Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 11, Problem 12P
(a) Compute the vector gravitational field at a point P on the perpendicular bisector of the line joining two objects of equal mass separated by a distance 2a as shown in Figure P11.12. (b) Explain physically why the field should approach zero as r → 0. (c) Prove mathematically that the answer to part (a) behaves in this way. (d) Explain physically why the magnitude of the field should approach 2GM/r2 as r → ∞. (e) Prove mathematically that the answer to part (a) behaves correctly in this limit.
Figure P11.12
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
(a) Compute the vector gravitational field at a point P on the perpendicular bisector of the line joining two objects of equal mass separated by a distance 2a as shown in Figure P13.6. (b) Explain physically why the field should approach zer as r → 0 (c) Prove mathematically that the answer to part (a) behaves in this way. (d) Explain physically why the magnitude of the field should approach 2GM/r2 as r → ∞. (e) Prove mathematically that the answer to part (a) behaves correctly in this limit
FigureP13.6
A 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).
An endless thin wire of density Y1 (unit: kg/m) is just above the x axis. An infinitely thin layer of density Y2 (unit: kg/m²) is parallel to the x-y plane and intersects the z-axis at the point z= -a.
Find the gravitational field at (x,y,z) position. Give your answer in terms of (G,Y1,Y2, a, x, y, z, ^x, ^y, ^z(unit vectors)).
Hint:
A hint is given in the figure. The result will be (+ and -).
Chapter 11 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 11.1 - A planet has two moons of equal mass. Moon 1 is in...Ch. 11.3 - An asteroid is in a highly eccentric elliptical...Ch. 11.4 - Prob. 11.3QQCh. 11.5 - Prob. 11.4QQCh. 11 - Prob. 1OQCh. 11 - The gravitational force exerted on an astronaut on...Ch. 11 - Prob. 3OQCh. 11 - Prob. 4OQCh. 11 - A system consists of five particles. How many...Ch. 11 - Suppose the gravitational acceleration at the...
Ch. 11 - Prob. 7OQCh. 11 - Prob. 8OQCh. 11 - Prob. 9OQCh. 11 - Rank the following quantities of energy from...Ch. 11 - Prob. 11OQCh. 11 - Prob. 12OQCh. 11 - Prob. 13OQCh. 11 - Prob. 14OQCh. 11 - Prob. 1CQCh. 11 - Prob. 2CQCh. 11 - Prob. 3CQCh. 11 - Prob. 4CQCh. 11 - Prob. 5CQCh. 11 - Prob. 6CQCh. 11 - Prob. 7CQCh. 11 - Prob. 8CQCh. 11 - In his 1798 experiment, Cavendish was said to have...Ch. 11 - Prob. 1PCh. 11 - Prob. 2PCh. 11 - A 200-kg object and a 500-kg object are separated...Ch. 11 - Prob. 4PCh. 11 - Prob. 5PCh. 11 - Prob. 6PCh. 11 - Prob. 7PCh. 11 - Prob. 8PCh. 11 - Prob. 9PCh. 11 - Prob. 10PCh. 11 - A spacecraft in the shape of a long cylinder has a...Ch. 11 - (a) Compute the vector gravitational field at a...Ch. 11 - Prob. 13PCh. 11 - Two planets X and Y travel counterclockwise in...Ch. 11 - Prob. 15PCh. 11 - Prob. 16PCh. 11 - Prob. 17PCh. 11 - Prob. 18PCh. 11 - Plasketts binary system consists of two stars that...Ch. 11 - As thermonuclear fusion proceeds in its core, the...Ch. 11 - Comet Halley (Fig. P11.21) approaches the Sun to...Ch. 11 - Prob. 22PCh. 11 - Prob. 23PCh. 11 - Prob. 24PCh. 11 - Prob. 25PCh. 11 - A space probe is fired as a projectile from the...Ch. 11 - Prob. 27PCh. 11 - Prob. 28PCh. 11 - Prob. 29PCh. 11 - Prob. 30PCh. 11 - Prob. 31PCh. 11 - Prob. 32PCh. 11 - Prob. 33PCh. 11 - Prob. 34PCh. 11 - Prob. 35PCh. 11 - Prob. 36PCh. 11 - Prob. 37PCh. 11 - Prob. 38PCh. 11 - Prob. 39PCh. 11 - Prob. 40PCh. 11 - Prob. 41PCh. 11 - Prob. 42PCh. 11 - Prob. 43PCh. 11 - Prob. 44PCh. 11 - Prob. 45PCh. 11 - Prob. 46PCh. 11 - Let gM represent the difference in the...Ch. 11 - Prob. 48PCh. 11 - Prob. 49PCh. 11 - Two stars of masses M and m, separated by a...Ch. 11 - Prob. 51PCh. 11 - Prob. 52PCh. 11 - Prob. 53PCh. 11 - Prob. 54PCh. 11 - Prob. 55PCh. 11 - Prob. 56PCh. 11 - Prob. 57PCh. 11 - Prob. 58PCh. 11 - Prob. 59PCh. 11 - Prob. 60PCh. 11 - Prob. 61PCh. 11 - Prob. 62PCh. 11 - Prob. 63PCh. 11 - Prob. 64PCh. 11 - Prob. 65P
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
- Calculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?arrow_forwardConsider 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_forward(a) Show that tidal force on a small object of mass m, defined as the difference in the gravitational force that would be exerted on m at a distance at the near and the far side of the object, due to the gravitational at a distance R from M, is given by Ftidal=2GMmR3r where r is the distance between the near and far side and rR .(b) Assume you are fallijng feet first into the black hole at the center of our galaxy. It has mass of 4 million solar masses. What would be the difference between the force at your head and your feet at the Schwarzschild radius (event horizon)? Assume your feet and head each have mass 5.0 kg and are 2.0 m apart. Would you survive passing through the event horizon?arrow_forward
