A 2.00-kg rock is released from rest at a height of 20.0 m....

A 2.00-kg rock is released from rest at a height of 20.0 m. Ignore air resistance and determine the kinetic energy, gravitational potential energy, and total mechanical energy at each of the following heights: $20.0,10.0,$ and $0 \mathrm{m}$

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Key Concepts

Conservation of Energy

This principle states that within an isolated system where non-conservative forces (like friction or air resistance) are negligible or absent, the total energy remains constant. In the context of the problem, it means that although the form of energy may change (from potential to kinetic), their sum will not change as the rock falls.

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion, typically given by the formula KE = ½ mv², where m is the mass and v is the velocity. As the rock falls and its speed increases, its kinetic energy increases correspondingly.

Gravitational Potential Energy

Gravitational potential energy is the energy stored by an object due to its position in a gravitational field, often calculated using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. As the rock descends, this energy decreases as it is converted into kinetic energy.

Total Mechanical Energy

Total mechanical energy is the sum of the kinetic and gravitational potential energies of an object. In the absence of non-conservative forces, this total remains constant, illustrating how energy transforms from one form to another without an overall loss.

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