A solid sphere of uniform density has a mass of 8.7 x 104 kg and a radius of 1.2 m. What is the magnitude of the gravitational force due to the sphere on a particle of mass 6.5 kg located at a distance of (a) 4.2 m and (b) 0.34 m from the center of the sphere? (c) Write a general expression for the magnitude of the gravitational force on the particle at a distance rs 1.2 m from the center of the sphere. (a) Number Units (b) Number Units (c) |Fon m| =kr, where k =

A solid sphere of uniform density has a mass of 8.7 x 104 kg and a radius of 1.2 m. What is the magnitude of the gravitational force due to the sphere on a particle of mass 6.5 kg located at a distance of (a) 4.2 m and (b) 0.34 m from the center of the sphere? (c) Write a general expression for the magnitude of the gravitational force on the particle at a distance rs 1.2 m from the center of the sphere. (a) Number Units (b) Number Units (c) |Fon m| =kr, where k =

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 56PQ: Consider the Earth and the Moon as a two-particle system. a. Find an expression for the...

See similar textbooks

Similar questions

Suppose 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/s2
Saturns ring system forms a relatively thin, circular disk in the equatorial plane of the planet. The inner radius of the ring system is approximately 92,000 km from the center of the planet, and the outer edge is about 137,000 km from the center of the planet. The mass of Saturn itself is 5.68 1026 kg. a. What is the period of a particle in the outer edge compared with the period of a particle in the inner edge? b. How long does it take a particle in the inner edge to move once around Saturn? c. While this inner-edge particle is completing one orbit abound Saturn, how far around Saturn does a particle on the outer edge move?
Consider the Earth and the Moon as a two-particle system. a. Find an expression for the gravitational field g of this two-particle system as a function of the distance r from the center of the Earth. (Do not worry about points inside either the Earth or the Moon.) b. Plot the scalar component of g as a function of distance from the center of the Earth.
(a) What is the acceleration due to gravity on the surface of the Moon? (b) On the surface of Mars? The mass of Mars is SW 6.4181023kg and its radius is 3.38106m .
(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
(a) In order to keep a small satellite from drifting into a nearby asteroid, it is placed in orbit with a period of 3.02 hours and radius of 2.0 km. What is the mass of the asteroid? (b) Does this mass seem reasonable for the size of the orbit?
The mass of the Earth is approximately 5.98 1024 kg, and the mass of the Moon is approximately 7.35 1022 kg. The Moon and the Earth are separated by about 3.84 108 m. a. What is the magnitude of the gravitational force that the Moon exerts on the Earth? b. If Serena is on the Moon and her mass is 25 kg, what is the magnitude of the gravitational force on Serena due to the Moon? The radius of the Moon is approximately 1.74 106 m.
Since March 2006, NASAs Mars Reconnaissance Orbiter (MRO) has been in a circular orbit at an altitude of 316 km around Mars (Fig. P6.81). The acceleration due to gravity on the surface of the planet Mars is 0.376g, and its radius is 3.40 103 km. Assume the acceleration due to gravity at the satellite is the same as on the planets surface. a. What is MROs orbital speed? B. What is the period of the spacecrafts orbit? FIGURE P6.81
(a) Using the data in the previous problem for the asteroid Vesta which has a diameter of 520 km and mass of 2.671020kg , what would be the orbital period for a space probe in a circular orbit of 10.0 km from its surface? (b) Why is this calculation marginally useful at best?
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.)
(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?
(a) Calculate Earth’s mass given the acceleratioln due to gravity at the North Pole is measured to be 9.832m/s2 and the radius of the Earth at the pole is 6356 km. (b) Compare this with the NASA’s Earth Fact Sheet value of 5.97261024kg .