State principle of conservation of mechanical energy. A...

State principle of conservation of mechanical energy. A block of mass $2 \mathrm{~kg}$ moving with speed $2 \mathrm{~m} / \mathrm{s}$ compresses a spring through a distance $20 \mathrm{~cm}$ before its speed is halved. The value of spring constant is $75 \mathrm{~N}$ then the value of $\mathrm{N}$ is ?

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Key Concepts

Conservation of Mechanical Energy

This principle states that in the absence of non-conservative forces (such as friction), the total mechanical energy of a system, which is the sum of its kinetic energy and potential energy, remains constant over time. It provides a framework for understanding energy transformations between different forms in a closed system.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. It is quantified as one half of the mass of the object multiplied by the square of its velocity, and it plays a central role in energy conservation problems where the speed of an object changes due to energy transfer.

Elastic Potential Energy

Elastic potential energy is the energy stored in elastic materials such as springs when they are deformed by compression or stretching. This energy is proportional to the square of the displacement from equilibrium and is governed by the spring constant, which measures the stiffness of the spring.

Energy Transformation

Energy transformation refers to the process in which energy changes from one form to another without any loss in total energy, under ideal conditions. In many mechanical systems, such as those involving moving objects and elastic springs, energy shifts between kinetic energy and potential energy.

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