Final answer:
Hydroelectric dams work by using the potential energy of stored water to generate electricity. When the water flows through turbines, it gains kinetic energy, which is converted into electrical energy. The energy generated can be calculated using the mass and velocity of the water.
Step-by-step explanation:
Hydroelectric dams work by storing water behind a dam and then allowing it to flow through turbines. The flowing water turns the turbines, which are connected to generators, and this mechanical energy is converted into electrical energy, generating hydroelectricity.
The key concept behind hydroelectric dams is the conversion of potential energy to kinetic energy. Water stored in the reservoir behind the dam has potential energy due to its height above the outlet. When the water flows through the turbines, it gains kinetic energy, which is used to do work on the generators, resulting in the generation of electricity.
In the case described, if 10,000 kg of water exited the dam at 2.0 m/s, the energy generated can be calculated using the equation:
energy = mass x velocity^2 / 2
Plugging in the values, we get energy = 10,000 kg x (2.0 m/s)^2 / 2 = 20,000 J.