A block of mass 5 ·0 kg is suspended from the end of a...

A block of mass $5 \cdot 0 \mathrm{~kg}$ is suspended from the end of a vertical spring which is stretched by $10 \mathrm{~cm}$ under the load of the block. The block is given a sharp impulse from below so that it acquires an upward speed of $2 \cdot 0$ $\mathrm{m} / \mathrm{s}$. How high will it rise ? Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$

Key Concepts

Hooke's Law

Hooke's Law describes the linear relationship between the force exerted by a spring and its displacement from its natural length. This law is fundamental when analyzing spring systems, establishing that the force is proportional to the displacement, with the constant of proportionality being the spring constant.

Equilibrium in Spring-Mass Systems

In a spring-mass system, equilibrium occurs when the upward spring force exactly balances the downward gravitational force acting on the mass. Understanding the equilibrium condition is essential for determining properties such as the spring constant and the initial displacement of the spring under load.

Conservation of Mechanical Energy

The conservation of mechanical energy principle states that the total mechanical energy (the sum of kinetic energy, gravitational potential energy, and elastic potential energy) remains constant in the absence of non-conservative forces. This principle is used to analyze how kinetic energy, gained from an impulse, is converted into potential energies as the mass moves.

Elastic Potential Energy

Elastic potential energy is the energy stored in a spring when it is deformed from its natural length. It is given by the expression (1/2) times the spring constant times the square of the displacement. This concept is crucial for understanding how energy is stored and released in spring systems during motion.

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