Assertion: Work done by spring force is always negative....

Assertion: Work done by spring force is always negative. Reason: In compression or stretching of a spring from its natural length, work is done on the spring against the restoring force.
(A) A
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Key Concepts

Elastic Potential Energy

When an external force compresses or stretches a spring, work is done on the system and energy is stored as elastic potential energy, typically expressed as U = ½ kx². This concept explains how energy is accumulated in the spring when work is done against its restoring force.

Sign Conventions in Work and Energy Transfer

The sign of the work done reflects the direction of energy transfer. A negative work done by a force means that energy is taken out of the moving system, such as the work done by the spring force during deformation, while positive work indicates energy being supplied to the system by an external force.

Work Done by a Force

Calculating work involves integrating the force over the displacement of the object. For variable forces like that of a spring, this integration takes into account the changing magnitude and direction of the force, leading to work expressions that often include a negative sign, which implies that the force is acting opposite to the direction of displacement.

Hooke's Law

Hooke's Law states that the force exerted by a spring is proportional to the displacement from its equilibrium position and acts in the opposite direction, expressed as F = -kx. The negative sign in this equation indicates that the spring's force is a restoring force, always acting to return the spring to its natural length.

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