Because the formulas for Coulomb's law and Newton's law of gravity have the same inverse-square law dependence on distance, a formula analogous to the formula for Gauss's law can be found for gravity. The gravitational ficld ĝ at a location is the force per unit mass on a test mass mo placed at that location. (Then, for a point mass m at the origin, the gravitational ficld g at some position 7' is j = – (Gym/r²) î.) (a) Compute the flux of the gravitational ficld through a sphcrical surface of radius r, and verify that the gravitational analog of Gauss's law is dÃ= -4TGNMencl· (b) What do you think is the differential form of Gauss's law for gravitation? (c) Determine the gravitational ficld, g, a distance r from the center of the Earth (where r < RE, where RE is the radius of the Earth), assuming that the Earth's density is uniform. Express your answer in terms of GN, the mass of the Earth, МЕ, and Rg.

Because the formulas for Coulomb's law and Newton's law of gravity have the same inverse-square law dependence on distance, a formula analogous to the formula for Gauss's law can be found for gravity. The gravitational ficld ĝ at a location is the force per unit mass on a test mass mo placed at that location. (Then, for a point mass m at the origin, the gravitational ficld g at some position 7' is j = – (Gym/r²) î.) (a) Compute the flux of the gravitational ficld through a sphcrical surface of radius r, and verify that the gravitational analog of Gauss's law is dÃ= -4TGNMencl· (b) What do you think is the differential form of Gauss's law for gravitation? (c) Determine the gravitational ficld, g, a distance r from the center of the Earth (where r < RE, where RE is the radius of the Earth), assuming that the Earth's density is uniform. Express your answer in terms of GN, the mass of the Earth, МЕ, and Rg.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter13: Gravitation

Section: Chapter Questions

Problem 13.11CYU: Check Your Understanding Consider the density required to make Earth a black hole compared to that...

See similar textbooks

Related questions

Q: In the simple Bohr model of the ground state of the hydrogen atom, the electron travels in a…

A: We have to determine the force on the electron. Given that, v=2.18×106 m/sr=5.28×10-11 mm=9.11×10-31…

Q: A planet is discovered orbiting a distant star. The mass of the planet is 40 times the mass of the…

A: The equation for the escape speed is given by, ve=2GMR Here, G is the universal gravitation…

Q: When the escape speed from the surface of a spherical object of mass M and radius R is equal to the…

Q: Two spheres A and B are placed in the arrangement shown below. (a) If m, = 3m and m, = 8m, where on…

Q: Problem 3.13 The gravitational force between two masses is F = -G (M₁ M2/r²) and the electrostatic…

A: We will answer the question using Newton's law of motion. The steps are as follows.

Q: 2. An earth-orbiting spacecraft is known to have the following orbital elements: a = 15000 km e =…

A: Question 2: Finding Position and Velocity Vectors in ECI CoordinatesAnswer:-Given Orbital…

Q: Because the formulas for Coulomb's law and Newton's law of gravity have the same inverse-square law…

A: Given, For a point mass 'm' at the origin, the gravitational field 'g' at some position r→ is given…

Q: g = 9.8 m/s?, Re = 6.4 x 106 m, w = 2t rad/day = 7.3 x 10-5 s-' Find the radius of the orbit of a…

A: Given- Radius of Earth RE=6.4×106mg=9.8 m/s2Mass of earth ME=5.98×1024kgUniversal constant of…

Q: This quesfion will require you to sketch out a thing. (Or at least I highly recommend you do it to…

A: Consider the free-body diagram of the package as follows.

Q: Use Stokes' Theorem to evaluate the line integral f F.Tds, where F = (-3y, 2x, z²) and C is the…

Q: Find Problem in the Attachement.

