A block of mass 0.250 kg is placed on top of a light,...

A block of mass 0.250 $\mathrm{kg}$ is placed on top of a light, vertical spring of force constant 5000 $\mathrm{N} / \mathrm{m}$ and pushed downward so that the spring is compressed by 0.100 $\mathrm{m}$ . After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise?

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Key Concepts

Conservation of Energy

This principle states that energy cannot be created or destroyed, only converted from one form to another. In physics problems involving springs and gravitational fields, it is important because it allows us to relate the energy stored in a compressed or stretched spring to the gravitational potential energy of an object, ultimately determining quantities like maximum height or velocity.

Spring Potential Energy (Hooke's Law)

Hooke's Law describes how the force exerted by a spring is proportional to its displacement from equilibrium. The energy stored in the spring, given by 1/2 kx², is a key concept in analyzing systems where a spring compresses or extends, as it provides the initial energy that will be transformed into kinetic and subsequently gravitational potential energy.

Gravitational Potential Energy

This form of energy is associated with the position of an object in a gravitational field and is quantified by the product mgh, where m is the mass, g is the acceleration due to gravity, and h is the height above a reference point. In problems involving objects launched vertically, gravitational potential energy helps determine the maximum elevation reached once the initial kinetic energy from a spring or any other source has been converted into height.

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