A 2 kg block is dropped from a height of 0.4 m on a spring of force constant K=1960 Nm^-1. The

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A 2 kg block is dropped from a height of 0.4 m on a spring...

A $2 \mathrm{~kg}$ block is dropped from a height of $0.4 \mathrm{~m}$ on a spring of force constant $K=1960 \mathrm{Nm}^{-1}$. The maximum compression of the spring is
(a) $0.1 m$
(b) $0.2 m$
(c) $0.3 m$
(d) $0.4 m$

Key Concepts

Conservation of Mechanical Energy

This principle states that in an isolated system where only conservative forces are present, the total mechanical energy remains constant. In problems involving gravitational and elastic potential energies, the energy lost by one form (e.g., gravitational potential energy during free fall) is entirely converted into another form (e.g., elastic potential energy in a spring), enabling calculations such as the maximum compression of the spring.

Gravitational Potential Energy

Gravitational potential energy is the energy that an object possesses due to its position in a gravitational field. It is quantified by the product of mass, gravitational acceleration, and height. In energy conversion problems, this form of energy is the initial stored energy that gets transformed into other energy forms when an object moves under gravity.

Elastic Potential Energy

Elastic potential energy is the energy stored in an elastic medium such as a spring when it is deformed (either compressed or stretched). The energy stored is proportional to the square of the displacement from the equilibrium position and is determined using the spring's stiffness or force constant. This concept is fundamental in understanding how energy is stored and released by elastic objects.

Spring Constant and Hooke's Law

The spring constant is a parameter that measures the stiffness of a spring. Hooke's Law relates the force exerted by the spring to its displacement from equilibrium, establishing a linear relationship between them. This concept is crucial for analyzing how much a spring will compress or extend under a given load.

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