A block of mass m=2.0 kg is dropped from height h=40 cm onto a spring of spring constant k=196

step 1 Here we have to determine the maximum spring compression. So using the given situation and conse

A block of mass m=2.0 kg is dropped from height h=40 cm...

A block of mass $m=2.0 \mathrm{~kg}$ is dropped from height $h=40 \mathrm{~cm}$ onto a spring of spring constant $k=1960 \mathrm{~N} / \mathrm{m}$ (Fig. 8-39). Find the maximum distance the spring is compressed.

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Key Concepts

Energy Conservation

In mechanics, the principle of energy conservation states that the total mechanical energy of a system remains constant if only conservative forces (like gravity and elastic forces) are acting. In problems involving a falling mass and a spring, gravitational potential energy is converted into elastic potential energy stored in the spring at maximum compression.

Gravitational Potential Energy

Gravitational potential energy is the energy that an object possesses because of its position relative to the Earth. It is calculated as mgh, where m is mass, g is the acceleration due to gravity, and h is the height. This energy is transformed into kinetic energy as the object falls.

Elastic Potential Energy

Elastic potential energy is the energy stored in an object when it is deformed elastically, such as when a spring is compressed or stretched. It is given by the expression (1/2)kx², where k is the spring constant and x is the displacement from the equilibrium position.

Hooke's Law

Hooke's Law describes the linear relationship between the force exerted by a spring and its displacement from equilibrium, expressed as F = kx. This law is fundamental in understanding how the spring force opposes the compression or extension caused by an external load.

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