bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 7, Problem 21PQ

(a)

To determine

The net gravitational force on the particle due to the two spheres.

(a)

Expert Solution
Check Mark

Answer to Problem 21PQ

The net gravitational force on the particle due to the two spheres is 4.27×108N towards 750 kg sphere_.

Explanation of Solution

Write the equation for the net force on the particle.

  Fnet=F1F2                                                                                                           (I)

Here, Fnet is the net force, F1 is the force due to first sphere and F2 is the force due to the second force.

Write the equation for the force due to first sphere.

  F1=GmM1r12                                                                                                           (II)

Here, G is the gravitational constant, m is the mass of the particle, M1 is the mass of the first sphere and r1 is the separation distance

Write the equation of the separation distance.

  r1=r2                                                                                                                   (III)

Here, r is the distance between two spheres.

Write the equation for the force due to first sphere.

  F2=GmM2r22                                                                                                        (IV)

Here, M2 is the mass of the second sphere, and r2 is the separation distance.

Write the equation of the separation distance.

  r2=r2                                                                                                                    (V)

Here, r is the distance between two spheres.

Rewrite the equation of net force from equation (I).

  Fnet=GmM1(r/2)2GmM2(r/2)2                                                                                      (VI)

Conclusion:

Substitute 6.67×1011N-m2/kg2 for G, 10.0kg for m, 750kg for M1, 350kg for M2 and 5.00m for r in equation (VI) to find Fnet.

  Fnet=[(6.67×1011N-m2/kg2)(10.0kg)(750kg)(5.00m/2)2][(6.67×1011N-m2/kg2)(10.0kg)(350kg)(5.00m/2)2]=(6.67×1011N-m2/kg2)(10.0kg)(5.00m/2)2[(750kg)(350kg)]=4.27×108N

Thus, the net gravitational force on the particle due to the two spheres is 4.27×108N towards 750 kg sphere_.

(b)

To determine

The position at which the net gravitational force on the particle will be zero.

(b)

Expert Solution
Check Mark

Answer to Problem 21PQ

The position at which the net gravitational force on the particle will be zero is 2.97m_.

Explanation of Solution

Considering the distance is d from M1.

Write the equation of net force from equation (VI).

  Fnet=GmM1d2GmM1((5.00m)d)2                                                                        (VII)

Here, d is the point at which the net force is zero.

Conclusion:

Substitute 0 for Fnet, 750kg for M1 and 350kg for M2  in equation (VII).

  0=GmM1d2GmM1((5.00m)d)2

Rearrange the equation to find d.

  0=400d27500d+18750d=2.97m, 15.77m

The value 15.77m is not valid.

Thus, the position at which the net gravitational force on the particle will be zero is 2.97m_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 7 Solutions

Bundle: Physics For Scientists And Engineers: Foundations And Connections, Volume 1, Loose-leaf Version + Webassign Printed Access Card For Katz's ... And Connections, Single-term Courses

Ch. 7 - Io and Europa are two of Jupiters many moons. The...Ch. 7 - Model the Moons orbit around the Earth as an...Ch. 7 - Prob. 8PQCh. 7 - Prob. 9PQCh. 7 - Prob. 10PQCh. 7 - Prob. 11PQCh. 7 - Prob. 12PQCh. 7 - A massive black hole is believed to exist at the...Ch. 7 - Since 1995, hundreds of extrasolar planets have...Ch. 7 - When Sedna was discovered in 2003, it was the most...Ch. 7 - Prob. 16PQCh. 7 - The mass of the Earth is approximately 5.98 1024...Ch. 7 - Prob. 18PQCh. 7 - Prob. 19PQCh. 7 - A black hole is an object with mass, but no...Ch. 7 - Prob. 21PQCh. 7 - Prob. 22PQCh. 7 - The Lunar Reconnaissance Orbiter (LRO), with mass...Ch. 7 - A Suppose a planet with mass m is orbiting star...Ch. 7 - Prob. 25PQCh. 7 - Three billiard balls, the two-ball, the four-ball,...Ch. 7 - Saturns ring system forms a relatively thin,...Ch. 7 - Prob. 28PQCh. 7 - Find the magnitude of the Suns gravitational force...Ch. 7 - Prob. 30PQCh. 7 - Prob. 31PQCh. 7 - Prob. 32PQCh. 7 - Prob. 33PQCh. 7 - Prob. 34PQCh. 7 - Prob. 35PQCh. 7 - In your own words, describe the difference between...Ch. 7 - The Sun has a mass of approximately 1.99 1030 kg....Ch. 7 - Prob. 38PQCh. 7 - Prob. 39PQCh. 7 - Prob. 40PQCh. 7 - Three billiard balls, the two-ball, the four-ball,...Ch. 7 - Prob. 42PQCh. 7 - Prob. 43PQCh. 7 - Prob. 44PQCh. 7 - Figure P7.45 shows a picture of American astronaut...Ch. 7 - Prob. 46PQCh. 7 - Prob. 47PQCh. 7 - Prob. 48PQCh. 7 - Prob. 49PQCh. 7 - Prob. 50PQCh. 7 - The International Space Station (ISS) experiences...Ch. 7 - Prob. 52PQCh. 7 - Two black holes (the remains of exploded stars),...Ch. 7 - Prob. 54PQCh. 7 - Prob. 55PQCh. 7 - Consider the Earth and the Moon as a two-particle...Ch. 7 - Prob. 57PQCh. 7 - Consider the Earth and the Moon as a two-particle...Ch. 7 - Prob. 59PQCh. 7 - You are a planetary scientist studying the...Ch. 7 - Prob. 61PQCh. 7 - Prob. 62PQCh. 7 - Planetary orbits are often approximated as uniform...Ch. 7 - Prob. 64PQCh. 7 - Prob. 65PQCh. 7 - Prob. 66PQCh. 7 - Prob. 67PQCh. 7 - Prob. 68PQCh. 7 - Prob. 69PQCh. 7 - Prob. 70PQ
Knowledge Booster
Background pattern image
Physics
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.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Gravitational Force (Physics Animation); Author: EarthPen;https://www.youtube.com/watch?v=pxp1Z91S5uQ;License: Standard YouTube License, CC-BY