A 1 kg stone is dropped down from a height of 2 m on a vertically fixed spring of spring const

step 1 We have problem number 145 in which there is a one kggy stone which is being dropped. So this is

A 1 kg stone is dropped down from a height of 2 m on a...

A $1 \mathrm{~kg}$ stone is dropped down from a height of $2 \mathrm{~m}$ on a vertically fixed spring of spring constant $\mathrm{k}=200 \mathrm{~N} \mathrm{~m}^{-1} .$ The maximum energy stored in the spring subsequently is. (in joule). Take $\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$. (a) $20.05$ (b) 25 (c) $26.2$ (d) 28

Key Concepts

Hooke's Law

Hooke's Law describes the behavior of springs and states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position, with the proportionality constant being the spring constant. This law is essential for calculating the elastic potential energy and analyzing the dynamics of spring systems.

Conservation of Mechanical Energy

The conservation of mechanical energy principle states that in an isolated system with only conservative forces, the total mechanical energy remains constant. This means that energy can transform between gravitational potential energy, kinetic energy, and elastic potential energy without any loss, which is critical in understanding how energy is stored in a spring when an object impacts it.

Elastic Potential Energy

Elastic potential energy is the energy stored in an elastic object, such as a spring, when it is deformed by stretching or compressing. It is given by one-half the spring constant multiplied by the square of the displacement from equilibrium. This form of energy is key when analyzing the behavior of spring-mass systems.

Gravitational Potential Energy

Gravitational potential energy is the energy stored by an object due to its position in a gravitational field. It is usually calculated as the product of the mass, gravitational acceleration, and the height above a reference point. In energy transformation problems, this energy is converted into other forms as the object moves.

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