Physics / Physics for Scientists and Engineer with Modern Physics 10 / Chapter 1.5 / Problem 19

Physics for Scientists and Engineer with Modern Physics | 10th Edition | ISBN: 9781337553292 | Authors: Raymond A. Serway; John W. Jewett

Textbook Solutions for Physics for Scientists and Engineer with Modern Physics

Chapter 1.5 Problem 19

Chapter

Problem

Question

Your roommate is playing a video game from the latest CR Star Wars movie while you are studying physics. Distracted by the noise, you go to see what is on the screen. The game involves trying to fly a spacecraft through a crowded field of asteroids in the asteroid belt around the Sun. You say to him, "Do you know that the game you are playing is very unrealistic? The asteroid belt is not that crowded and you don't have to maneuver through it like that!" Distracted by your statement, he accidentally allows his spacecraft to strike an asteroid, just missing the high score. He turns to you in disgust and says, "Yeah, prove it." You say, "Okay, I've learned recently that the highest concentration of asteroids is in a doughnut-shaped region between the Kirkwood gaps at radii of 2.06 AU and 3.27 AU from the Sun. There are an estimated \(10^9\) asteroids of radius 100 m or larger, like those in your video game, in this region ..." Finish your argument with a calculation to show that the number of asteroids in the space near a spacecraft is tiny. (An astronomical unit-AU-is the mean distance of the Earth from the Sun: 1 AU = \(1.496 \times 10^{11} \mathrm{~m}\).)

Solution

Step 1 of 4)

The first step in solving 1.5 problem number trying to solve the problem we have to refer to the textbook question: Your roommate is playing a video game from the latest CR Star Wars movie while you are studying physics. Distracted by the noise, you go to see what is on the screen. The game involves trying to fly a spacecraft through a crowded field of asteroids in the asteroid belt around the Sun. You say to him, "Do you know that the game you are playing is very unrealistic? The asteroid belt is not that crowded and you don't have to maneuver through it like that!" Distracted by your statement, he accidentally allows his spacecraft to strike an asteroid, just missing the high score. He turns to you in disgust and says, "Yeah, prove it." You say, "Okay, I've learned recently that the highest concentration of asteroids is in a doughnut-shaped region between the Kirkwood gaps at radii of 2.06 AU and 3.27 AU from the Sun. There are an estimated \(10^9\) asteroids of radius 100 m or larger, like those in your video game, in this region ..." Finish your argument with a calculation to show that the number of asteroids in the space near a spacecraft is tiny. (An astronomical unit-AU-is the mean distance of the Earth from the Sun: 1 AU = \(1.496 \times 10^{11} \mathrm{~m}\).)
From the textbook chapter Estimates and Order-of-Magnitude Calculations you will find a few key concepts needed to solve this.

Step 2 of 7)

Visible to paid subscribers only

Step 3 of 7)

Visible to paid subscribers only

Subscribe to view the
full solution

Title Physics for Scientists and Engineer with Modern Physics 10

Author Raymond A. Serway; John W. Jewett

ISBN 9781337553292

Your roommate is playing a video game from the latest CR Star Wars movie while you are studying physics. Distracted by the noise, you go to see what is on the screen. The game involves trying to fly a spacecraft through a crowded field of asteroids in the asteroid belt around the Sun. You say to him, "Do you know that the game you are playing is very unrealistic? The asteroid belt is not that crowded and you don't have to maneuver through it like that!" Distracted by your statement, he accidentally allows his spacecraft to strike an asteroid, just missing the high score. He turns to you in disgust and says, "Yeah, prove it." You say, "Okay, I've learned recently that the highest concentration of asteroids is in a doughnut-shaped region between the Kirkwood gaps at radii of 2.06 AU and 3.27 AU from the Sun. There are an estimated \(10^9\) asteroids of radius 100 m or larger, like those in your video game, in this region ..." Finish your argument with a calculation to show that the number of asteroids in the space near a spacecraft is tiny. (An astronomical unit-AU-is the mean distance of the Earth from the Sun: 1 AU = \(1.496 \times 10^{11} \mathrm{~m}\).)

Chapter 1.5 textbook questions

Chapter 1: Problem 17 Physics for Scientists and Engineer with Modern Physics 10
Note: In your solutions to Problem 17, state the quantities you measure or estimate and the values you take for them. (a) Compute the order of magnitude of the mass of a bathtub half full of water. (b) Compute the order of magnitude of the mass of a bathtub half full of copper coins.
Read more
Chapter 1: Problem 18 Physics for Scientists and Engineer with Modern Physics 10
Note: In your solutions to Problem 18 , state the quantities you measure or estimate and the values you take for them. To an order of magnitude, how many piano tuners reside in New York City? The physicist Enrico Fermi was famous for asking questions like this one on oral Ph.D. qualifying examinations.
Read more
Chapter 1: Problem 19 Physics for Scientists and Engineer with Modern Physics 10
Your roommate is playing a video game from the latest CR Star Wars movie while you are studying physics. Distracted by the noise, you go to see what is on the screen. The game involves trying to fly a spacecraft through a crowded field of asteroids in the asteroid belt around the Sun. You say to him, "Do you know that the game you are playing is very unrealistic? The asteroid belt is not that crowded and you don't have to maneuver through it like that!" Distracted by your statement, he accidentally allows his spacecraft to strike an asteroid, just missing the high score. He turns to you in disgust and says, "Yeah, prove it." You say, "Okay, I've learned recently that the highest concentration of asteroids is in a doughnut-shaped region between the Kirkwood gaps at radii of 2.06 AU and 3.27 AU from the Sun. There are an estimated \(10^9\) asteroids of radius 100 m or larger, like those in your video game, in this region ..." Finish your argument with a calculation to show that the number of asteroids in the space near a spacecraft is tiny. (An astronomical unit-AU-is the mean distance of the Earth from the Sun: 1 AU = \(1.496 \times 10^{11} \mathrm{~m}\).)
Read more

Table of Contents

Textbook Solutions for Physics for Scientists and Engineer with Modern Physics

Question

Solution

Chapter 1.5 textbook questions

Register

Table of Contents

Textbook Solutions for Physics for Scientists and Engineer with Modern Physics

Question

Solution

Chapter 1.5 textbook questions

Login

Register

Reset password