You are in the high-speed package Earth delivery business. Your competitor in the next building gains the right-of-way to build an evacuated tunnel just above the m ground all the way around the Earth. By firing packages into this tunnel at just the right speed, your competitor is able to send the packages into orbit around the Earth in this tunnel so that they arrive on the exact opposite side of the Earth in a very short time interval. You come up with a competing idea. Figuring that the Tunnel distance through the Earth is shorter than the distance around the Earth, you obtain permits to build an evacuated tunnel through the center of the Earth. By simply dropping packages into this tunnel, they fall downward and arrive at the other end of your tunnel, which is in a building right next to the other end of your competitor's tunnel. Because your packages arrive on the other side of the Earth in a shorter time interval, you win the competition and your business flourishes. Show that it is possible to deliver the package through the tunnel since it undergoes simple harmonic motion. What is its frequency of oscillation? Note: An object at a distance r from the center of the Earth is pulled toward the center of the Earth only by the mass within the sphere of radius r (the reddish region in the figure). Assume the Earth has uniform density, (Serway & Jewett, 2014)
You are in the high-speed package Earth delivery business. Your competitor in the next building gains the right-of-way to build an evacuated tunnel just above the m ground all the way around the Earth. By firing packages into this tunnel at just the right speed, your competitor is able to send the packages into orbit around the Earth in this tunnel so that they arrive on the exact opposite side of the Earth in a very short time interval. You come up with a competing idea. Figuring that the Tunnel distance through the Earth is shorter than the distance around the Earth, you obtain permits to build an evacuated tunnel through the center of the Earth. By simply dropping packages into this tunnel, they fall downward and arrive at the other end of your tunnel, which is in a building right next to the other end of your competitor's tunnel. Because your packages arrive on the other side of the Earth in a shorter time interval, you win the competition and your business flourishes. Show that it is possible to deliver the package through the tunnel since it undergoes simple harmonic motion. What is its frequency of oscillation? Note: An object at a distance r from the center of the Earth is pulled toward the center of the Earth only by the mass within the sphere of radius r (the reddish region in the figure). Assume the Earth has uniform density, (Serway & Jewett, 2014)
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)...
Related questions
Question
![You are in the high-speed package
Earth
delivery business. Your competitor in the
next building gains the right-of-way to
build an evacuated tunnel just above the
m
ground all the way around the Earth. By
firing packages into this tunnel at just the
right speed, your competitor is able to
send the packages into orbit around the
Earth in this tunnel so that they arrive on
the exact opposite side of the Earth in a
very short time interval. You come up with
Tunnel
a competing idea. Figuring that the
distance through the Earth is shorter than the distance around the Earth, you obtain
permits to build an evacuated tunnel through the center of the Earth. By simply
dropping packages into this tunnel, they fall downward and arrive at the other end of
your tunnel, which is in a building right next to the other end of your competitor's
tunnel. Because your packages arrive on the other side of the Earth in a shorter time
interval, you win the competition and your business flourishes. Show that it is possible
to deliver the package through the tunnel since it undergoes simple harmonic motion.
What is its frequency of oscillation? Note: An object at a distance r from the center of
the Earth is pulled toward the center of the Earth only by the mass within the sphere
of radius r (the reddish region in the figure). Assume the Earth has uniform
density. (Serway & Jewett, 2014)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F502683df-dbb0-4eca-8b4c-146ab99a5f22%2Ff6aafeb2-b04c-4a58-9422-a1a43ece19d9%2Ff2b5ogp_processed.png&w=3840&q=75)
Transcribed Image Text:You are in the high-speed package
Earth
delivery business. Your competitor in the
next building gains the right-of-way to
build an evacuated tunnel just above the
m
ground all the way around the Earth. By
firing packages into this tunnel at just the
right speed, your competitor is able to
send the packages into orbit around the
Earth in this tunnel so that they arrive on
the exact opposite side of the Earth in a
very short time interval. You come up with
Tunnel
a competing idea. Figuring that the
distance through the Earth is shorter than the distance around the Earth, you obtain
permits to build an evacuated tunnel through the center of the Earth. By simply
dropping packages into this tunnel, they fall downward and arrive at the other end of
your tunnel, which is in a building right next to the other end of your competitor's
tunnel. Because your packages arrive on the other side of the Earth in a shorter time
interval, you win the competition and your business flourishes. Show that it is possible
to deliver the package through the tunnel since it undergoes simple harmonic motion.
What is its frequency of oscillation? Note: An object at a distance r from the center of
the Earth is pulled toward the center of the Earth only by the mass within the sphere
of radius r (the reddish region in the figure). Assume the Earth has uniform
density. (Serway & Jewett, 2014)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![Physics for Scientists and Engineers](https://www.bartleby.com/isbn_cover_images/9781337553278/9781337553278_smallCoverImage.gif)
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
![Lecture- Tutorials for Introductory Astronomy](https://www.bartleby.com/isbn_cover_images/9780321820464/9780321820464_smallCoverImage.gif)
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
![College Physics: A Strategic Approach (4th Editio…](https://www.bartleby.com/isbn_cover_images/9780134609034/9780134609034_smallCoverImage.gif)
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON