Question

The water passing over Victoria Falls, located along the Zambezi River on the border of Zimbabwe and Zambia, drops about \(105 \mathrm{m} .\) How much internal energy is produced per kilogram as a result of the fall?

Short answer

The internal energy produced per kilogram of water is approximately 1030.05 J/kg.

Step-by-step solution

Understand the Problem

The water falling from a height will convert its potential energy into internal energy due to gravity. We need to calculate the internal energy produced per kilogram of water as it falls 105 meters.

Know the Formula for Potential Energy

Potential energy (PE) is given by the formula \(PE = mgh\), where \(m\) is mass, \(g\) is the acceleration due to gravity, and \(h\) is the height.

Simplify for Energy per Kilogram

Since we need the energy per kilogram, we can simplify the formula to \(PE = gh\), assuming \(m = 1 \text{ kg}\). This is because we will calculate the energy produced for 1 kilogram of water.

Use the Gravitational Constant

In most physics problems, the gravitational constant \(g\) is approximately \(9.81 \text{ m/s}^2\). Use this value for calculations.

Calculate Internal Energy Per Kilogram

Substitute the values into the formula: \[ PE = gh = 9.81 \, \text{m/s}^2 \times 105 \, \text{m} \]This yields: \[ PE = 1030.05 \, \text{J} \]

Conclude the Calculation

The potential energy, which converts to internal energy per kilogram of water, is approximately \(1030.05 \text{ J/kg}\). Therefore, this is the amount of internal energy produced per kilogram as the water falls.

Key concepts

Gravitational Potential Energy

Gravitational potential energy is an essential concept in physics that describes the energy an object has due to its position in a gravitational field. Imagine holding an apple above the ground; it has potential energy because of its elevated position. This energy can be described using the formula:

• \( PE = mgh \)

where:

• \(m\) represents the mass of the object
• \(g\) is the acceleration due to gravity
• \(h\) refers to the height above a reference point

When the apple falls, this potential energy gets converted into kinetic energy. Similarly, when water cascades over a waterfall like Victoria Falls, the energy transformations follow the same principles.

Internal Energy Conversion

As the water plummets over the majestic Victoria Falls, a fascinating energy transformation occurs. The potential energy at the top of the fall is not lost but rather changes form. As the water descends, its potential energy transforms into internal energy. This could include thermal energy, resulting from the friction and turbulence as the water hits the rocks and water below, and kinetic energy is briefly increased before being dissipated. This illustrates the law of conservation of energy, which states that energy cannot be created or destroyed but only changed from one form to another. In real-world scenarios like this, the energy transformations are complex but can be predicted by understanding fundamental physics concepts.

Energy per Kilogram Calculations

When we discuss energy in terms of per kilogram, it becomes easier to standardize calculations, especially when dealing with fluids like water. By calculating energy per kilogram, we can focus on the work done on a single unit mass, simplifying our measurements.For the water at Victoria Falls, simplifying calculations involves using a mass of 1 kilogram while considering the height of the fall. This leads to using a modified version of the potential energy formula where:

• \( PE = gh \)

This simplification makes it easier to understand the energy conversion per kilogram of water, yielding clear, interpretable results.

Victoria Falls Physics

Victoria Falls is not just a breathtaking natural wonder; it's also a perfect example to apply physics concepts. Located on the border between Zimbabwe and Zambia, the falls present an extraordinary setting for studying gravitational effects and energy transformations. When water falls from the height of approximately 105 meters, it undergoes significant energy changes. The potential energy at the top is maximum, converting to internal energy at the bottom. The scale and power of Victoria Falls provide a dynamic illustration of how physics operates in nature on a grand scale. Such examples help in visualizing basic physics concepts and their real-world applications.

Gravitational Constant

The gravitational constant \(g\) is a fundamental value in physics, representing the acceleration due to gravity at Earth's surface. This value is approximately \(9.81 \ ext{m/s}^2\), although it can slightly vary based on location.In physics problems, this constant helps calculate forces and energies involving gravity. It's crucial when determining potential energy, as we rely on this value to understand how gravity influences objects. Without a consistent gravitational constant, calculations like those for Victoria Falls would become inaccurate.By using \(9.81 \ ext{m/s}^2\) in our calculations, we can reliably predict how gravitational forces will affect falling water, illustrating the consistent power of gravity on Earth.