Part B Suppose the dam is 80% efficient at converting the water's potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 48 MW of electricity? This is a typical value for a small hydroelectric dam,

Part B Suppose the dam is 80% efficient at converting the water's potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 48 MW of electricity? This is a typical value for a small hydroelectric dam,

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Instantaneous Power

Power is defined in physics as the amount of energy transmitted or transformed per unit time. The watt is the unit of electricity in the International System of Units, equivalent to one joule per second.

Question

### Educational Content: Energy Conversion in Hydroelectric Dams

#### Context
In a hydroelectric dam, water falls 35 meters and then spins a turbine to generate electricity.

#### Part A

**Question:** What is the change in potential energy (\(\Delta U\)) of 1.0 kg of water?

*Express your answer with the appropriate units.*

**Solution:**
The change in potential energy of 1.0 kg of water in falling 35 m is calculated as:
\[ \Delta U = -mgh = -(1.0 \, \text{kg})(9.8 \, \text{m/s}^2)(35 \, \text{m}) = -340 \, \text{J} \]

- **Result:** \(\Delta U = -340 \, \text{J}\)

(The answer is marked correct.)

#### Part B

**Problem Statement:**
Suppose the dam is 80% efficient at converting the water’s potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 48 MW of electricity? This is a typical value for a small hydroelectric dam.

*Express your answer in kilograms per second.*

**Input Section:**
An equation box is provided where the student is expected to input the required mass flow rate in \(\, \text{kg/s}\).

**Provide Feedback:**
Links are available for submitting the answer and accessing hints or feedback.

---

### Additional Explanation:
In Part A, the concept of gravitational potential energy is explored. The formula \(\Delta U = -mgh\) is used to find the energy change due to the fall of water.

Part B focuses on energy conversion efficiency. The task requires understanding the relationship between potential energy, efficiency, and power output to find water mass flow rate.

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