Q: You need to drag a very heavy table (m = 75kg) across the kitchen floor, so you provide 450N [R 35…

Q: #5 - If the field from problem #4 is tilted to make a 30 degree angle with the z-axis (i.e. the…

A: The lorentz force on the charged particle interms of magnitude is F = qvB This…

Q: a infinitesimally thin çırcular diSK of rodius R and mass M cenicred at the origin sitting in…

A: Given disc has mass M and radius R it has density σ=cr. to determine gravitational field let's…

Q: An astronaut marooned on the surface of an asteroid, of radius r and mean density equal to that of…

Q: How would you solve this: In the search for the Higgs Boson, it was posited that the potnetial…

A: Here U = c + ax2 - bx4 Force is given as F = -dU/dx

Q: a) Derive the escape speed vII (sometimes called the second cosmic speed) from the surface of body…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: r -e Physical constants Bohr Model mv² r mvr = n (A) What is the radius of the orbit with n = 4? (B)…

Q: on the mass at the origin. YA FAB m, 0). Find the net gravitational force kg lies in the x-y plane…

A: The objective of the question is to find the net gravitational force at the origin due to three…

Q: 9. Consider the falling object of mass 10 kg in Example 2, but assume now that the drag force is…

A: Given: Mass = m = 10 kg Limiting velocity= vL = 49 m/s Gravitational acceleration = g = 9.8 m/s2…

Q: Problem 2. If all the forces other than gravitation are switched off, calculate the time taken by…

Q: In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational…

A: Given, Mass (M)= 1.20kg Mass(m)= 12g= 0.012 kg Distance between these two masses(d)= 4.90cm= 0.049m…

Q: A body of mass m is attracted toward a 11.1 kg mass, 31.5 cm away, with a force of magnitude 6.60…

Q: As an electron moves in the direction the electric field lines A) it is moving from low potential to…

A: An electron has a negative charge. So, when placed in an electric field, it experiences a force in…

Q: Determine the angle 0 between the 350-lb force and the line OC.

A: Given :

Q: Two masses m1and m2 with a separation distance of d, attract each with a force F. What is the…

Concept explainers

Ising model of Ferromagnets

The Ising model is one of the easiest and most famous theoretical models for ferromagnetism in statistical mechanics. When a group of atomic spins aligns such that their magnetic moments are pointed in the same direction and produce a strong permanent magnetic moment in macroscopic size, the phenomenon is called ferromagnetism. The relative permeability of these magnets is greater than unity and increasing magnetization with the applied external field. Even in the absence of an external magnetic field, these substances retain spontaneous magnetization. An example of ferromagnets is iron.

Question

Because the formulas for Coulomb's law and Newton's law of gravity have the same
inverse-square law dependence on distance, a formula analogous to the formula for
Gauss's law can be found for gravity. The gravitational ficld g at a location is the force
per unit mass on a test mass mo placed at that location. (Then, for a point mass m
at the origin, the gravitational field g at some position is g = - (GNm/r²)î.)
(a) Compute the flux of the gravitational ficld through a spherical surface of radius
r, and verify that the gravitational analog of Gauss's law is
*, = f i
dÃ = -4TGNMenel·
(b) What do you think is the differential form of Gauss's law for gravitation?
(c) Determine the gravitational field, g, a distance r from the center of the Earth
(where r < RE, where RE is the radius of the Earth), assuming that the Earth's
density is uniform. Express your answer in terms of GN, the mass of the Earth,
МЕ, and Rp-
Using the results of the problem above, suppose that you were to drill a tunnel all
the way through the Earth, and then drop a ball down the tunnel. Neglecting any
friction/air resistance/cffects due to the rotation of the Earth, cxplain what would
happen to the ball and how long you would have to wait (in minutes!) to get it back!
Hint: consider the force on the ball when it is inside the Earth. Does this form of the
force look familiar? This same method also works for a small charge falling through an
oppositely-charged big ball of charge, of course.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

