = 300 \text{ N/m}^2$ . Calculate the net work done by the restoring force of the cord over the complete cycle.

Options

A.
$-0.2 \text{ J}$
B.
$0 \text{ J}$
C.
$+0.2 \text{ J}$
D.
$-0.1 \text{ J}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

State Function vs Path Function|Work against Conservative Force|Elastic Hysteresis Loop

Why This Question Is Tricky

Common Mistakes

This question tests the distinction between state functions (like potential energy in conservative fields) and path functions (like work in non-conservative fields).

Students often fall into the trap of assuming that any elastic restoring force is conservative, leading them to incorrectly conclude that the net work done in a closed cycle is zero (Option B).

By introducing an elastic hysteresis loop where the force depends on the direction of deformation, the problem requires explicit integration over the path, demonstrating that mechanical energy is dissipated as heat and the system cannot be described by a unique potential energy state function.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermodynamics - Class 11 Part 2
Concept	State Function vs Path Function
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free