Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 11, Problem 67P
(a)
To determine
The total mass of the rod.
(b)
To determine
The gravitational field due to rod on x -axis at
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A solid uniform sphere has a mass of 4.00 x 10* kg and a radius of 1.5 m. (Use the following as necessary: r and m. Assume SI units. Do not enter units in your ansWers.)
(a) What is the magnitude of the gravitational force due to the sphere on a particle of mass m located at a distance of 1.6 m from the center of the sphere?
F =
N.
(b) What if it is 1.4 m from the center of the sphere?
F =
N.
(c) Write a general expression for the magnitude of the gravitational force on the particle at a distancer 1.5 m from the center of the sphere.
F =
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In introductory physics laboratories, a typicalCavendish balance for measuring the gravitational constant G uses lead spheres of masses1.68 kg and 14.4 g whose centers are separatedby 2.7 cm.Calculate the gravitational force betweenthese spheres, treating each as a point masslocated at the center of the sphere. Thevalue of the universal gravitational constantis 6.67259 × 10−11 N · m2/kg2.Answer in units of N.
Chapter 11 67. A nonuniform thin rod of length L lies on the x axis. One end of the rod is at the origin, and the other end is at x=L. the rod's mass per unit length λ varies as λ=Cx, where C is a constant.(Thus, an element of the rod has mass dm=λ dx.) (a) Determine the total mass of the rod. (b)Determine the gravitational field due to the rod on the x axis at x=x0, there x0 >L.
Chapter 11 Solutions
Physics for Scientists and Engineers
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- The gravitational force exerted on an astronaut on the Earths surface is 650 N directed downward. When she is in the space station in orbit around the Earth, is the gravitational force on her (a) larger, (b) exactly the same, (c) smaller, (d) nearly but not exactly zero, or (e) exactly zero?arrow_forwardLet 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.)arrow_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_forward
- What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?arrow_forwardThe 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?arrow_forwardOn a planet whose radius is 1.2107m , the acceleration due to gravity is 18m/s2 . What is the mass of the planet?arrow_forward
- A point mass m is located a distance D from the nearest end of a thin rod of mass M and length L along the axis of the rod. Find the gravitational force exerted on the point mass by the rod.arrow_forward(a) Find the magnitude of the gravitational force between a planet with mass 7.50 1024 kg and its moon, with mass 2.70 1022 kg, if the average distance between their centers is 2.80 108 m. (b) What is the acceleration of the moon towards the planet? (c) What is the acceleration of the planet towards the moon?arrow_forwardWhat is the average speed in mi/h of a person at the equator as a result of the Earths rotation? (Take the radius of the Earth to be RE = 4000 mi.)arrow_forward
- The density inside a solid sphere of radius a is given by p=Po a/r, where Po is the density at the surface and r denotes the distance from the center. Find the gravitational field due to this sphere at a distance 2 a from its center.arrow_forwardThe drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force FSM that the sun exerts on the moon is perpendicular to the force FEM that the earth exerts on the moon. The masses are: mass of sun = 1.99 × 10³0 kg, mass of earth = 5.98 × 1024 kg, mass of moon = 7.35 × 1022 kg. The distances shown in the drawing are rsM = 1.50 × 10¹1 m and rEM = 3.85 × 108 m. Determine the magnitude of the net gravitational force on the moon. Number i Sun Units ISM FSM FEM Earth Moon TEMarrow_forwardA satellite is orbiting around a planet in a circular orbit. The radius of the orbit, measured from the center of the planet is R = 1.8 × 107 m. The mass of the planet is M = 4.8 × 1024 kg. a)Express the magnitude of the gravitational force F in terms of M, R, the gravitational constant G, and the mass m of the satellite. b)Express the magnitude of the centripetal acceleration ac of the satellite in terms of the speed of the satellite v, and R. c) Express the speed v in terms of G, M and R.arrow_forward
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