/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 Astrid works as an intern in a w... [FREE SOLUTION] | 91Ó°ÊÓ

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Astrid works as an intern in a windmill park in Holland. She has learned that the anemometer, which measures wind speed, gives off electrical pulses and that the pulses are counted each second. The ratio of pulses per second to wind speed in meters per second is always \(4.5\) to 1 . a. If the wind speed is 40 meters per second, how many pulses per second should the anemometer be giving off? b. If the anemometer is giving off 84 pulses per second, what is the wind speed?

Short Answer

Expert verified
a. 180 pulses per second; b. 18.67 meters per second.

Step by step solution

01

Understanding the Ratio

The problem states that the ratio of pulses per second to wind speed is 4.5:1. This means that for every 1 meter per second of wind speed, there are 4.5 pulses per second.
02

Converting Wind Speed to Pulses

To find the pulses per second when the wind speed is 40 meters per second, use the given ratio: multiply the wind speed (40 m/s) by 4.5 pulses per meter/second. Using this, pulses per second = 40 m/s * 4.5 = 180 pulses.
03

Calculating Wind Speed from Pulses

If the anemometer gives off 84 pulses per second, we need to find the wind speed. Since the ratio is 4.5 pulses per meter per second, divide the pulses by 4.5 to find the wind speed. Wind speed = 84 pulses / 4.5 = 18.67 meters per second.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Wind Speed Measurement
Wind speed measurement is essential for a variety of applications, especially in fields like meteorology, aviation, and renewable energy. Knowing the wind speed helps in predicting weather patterns, determining the safest moments for flights, and optimizing windmill energy production, among others. There are various methods and instruments used to measure wind speed, with varying degrees of accuracy and applications. One common tool is the anemometer, which we'll dive deeper into in this article. The basic concept of measuring wind speed involves capturing the movement of air over time. By understanding how fast the air is moving, one can deduce how much kinetic energy the wind has. This, in turn, becomes useful information for making decisions in industries and scientific studies. With consistent and reliable measurements, professionals can forecast storms or optimize energy harnessing cycles from wind turbines.
Anemometer
An anemometer is a device used to measure wind speed, and sometimes wind direction. The simplest type of anemometer consists of rotating cups connected to a vertical shaft. As the wind blows, it rotates the cups, and this rotation translates to a measurement of wind speed. More sophisticated versions may use sonic or laser technologies for precise readings. - **Cup Anemometers**: These have three or four cups mounted on horizontal arms, which catch the wind and cause the assembly to spin. - **Vane Anemometers**: They use a vane or propeller that rotates when the wind hits it, suitable for multi-directional readings. - **Sonic Anemometers**: Using ultrasonic sound waves, they measure how these are influenced by the wind to calculate speed and direction. These different types can be chosen based on the required precision and the specific application of wind measurement. The ratio of electrical pulses emitted by an anemometer to the wind speed is vital. This consistent ratio allows for easy conversions between the two measurements, aiding in accurate environmental assessments.
Mathematical Calculations in Physics
Mathematical calculations in physics are a crucial aspect of understanding and explaining phenomena in the natural world. In the context of the given exercise involving anemometers, these calculations help us determine relationships between different physical quantities, such as wind speed and the number of pulses anemometers give per second. Understanding ratios is an essential skill in mathematics and physics. A ratio is a comparative relation between two amounts showing the number of times one value contains or is contained within the other. In our exercise, the ratio given is 4.5 pulses per second per meter per second of wind speed. To solve problems like the ones provided, one often follows a straightforward calculation using this ratio: 1. When determining pulses based on known wind speed, you multiply the wind speed by the ratio value (4.5 in this case). 2. Conversely, when you have a pulse count and need to calculate the wind speed, you divide the pulse count by the ratio. These operations highlight basic yet powerful applications of mathematics in physics, facilitating the practical use of theoretical principles for real-world tasks.

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Most popular questions from this chapter

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