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Chapter 6: Problem 33

Explain the conversion of energy that takes place when the sluice of a dam is opened. a. Potential energy stored in the water held by the dam will convert to kinetic energy when it falls through the opening of the sluice. b. Kinetic energy stored in the water held by the dam will convert to potential energy when it falls through the opening of the sluice. c. Potential energy stored in the water held by the dam will convert to electrical energy, when it falls through the opening of the sluice. d. Hydrothermal energy stored in the water held by the dam will convert to kinetic energy, when it falls through the opening of the sluice.

Short Answer

Expert verified
a. Potential energy stored in the water held by the dam will convert to kinetic energy when it falls through the opening of the sluice.

Step by step solution

01

Identify the Stored Energy Type

The water held by the dam has a certain amount of energy due to its elevated position. This energy is known as potential energy.
02

Energy Conversion Process

When the sluice of the dam is opened, the water starts to fall. During this fall, the potential energy of the water is converted into another type of energy.
03

Determine the Resulting Energy Type

As the water falls, it gains speed and motion. The initial potential energy is converted into kinetic energy due to the movement of the water.
04

Rule Out Incorrect Options

Analyze each option: (a) describes the conversion from potential to kinetic energy accurately. (b) is incorrect because it suggests the inverse conversion. (c) describes the conversion to electrical energy, which doesn't directly occur just from water falling. (d) introduces hydrothermal energy, which isn't relevant here.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

potential energy
When water is held behind a dam, it is positioned at a higher elevation compared to the downstream side. This elevated position gives the water potential energy. Potential energy is the energy that is stored due to an object鈥檚 position relative to other objects.

In the context of a dam, the higher the water level, the more potential energy it possesses. This energy can be calculated using the formula: \(PE = m \times g \times h\) where:
  • \(PE\) is the potential energy in joules (J),
  • \(m\) is the mass of the water in kilograms (kg),
  • \(g\) is the acceleration due to gravity (9.8 m/s^2),
  • \(h\) is the height of the water above a reference point in meters (m).

Thus, the potential energy of the water depends on its height and mass. This stored energy is what is converted when the sluice gates of the dam are opened.
kinetic energy
Once the sluice gates are opened, the water held by the dam begins to fall due to gravity. As it falls, the potential energy stored in the water is converted into kinetic energy. Kinetic energy is the energy of motion, and it can be calculated using the formula: \(KE = \frac{1}{2}mv^2\) where:
  • \(KE\) is the kinetic energy in joules (J),
  • \(m\) is the mass of the water in kilograms (kg),
  • \(v\) is the velocity of the moving water in meters per second (m/s).

As the water accelerates downwards, its speed increases, thus increasing its kinetic energy. The initial potential energy the water had due to its height is transformed into kinetic energy, explaining why fast-moving water has the capacity to do work, such as generating electricity through turbines.
hydropower
Hydropower is a form of renewable energy that harnesses the power of moving water to generate electricity. The process begins with potential energy stored in elevated water behind a dam. As the water flows down, this potential energy converts to kinetic energy. This kinetic energy can then be harnessed by turbines to generate electricity.

Here's a simplified explanation of how it works:
  • Water is stored in a reservoir behind a dam, possessing potential energy.
  • When the dam鈥檚 sluice gates open, water flows down, converting potential energy to kinetic energy.
  • The kinetic energy of moving water turns turbines, which are connected to generators.
  • These generators then convert mechanical energy into electrical energy, providing power for various uses.
Hydropower is a clean source of energy because it does not produce greenhouse gases during operation. Furthermore, it is a reliable and efficient energy source, especially in regions with abundant water resources.

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