A 2.0 kg block is dropped from a height of 40 cm onto a spring of spring constant k=1960 Nm^-1

step 1 In this question we have given that a 2 kilogram block is dropped from a height of 40 semi onto

A 2.0 kg block is dropped from a height of 40 cm onto a...

A $2.0 \mathrm{~kg}$ block is dropped from a height of $40 \mathrm{~cm}$ onto a spring of spring constant $k=1960 \mathrm{Nm}^{-1}$, Find the maximum distance the spring is compressed.
(a) $0.080 \mathrm{~m}$
(b) $0.20 \mathrm{~m}$
(c) $0.40 \mathrm{~m}$
(d) $0.10 \mathrm{~m}$

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Key Concepts

Conservation of Energy

This principle states that in a closed system, the total energy remains constant, though it can change forms. In mechanical problems, gravitational potential energy can transform into elastic potential energy, and vice versa, which allows us to set up equations to solve for unknown quantities such as displacement or velocity.

Gravitational Potential Energy

This is the energy an object possesses due to its position in a gravitational field. It depends on the object's mass, the height above a reference level, and the acceleration due to gravity, and is calculated by the product of these factors.

Elastic Potential Energy

This is the energy stored when a spring is compressed or stretched. It is proportional to the square of the displacement from the spring's equilibrium position and the spring constant, which measures the stiffness of the spring.

Energy Transformation in Mechanical Systems

This concept involves the conversion of energy from one form to another, such as from gravitational potential energy to elastic potential energy in systems involving springs. Understanding this transformation is crucial to analyzing the behavior of mechanical systems and solving for unknown parameters.

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