A river descends 15 m through rapids. The speed of the water is 3.2 m / s upon entering the ra

step 1 Well, the increase in the kinetic energy of water is given by delta K is equal to half mvf squar

A river descends 15 m through rapids. The speed of the...

A river descends $15 \mathrm{~m}$ through rapids. The speed of the water is $3.2 \mathrm{~m} / \mathrm{s}$ upon entering the rapids and $13 \mathrm{~m} / \mathrm{s}$ upon leaving. What percentage of the gravitational potential energy of the water-Earth system is transferred to kinetic energy during the descent? (Hint: Consider the descent of, say, $10 \mathrm{~kg}$ of water.)

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Key Concepts

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. In the context of a river descending through rapids, it represents the energy available from the height difference that can be converted into other forms, such as kinetic energy.

Kinetic Energy

Kinetic energy is the energy associated with the motion of an object. For a river, the speeds of the water entering and leaving the rapids determine the kinetic energy at those points, which is used to assess the change resulting from the energy conversion during the descent.

Conservation of Energy

The principle of conservation of energy states that energy in an isolated system remains constant over time, transitioning between different forms without being created or destroyed. It is used here to relate the decrease in gravitational potential energy of the water to the increase in its kinetic energy.

Energy Conversion Efficiency

Energy conversion efficiency quantifies how effectively one form of energy is transformed into another. In this problem, calculating the percentage of gravitational potential energy that is converted into kinetic energy allows for an evaluation of the efficiency of energy transfer during the water’s descent.

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