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

Check Your Understanding Why not use the simpler expression U=mg(y2y1) ? How significant would the error be? (Recall the previous result, in Example 13.4, that the value g at 400 km above the Earth is 8.67m/s2 .)
Check Your Understanding How would the above limit change with a uniformly rectangle instead of a disk?
A circular area S is concentric with the origin, has radius a, and lies in the yz-plane. Calculate s E ndA for E=2z2i.
A particle of charge q and mass m is placed at the center of a uniformly charged ring of total charge Q and radius R. The particle is displaced a small distance along the axis perpendicular to the plane of the ring and released. Assuming that the particle is constrained to move along the axis, show that the particle oscillates in simple harmonic motion with a frequency f=12qQ40mR3.
Charge is distributed throughout a very long cylindrical volume of radius R such that the charge density increases with the distance r from the central axis of the cylinder according to p=ar , where a is a constant. Show that the field of this charge distribution is directed radially with respect to the cylinder and that E=ar230 (rR); E=aR330r (rR).
Because the formulas for Coulomb's law and Newton's law of gravity have the same inverse-square law dependence on distance, a formula analogous to the formula for Gauss's law can be found for gravity. The gravitational ficld g at a location is the force per unit mass on a test mass mo placed at that location. (Then, for a point mass m at the origin, the gravitational ficld g at some position 7 is g = - (GNm/r2)î.) (a) Compute the flux of the gravitational field through a spherical surface of radius r, and verify that the gravitational analog of Gauss's law is dÃ= -4nGNMencl- 6. (b) What do you think is the differential form of Gauss's law for gravitation? (c) Determine the gravitational ficld, g, a distance r from the center of the Earth (where r < Rp, where Rp is the radius of the Earth), assuming that the Earth's density is uniform. Express your answer in terms of GN, the mass of the Earth, МЕ, and Rp.
In a thundercloud there may be electric charges of +45.0 C near the top of the cloud and -45.0 C near the bottom of the cloud. These charges are separated by 2.50 km. What is the electric force on the top charge? magnitude Ndirection Read It O attractive O repulsive Need Help?
The gravitational force between two masses m and m2 located a distance r apart has a magnitude of FG =Gmm2, where G = 6.674×10 N ⋅ m2/kg2; this has a nearly identical form to the Coulomb force law between two charges (except the force constants are different and masses are always positive). Suppose two identical spherical masses with radius a = 30 μm and mass density ρm = 2.2 × 103 kg/m3 are located a distance L apart. If they are released rest, their gravitational attraction will cause them to eventually collide. If, however, each mass has the same charge, then a Coulomb force will oppose the gravitation force. Suppose each mass has an excess of n extra electrons that causes both to be negatively charged. Find the minimum number n that would prevent the masses from colliding.
In the Rutherford model of the hydrogen atom, a proton (mass M, charge Q) is the nucleus and an electron (mass m, charge q) moves around the proton in a circle of radius r. Let k denote the Coulomb force constant (1/4TTE0) and G the universal gravitational constant. The ratio of the electrostatic force to the gravitational force between electron and proton is: O kMm/GQq O kQq/GMm O GQq/kMm O GMm/kQq O kQq/GMmr²
An electron (charge -e, mass m) and a positron (charge +e, mass m) revolve around their common center of mass under the influce of their attactive coulomb force. Find the speed v of each particle in terms of e, m, k, and their separation distance L.
Considering electron and proton as two charged particles separated by d = 5.9 × 10-11 m calculate the gravitational force between the proton and electron and find its ratio to the Coulomb force. Take the mass of the proton 1.7 x 10-27 kg, the mass of the electron 9.1 x 10-31 kg, the value of = 9x10⁹ m/F. Give the answer for the universal gravitational constant 6.7 x 10-11 N kg 2m-2, the electron charge -1.6 x 10-¹9 C and the gravitational force in 10-47 N. 1 Απερ Answer:
At some instant the velocity components of an electron moving between two charged parallel plates are v. and vy. Suppose the electric field between the plates is E (it is uniform and points only in the y direction). NOTE: Express your answers in terms of the given variables, using e for the fundamental charge and me for the mass of an electron. (a) What is the magnitude of the acceleration of the electron? E a= X me (b) What is the y-component of electron's velocity when its x coordinate has changed by a distance d? Ed Vd=vy + X Ux me