The mass of 1 cubic meter of freshwater at the top of a 100 m hydroelectric dam is 1,000 kg and...

Question:

The mass of 1 cubic meter of freshwater at the top of a 100 m hydroelectric dam is 1,000 kg and it has a potential energy of 980,000 J. At the bottom of the dam, the speed of the moving water is:

a. 44.3 m/s

b. 98 m/s

c. 1,960 m/s

d. 9,800 m/s

Kinetic Energy and Potential Energy

Kinetic energy describes the motion of an object; while, potential energy is energy due position or location of the object. Here, we are investigating the potential and kinetic energy of a freshwater.

Answer and Explanation:

Given:

  • mass of freshwater {eq}m = 1000 \ \text{kg}{/eq}
  • height {eq}h = 100 \ \text{m}{/eq}
  • Potential energy {eq}PE = 980000 \ \text{J}{/eq}

Required:

  • velocity of the moving water {eq}v = ?{/eq}

Using the relationship between potential and kinetic energy, we can solve for the velocity of the moving water.

{eq}KE = PE\\ \frac{1}{2}mv^2 = 980000 \ \text{J}\\ \Rightarrow v = \sqrt{\frac{(2)(980000 \ \text{J})}{1000 \ \text{kg}}} \Rightarrow \boxed{v = 44.3 \ \text{m}/\text{s}} {/eq}

Thus, the answer is

{eq}\boxed{a. \ 44.3 \ \text{m}/\text{s}} {/eq}


Learn more about this topic:

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Kinetic Energy to Potential Energy: Relationship in Different Energy Types

from CLEP Natural Sciences: Study Guide & Test Prep

Chapter 3 / Lesson 2
310K

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