Explanation Figure 1 From the figure 1 it is shown that the horizontal components of force will be acting towards the left and the force due to off axis components will be zero. Write the expression for the infinitesimal horizontal force on m due to an infinitesimal mass d M . d F d M m = G m ( x 2 + r 2 ) d M (I) Here, d F d M m is the infinitesimal horizontal force on m due to an infinitesimal mass d M , G is the constant, m is the mass of the smaller object, M is the mass of the mass of the ring, x is the distance of the smaller mass along rings axis, r is the radius. The horizontal component of force is given by, ( d F d M m ) x = G m ( x 2 + r 2 ) cos θ d M (II) From the figure the value of the cosine angle is given by, cos θ = x ( x 2 + r 2 ) (III) Use equation (III) in equation (II),’ (

4th Edition

ISBN: 9780133899634

Author: GIANCOLI

Publisher: PEARSON CO

See similar textbooks

Concept explainers

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force betwe…

Question

Chapter 6, Problem 18P

To determine

To show that F=GMmx(x2+r2)32 is the magnitude for the gravitational force on the mass m due to the ring which is directed inward along the axis.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 17P

Chapter 6, Problem 19P

Students have asked these similar questions

No chatgpt pls will upvote

Chapter 6 Solutions

EP PHYSICS F/SCI.+ENGR.W/MOD..-MOD MAST

Ch. 6.3 - Suppose you could double the mass of a planet but...Ch. 6.4 - Two satellites orbit the Earth in circular orbits...Ch. 6.4 - Could astronauts in a spacecraft far out in space...Ch. 6.5 - Suppose there were a planet in circular orbit...Ch. 6 - Does an apple exert a gravitational force on the...Ch. 6 - The Suns gravitational pull on the Earth is much...Ch. 6 - Will an object weigh more at the equator or at the...Ch. 6 - Why is more fuel required for a spacecraft to...Ch. 6 - The gravitational force on the Moon due to the...Ch. 6 - How did the scientists of Newton's era determine...

