A block of mass 2 kg is held over a vertical spring with...

A block of mass $2 \mathrm{~kg}$ is held over a vertical spring with spring unstretched. Suddenly, if block is left free, maximum compression of spring is [spring constant $K=200 \mathrm{~N} / \mathrm{m}]:$ (A) $0.2 \mathrm{~m}$ (B) $0.1 \mathrm{~m}$ (C) $0.4 \mathrm{~m}$ (D) $0.05 \mathrm{~m}$

A block of mass $2 \mathrm{~kg}$ is held over a vertical spring with spring unstretched. Suddenly, if block is left free, maximum compression of spring is [spring constant $K=200 \mathrm{~N} / \mathrm{m}]:$
(A) $0.2 \mathrm{~m}$
(B) $0.1 \mathrm{~m}$
(C) $0.4 \mathrm{~m}$
(D) $0.05 \mathrm{~m}$

Key Concepts

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field, typically expressed as mgh, where m is mass, g is the acceleration due to gravity, and h is the height above a reference point. In the context of a falling mass attached to a spring, the loss in gravitational potential energy directly contributes to the increase in the spring's elastic potential energy, enabling the calculation of the spring's maximum compression.

Conservation of Energy

This concept states that energy in a closed system is conserved, meaning that the energy lost by one part of the system is gained by another. In a mass-spring system, as the block falls, the gravitational potential energy lost is converted into the elastic potential energy stored in the spring. Analyzing the energy conversion provides the basis for calculating factors such as the maximum compression of the spring.

Elastic Potential Energy

Elastic potential energy is the energy stored in a deformable object, such as a spring, when it is compressed or stretched. It is quantified by the formula (1/2)kx², where k is the spring constant and x is the displacement from the spring's unstressed position. This concept is crucial in problems involving spring systems, as it relates the mechanical properties of the spring to the work done during compression or elongation.

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