In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity. (a) What is (delta)Ug of 1.0 kg of water?

Verified step by step guidance

1. Identify the relevant formula for gravitational potential energy, which is \\(\\Delta U_g = mgh\\), where \\m\\ is the mass of the object, \\g\\ is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and \\h\\ is the height through which the object falls.
2. Substitute the given values into the formula. Here, the mass \\m\\ of the water is 1.0 kg, \\g\\ is 9.8 m/s^2, and \\h\\ is 25 m.
3. Calculate the product of the values substituted into the formula to find the change in gravitational potential energy \\(\\Delta U_g\\).
4. Keep in mind that the result will be negative, indicating a loss in potential energy as the water falls.
5. This calculated gravitational potential energy represents the energy available to be converted into other forms, such as mechanical energy to spin the turbine.

Key Concepts

Gravitational Potential Energy (Ug)

Gravitational potential energy (Ug) is the energy an object possesses due to its position in a gravitational field. It is calculated using the formula Ug = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height above a reference point. In this context, the height is the distance the water falls, which is 25 m.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In the case of the hydroelectric dam, the gravitational potential energy of the falling water is converted into kinetic energy as it falls, and then into mechanical energy as it spins the turbine, ultimately generating electrical energy.

Work Done by Gravity

The work done by gravity on an object is equal to the change in gravitational potential energy as the object moves in the gravitational field. For the falling water, the work done by gravity can be calculated as the product of the weight of the water and the height it falls. This work is what allows the water to do useful work on the turbine, contributing to electricity generation.