Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Field Trip Mrs. West has decided to take her fift…

03:24

Question

Answered step-by-step

Problem 78 Hard Difficulty

According to Newton's Law of Universal Gravitation, the attractive force $F$ between two bodies is given by $F=G \frac{m_{1} m_{2}}{r^{2}}$ where $m_{1}, m_{2}=$ the masses of the two bodies $\begin{aligned} r=& \text { distance between the two bodies } \\ G=& \text { gravitational constant }=6.6742 \times 10^{-11} \\ & \text { newtons } \cdot \text { meter }^{2} \cdot \text { kilogram }^{-2} \end{aligned}$ Suppose an object is traveling directly from Earth to the moon. The mass of Earth is $5.9742 \times 10^{24}$ kilograms, the mass of the moon is $7.349 \times 10^{22}$ kilograms, and the mean distance from Earth to the moon is $384,400$ kilometers. For an object between Earth and the moon, how far from Earth is the force on the object due to the moon greater than the force on the object due to Earth?


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

AG
Ankit Gupta
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Ankit Gupta

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Algebra

College Algebra

Chapter 5

Polynomial and Rational Functions

Section 4

Polynomial and Rational Inequalities

Related Topics

Exponents and Polynomials

Polynomials

Rational Functions

Discussion

You must be signed in to discuss.
Top Algebra Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Maria Giefer
Kristen Karbon

University of Michigan - Ann Arbor

Algebra Courses

Lectures

Join Course
Recommended Videos

02:41

According to the Law of Un…

02:54

The Moon, whose mass is $7…

01:41

The Moon, whose mass is $7…

02:38

According to the Law of Un…

01:56

The force with which the e…

02:28

According to the Law of Un…

04:24

Refer to the formula $F=\f…

Watch More Solved Questions in Chapter 5

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86
Problem 87

Video Transcript

According to Newton's Law of Gravitation, the force of attraction between two objects has given us G multiplied with M one m two divided by r squared very modern him two of the mass of the two objects Jeez, universal gravitation, constant and RSD distance between the centres off these two bodies. So let's speak X as the distance from the earth. Very the force off attraction Due to the moon, it will be greater than the force off attraction due to the earth. Now we need to find X such that force off attraction doodle The moon at this distance will be greater than force of attraction due to the earth at this distance. So we can say that we need to find the force of attraction due to moon divided by the force of attraction due to ought at this distance should be greater than one. So putting the values according to the formula for the force of attraction. As per Newton, we'll get G multiplied wit m where m is the moss off the body m m being the moss off moon divided by R minus X squared, divided by G. M m E, where m is the mass off the earth divided by X squares should be greater than one. So then g, m and G m will get cancelled because they're the same. So the inequality of allow change toe m m multiplied with X squared is greater than M E multiplied with ar minus. X holds Quit. Now let's all photo Now if we take away mm X squared from both sides so the inequality will become M M X squared minus M m X Trail is greater than M E R Square plus M E X squared minus twice off m E multiplied with ar minus X minus M m X square. So now cancelling out and rearranging, we are going to get the final inequality as zero is greater than M E multiplied with R squared minus to our X plus X squared minus m m exquisite, which will become Mars offered. Miners mass off moon multiplied with X squared minus two are must off Earth multiplied. Videx plus R squared multiplied with Marceau Effort is less than zero now, putting the values form us off earth mass off Moon on the radius. We're going to get 5.9742 multiplied with 10 to the power of 24 miners, 7.349 multiplied with 10 to the power off 20 to minus two multiplied with 384,400 multiplied with 5.9742 multiplied with tend to the part of 24 plus 384,000 and 400 squared multiplied with five point 9749 into 10. Raise to the part of 24 will be less than zero, which will give us on solving that X should lie between one point through seven multiplied with 10 days to the bar seven on day zero. So therefore the solution said will be zero on 1.27 into 10 race to the par off seven kilometers.

Get More Help with this Textbook
Michael Sullivan

College Algebra

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
129
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
63
Hosted by: Alonso M
See More

Related Topics

Exponents and Polynomials

Polynomials

Rational Functions

Top Algebra Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Maria Giefer

Numerade Educator

Kristen Karbon

University of Michigan - Ann Arbor

Recommended Videos

02:41

According to the Law of Universal Gravitation, the attractive force $F$ in Newt…

02:54

The Moon, whose mass is $7.35 \times 10^{22} \mathrm{~kg}$, orbits the Earth, w…

01:41

The Moon, whose mass is $7.35 \times 10^{22} \mathrm{~kg}$, orbits the Earth, w…

02:38

According to the Law of Universal Gravitation, the attractive force $F$ in Newt…

01:56

The force with which the earth attracts an object is called the weight of the o…

02:28

According to the Law of Universal Gravitation, the attractive force $F$ in Newt…

04:24

Refer to the formula $F=\frac{G m_{1} m_{2}}{d^{2}}$. This gives the gravitatio…
Additional Mathematics Questions

01:29

t takes Franklin 14 hours to make a 200-square-foot cement patio. It takes S…

00:48

If a baker doubles a recipe that calls for 6-2/3 cups of flour. How many cup…

03:47

If the similarity ratio of two similar solids is 3 : 14, what is the ratio o…

00:49

From the top of the CN Tower, the angle of depression to to tip of the tower…

01:33

Jared is building a rectangular prism garden box and wants to use soil that …

01:21

Find the rate of change: Jame scan earn $300 in royalties for 250 books. Rou…

01:58

George is 1.94 meters tall and wants to find the height of a tree in his yar…

00:44

A company's monthly profit increases by $1,000 each month. In January, …

00:43

Consider a political discussion group consisting of 9 Democrats, 7 Republica…

03:22

Frank corporation manufacturers a single product that has a selling price of…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started