Two concentric spherical shells with uniformly distributed masses M, and M, are situated as shown in the figure below. M1 M2 Find the magnitude of the net gravitational force on a particle of mass m, due to the shells, when the particle is located at the following radial distances. (Use any variable or symbol stated above along with the following as necessary: a, b, c, and G for the gravitational constant.) (a) r= a F = (b) r= b F = (c) r=c F =

Two concentric spherical shells with uniformly distributed masses M, and M, are situated as shown in the figure below. M1 M2 Find the magnitude of the net gravitational force on a particle of mass m, due to the shells, when the particle is located at the following radial distances. (Use any variable or symbol stated above along with the following as necessary: a, b, c, and G for the gravitational constant.) (a) r= a F = (b) r= b F = (c) r=c F =

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 38PQ

See similar textbooks

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?
Compute directly the gravitational force on a unit mass at a point exterior to a homogeneous sphere of matter.
On a planet whose radius is 1.2107m , the acceleration due to gravity is 18m/s2 . What is the mass of the planet?
Let gM represent the difference in the gravitational fields produced by the Moon at the points on the Earths surface nearest to and farthest from the Moon. Find the fraction gM/g, where g is the Earths gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)
Show that for eccentricity equal to one in Equation 13.10 for conic sections, the path is a parabola. Do this by substituting Cartersian coordinates, x and y, for the polar coordinates, r and , and showing that it has the general form for a parabola, x=ay2+by+c .
What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?
Find the Hohmann transfer velocities, vEllipseEarth and vEllipseMars ,needed for a trip to Mars. Use Equation 13.7 to find the circular orbital velocities for Earth and Mars. Using Equation 13.4 and the total energy of the ellips (with semi-major asix a), given by E=GmMs2a , find the velocities at Earth (perihelion) and at Mars (aphelion) required to be on the transfer ellipse. The difference, v , at each point is the velocity boost or transfer velocity needed.
Show that the areal velocity for a circular orbit of radius r about a mass M is At=12GMr . Does your expression give the correct value for Earth’s areal vilocity about the Sun?
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 Earth exerts a tidal force on the Moon. Is it greater than, the same as, or less than that of the Moon on Earth? Be careful in your response, as tidal forces arise from the difference in gravitational forces between one side and the other. Look at the calculations we performed for the tidal force on Earth and consider the values that would change significantly for the Moon. The diameter of the Moon is one-fourth that of Earth. Tidal forces on the Moon are not easy to detect, since there is no liquid on the surface.
Astronomical observatrions of our Milky Way galaxy indicate that it has a mass of about 8.01011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0104 light-years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way.
The Sun has a mass of approximately 1.99 1030 kg. a. Given that the Earth is on average about 1.50 1011 m from the Sun, what is the magnitude of the Suns gravitational field at this distance? b. Sketch the magnitude of the gravitational field due to the Sun as a function of distance from the Sun. Indicate the Earths position on your graph. Assume the radius of the Sun is 7.00 108 m and begin the graph there. c. Given that the mass of the Earth is 5.97 1024 kg, what is the magnitude of the gravitational force on the Earth due to the Sun?