Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 5, Problem 5.20P
A thin disk of mass M and radius R lies in the (x, y) plane with the z-axis passing through the center of the disk. Calculate the gravitational potential Φ (z) and the gravitational field
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
(b) Determine the gravitational field g(r) at the point (0, 0, z) above the disk.
(c) Determine the gravitational potential (r) at the point (0, 0, z) above the disk.
The density of a star measured from the center of a star is equal to Z. a is constant. find the gravitational potential and g as a function of r.
A satellite in Earth orbit has a mass of 96 kg and is at an altitude of
1.98 x 10° m. (Assume that U
= 0 as r – ∞.)
(a) What is the potential energy of the satellite-Earth system?
(b) What is the magnitude of the gravitational force exerted by the
Earth on the satellite?
97671.15
What is the equation for gravitational force when the altitude is
comparable to the radius of the Earth? N
(c) What force, if any, does the satellite exert on the Earth? (Enter the
magnitude of the force, if there is no force enter 0.)
Chapter 5 Solutions
Classical Dynamics of Particles and Systems
Ch. 5 - Prob. 5.3PCh. 5 - Compute directly the gravitational force on a unit...Ch. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - A planet of density 1 (spherical core, radius R1)...Ch. 5 - Prob. 5.16PCh. 5 - A thin disk of mass M and radius R lies in the (x,...Ch. 5 - A point mass m is located a distance D from the...
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.Similar questions
- A system consists of five particles. How many terms appear in the expression for the total gravitational potential energy of the system? (a) 4 (b) 5 (c) 10 (d) 20 (e) 25arrow_forwardSuppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2arrow_forwardA small particle of mass m is pulled to the top of a friction less half-cylinder (of radius R) by a light cord that passes over the top of the cylinder as illustrated in Figure P7.15. (a) Assuming the particle moves at a constant speed, show that F = mg cos . Note: If the particle moves at constant speed, the component of its acceleration tangent to the cylinder must be zero at all times. (b) By directly integrating W=Fdr, find the work done in moving the particle at constant speed from the bottom to the top of the hall-cylinder. Figure P7.15arrow_forward
- Consider the Earth and the Moon as a two-particle system, a. How far from the center of the Earth is the gravitational field of this two-particle system zero? b. Sketch gravitational field vectors g along the line joining the Earth and the Moon. Indicate the point at which g=0 (Do not consider positions inside either object.)arrow_forwardA very massive star with an M mass has a geometric shape of a sphere hollow, where the mass is distributed on the surface only with the radius R. Determine the gravitational potential inside (r R), where r is radial distance from the center of the star. (Hint: You can use Gauss's Law to gravitational field).arrow_forwardA satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.1 × 104 m/s. The mass of the planet is M = 6.04 × 1024 kg. The mass of the satellite is m = 1.2 × 103 kg. First, find an expression for the gravitational potential energy PE in terms of G, M, m, and R. a)Calculate the value of PE in joules. b)Enter an expression for the total energy E of the satellite in terms of m and v. c)Calculate the value of the total energy E in joules.arrow_forward
- The three spheres in the figure, with masses m. = 77 g, ma = 8 g, and m, = 23 g, have their centers on a common line, with L = 21 cm and d = 4 cm. You move sphere B along the line until its center-to-center separation from C is d = 4 cm. How much work is done on sphere B(a) by you and (b) by the net gravitational (a) Number Units (b) Number Unitsarrow_forwardcalculate the gravitational potential due to a thin rod of length l and mass m.arrow_forwardOne model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M = 4.07 × 1024 kg and R = 5.79 x 106 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet? (a) Number i Units (b) Number i Unitsarrow_forward
- Calculate the gravitational potential V for a hemisphere of radius R with uniform mass distribution.arrow_forwardThe gravitational force on a point mass m due to a point mass M is a gradient field with GMm potential U(r) = - where G is the gravitational constant and r = √√x² + y² + z² is the 1 r distance between the masses. Answer parts a through c. What is a vector t that is always tangent to this shape? O A. (-yz, -xz,2xy) OB. (x,y,z) OC. (-y,z,-x) O D. (xy.yz,2xz)arrow_forwardOne of your summer lunar space camp activities is to launch a 1130 kg rocket from the surface of the Moon. You are a serious space camper and you launch a serious rocket: it reaches an altitude of 217 km. What gain AU in gravitational potential energy does the launch accomplish? The mass and radius of the Moon are 7.36 × 1022 kg and 1740 km, respectively. AU = Jarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Kinetic Energy and Potential Energy; Author: Professor Dave explains;https://www.youtube.com/watch?v=g7u6pIfUVy4;License: Standard YouTube License, CC-BY