Ch. 6 - If it were possible to drill a hole all the way...Ch. 6 - A satellite in a geosynchronous orbit stays over...Ch. 6 - Which pulls harder gravitationally, the Earth on...Ch. 6 - Would it require less speed to launch a satellite...Ch. 6 - An antenna loosens and becomes detached from a...Ch. 6 - Describe how careful measurements of the variation...Ch. 6 - The Sun is below us at midnight, nearly in line...Ch. 6 - When will your apparent weight be the greatest, as...Ch. 6 - If the Earths mass were double what it actually...Ch. 6 - The source of the Mississippi River is closer to...Ch. 6 - People sometimes ask. What keeps a satellite up in...Ch. 6 - Explain how a runner experiences free fall or...Ch. 6 - If you were in a satellite orbiting the Earth, how...Ch. 6 - Is the centripetal acceleration of Mars in its...Ch. 6 - The mass of the planet Pluto was not known until...Ch. 6 - The Earth moves faster in its orbit around the Sun...Ch. 6 - Keplers laws tell us that a planet moves faster...Ch. 6 - Does your body directly sense a gravitational...Ch. 6 - Discuss the conceptual differences between g as...Ch. 6 - (I) Calculate the force of Earths gravity on a...Ch. 6 - (I) Calculate the acceleration due to gravity on...Ch. 6 - Prob. 3P Ch. 6 - Prob. 4P Ch. 6 - Prob. 5P Ch. 6 - (II) Calculate the effective value of g, the...Ch. 6 - (II) You are explaining to friends why astronauts...Ch. 6 - Prob. 8P Ch. 6 - (II) Four 8.5-kg spheres are located at the...Ch. 6 - (II) Two objects attract each other...Ch. 6 - (II) Four masses are arranged as shown in Fig....Ch. 6 - (II) Estimate the acceleration due to gravity at...Ch. 6 - (II) Suppose the mass of the Earth were doubled,...Ch. 6 - Prob. 14P Ch. 6 - (II) At what distance from the Earth will a...Ch. 6 - (II) Determine the mass of the Sun using the known...Ch. 6 - (II) Two identical point masses, each of mass M,...Ch. 6 - Prob. 18P Ch. 6 - (III) (a) Use the binomial expansion...Ch. 6 - Prob. 20P Ch. 6 - Prob. 21P Ch. 6 - Prob. 22P Ch. 6 - Prob. 23P Ch. 6 - Prob. 24P Ch. 6 - (II) You know your mass is 65 kg, but when you...Ch. 6 - (II) A 13.0-kg monkey hangs from a cord suspended...Ch. 6 - (II) Calculate the period of a satellite orbiting...Ch. 6 - Prob. 28P Ch. 6 - (II) What will a spring scale read for the weight...Ch. 6 - Prob. 30P Ch. 6 - (II) What is the apparent weight of a 75-kg...Ch. 6 - (II) A Ferris wheel 22.0 m in diameter rotates...Ch. 6 - Prob. 33P Ch. 6 - Prob. 34P Ch. 6 - Prob. 35P Ch. 6 - (III) An inclined plane, fixed to the inside of an...Ch. 6 - (I) Use Keplers laws and the period of the Moon...Ch. 6 - (I) Determine the mass of the Earth from the known...Ch. 6 - (I) Neptune is an average distance of 4.5109 km...Ch. 6 - (II) Planet A and planet B are in circular orbits...Ch. 6 - (II) Our Sun rotates about the center of our...Ch. 6 - (II) Table 63 gives the mean distance, period, and...Ch. 6 - (II) Determine the mean distance from Jupiter for...Ch. 6 - (II) The asteroid belt between Mars and Jupiter...Ch. 6 - (III) The comet Hale-Bopp has a period of 2400...Ch. 6 - Prob. 46P Ch. 6 - (III) The orbital periods and mean orbital...Ch. 6 - (II) What is the magnitude and direction of the...Ch. 6 - (II) (a) What is the gravitational field at the...Ch. 6 - Prob. 50P Ch. 6 - How far above the Earths surface will the...Ch. 6 - At the surface of a certain planet, the...Ch. 6 - A certain white dwarf star was once an average...Ch. 6 - What is the distance from the Earths center to a...Ch. 6 - The rings of Saturn are composed of chunks of ice...Ch. 6 - During an Apollo lunar landing mission, the...Ch. 6 - Prob. 57GP Ch. 6 - Prob. 58GP Ch. 6 - Jupiter is about 320 limes as massive as the...Ch. 6 - The Sun rotates about the center of the Milky Way...Ch. 6 - Prob. 61GP Ch. 6 - A satellite of mass 5500 kg orbits the Earth and...Ch. 6 - Show that the rate of change of your weight is...Ch. 6 - Astronomers using the Hubble Space Telescope...Ch. 6 - Suppose all the mass of the Earth were compacted...Ch. 6 - A plumb bob (a mass m hanging on a string) is...Ch. 6 - A geologist searching for oil finds that the...Ch. 6 - Prob. 68GP Ch. 6 - A science-fiction tale describes an artificial...Ch. 6 - How long would a day be if the Earth were rotating...Ch. 6 - An asteroid of mass m is in a circular orbit of...Ch. 6 - Newton had the data listed in Table 64, plus the...Ch. 6 - A satellite circles a spherical planet of unknown...Ch. 6 - Prob. 74GP Ch. 6 - The gravitational force at different places on...Ch. 6 - Prob. 76GP Ch. 6 - Estimate the value of the gravitational constant G...Ch. 6 - Between the orbits of Mars and Jupiter, several...

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.

To show that F = G M m x ( x 2 + r 2 ) 3 2 is the magnitude for the gravitational force on the mass m due to the ring which is directed inward along the axis.

Solution Summary: The author explains the magnitude of the gravitational force on the mass m due to the ring which is directed inward along axis. The horizontal components of force will be acting towards the left and the force due

Concept explainers

To show that F=GMmx(x2+r2)32 is the magnitude for the gravitational force on the mass m due to the ring which is directed inward along the axis.

Want to see the full answer?

Chapter 6 Solutions