- Chapter 13, Problem 088 In Pole to Pole, an early science fiction story by George Griffith, three explorers attempt to travel by capsule through a naturally formed (and, of course, fictional) tunnel directly from the south pole to the north pole. According to the story, as the capsule approaches Earth's center, the gravitational force on the explorers becomes alarmingly large and then, exactly at the center, it suddenly but only momentarily disappears. Then the capsule travels through the second half of the tunnel, to the north pole. With what speed would mail pass through the center of Earth if falling in this tunnel? Ignore air resistance. Mans Number Units the tolerance is +/-2% Click if you would like to Show Work for this question: Open Show Workarrow_forwardA ring of radius 7 m lies in the x-y plane, centered on the origin. The portions of the ring in the first and third quadrants have a mass density of 7.4 kg/m, while the portions of the ring in the second and forth quadrants have a mass density of 7.3 kg/m. Find the z component of the gravitational field due to the ring at a point P on the z axis a distance 6 meters from the origin. Use G = 6.673E-11 N m2/kg2.arrow_forwardSuppose we drill a hole through the Earth along its diameter and drop a small mass m down the hole. Assume that the Earth is not rotating and has a uniform density throughout its volume. The Earth’s mass is ME and its radius is RE. Let r be the distance from the falling object to the center of the Earth. Derive an expression for the gravitational force on the small mass as a function of r when it is moving inside the Earth. Derive an expression for the gravitational force on the small mass as a function of r when it is outside the Earth. On the graph below, plot the gravitational force on the small mass as a function of its distance r from the center of the Earth. Determine the work done by the gravitational force on the mass as it moves from the surface to the center. What is the speed of the mass at the center of the Earth if the Earth has a given density Determine the time it takes the mass to move from the surface to the center of the Earth.arrow_forward
- Two concentric spherical shells with uniformly distributed masses M₁ and M₂ are situated as shown in the figure. Find the magnitude of the net gravitational force on a particle of mass m, due to the shells, when the particle is located at each of the radial distances shown in the figure. Fa NOTE: Give your answer in terms of the variables given and G when applicable (a) What is the magnitude of the net gravitational force if the particle is located outside both shells with a radial distance a? F = M₁ (b) What is the magnitude of the net gravitational force if the particle is located between the two shells with a radial distance b? Fc M₂ ****** - a (c) What is the magnitude of the net gravitational force if the particle is located inside both shells with a radial distance c? =arrow_forwardFive small sphere each with a mass of 23 kg are attached to the vertices of a pentagon. A set of coordinate axes are chosen such that the pentagon lies in the x,y plane with the origin and the center of the pentagon, and one of the spheres is located along the x-axis 11 m away from the origin. See figure below. X 9z Z P y Find the z component of the gravitational field due to these five point masses at a point P on the z axis a distance of 6 m away from the origin. Use G = 6.673E-11 kg*m^2/s^2.arrow_forwardMultiple Choice Questions (MCQ’s): 1. The dimensions of gravitational constant are: (2) [M*LT*] (b) [M"LT*] (e) [M'L°T*] (a) [M"L?T*] 2. If V is the gravitational potential on the surface of a thin spherical shell, then the potential at the centre of the shell is : (a) Zero (b) V (c) V/2 (d) infinite 3. The ratio of the gravitational potential at the surface of a solid sphere to that at the centre is (a) :1 (b) 1:2 (c) 2:3 (d) 3:2 4. The ratio of the gravitational potentials at the centre and on the surface of a solid sphere is: (a) 히 (c) :1 (b) 1:1 (d) 2:1 5. The value of gravitational potentials energy is: (a) Always positive (c) positive or negative 6. The nature of gravitational field is: (a) Conservative field (c) pseudo field 7. The gravitational potential on the earth's surface is: (a) - 6.2 X 10' joule/kg (b) always negative (d) always zero (b) non conservative field (d) solenoidal field. (b) 11.2 X 10' joule/kgarrow_forward
- the figure with a separation of dAB = 0.519 m at angle O = 30°. Particle C, with mass 9 g, is not shown. The net gravitational force acting on particle A due to particles Band C is 2.71 x 1o-14 N at an angle of -163.8°. from the positive x axis. What are (a) the x coordinate and (b) the y coordinate of particle C? Three point particles are fixed in position in an xy plane. Two of them, particle A of mass 5 g and particle B of mass 11 g, are shown in В dAB Aarrow_forwardMembers of the Star Trek exploration committee find themselves on Physitopia, a planet with its own unique gravitational characteristics. The Force-sensitive individuals on the committee, accustomed to manipulating the Force on various planets, are now faced with a new challenge: understanding and adapting to the gravitational force on Physitopia. Physitopia has a mass of 6.46 × 1023 kg and a radius of 3.39 × 106 m, poses an intriguing gravitational scenario. To address the concerns of the Star Trek characters, we must calculate the acceleration due to gravity on Physitopia and determine the weight of a 65 kg individual.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
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 with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Gravitational Force (Physics Animation); Author: EarthPen;https://www.youtube.com/watch?v=pxp1Z91S5uQ;License: Standard YouTube License, CC-BY