**37. Two particles are located on the x axis. Particle 1 has a mass m andis at the origin. Particle 2 has a mass 2m and is at x = +L. A third par-ticle is placed between particles 1 and 2. Where on the x axis should thethird particle be located so that the magnitude of the gravitational forceon both particle 1 and particle 2 doubles? Express your answer in termsof L.

Case 1: When particle 1 and particle 2 are separated by the distance L. The free body diagram is…

Answered: **37. Two particles are located on the…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 1P

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(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?
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
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?
Planetary orbits are often approximated as uniform circular motion. Figure P7.9 is a scaled representation of a planets orbit with a semimajor axis of 1.524 AU. a. Use Figure P7.9 to find the ratio of the Suns maximum gravitational field to its minimum gravitational field on the planets orbit. b. What is the ratio of the planets maximum speed to its minimum speed? c. Comment on the validity of approximating this orbit as uniform circular motion.
two particles, of masses m and 2m, are fixed in place on an axis. (a) Where on the axis can a third particle of mass 3m be placed (other than at infinity) so that the net gravitational force on it from the first two particles is zero: to the left of the first two particles, to their right, between them but closer to the more massive particle, or between them but closer to the less massive particle? (b) Does the answer change if the third particle has, instead, a mass of 16m? (c) Is there a point off the axis (other than infinity) at which the net force on the third particle would be zero?
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Three identical very dense masses of 7100 kg each are placed on the x axis. One mass is at x1 = -110 cm , one is at the origin, and one is at x2 = 320 cm. What is the magnitude of the net gravitational force Fgrav on the mass at the origin due to the other two masses? Take the gravitational constant to be G = 6.67×10−11 N⋅m2/kg2 . What is the direction of the net gravitational force on the mass at the origin due to the other two masses?
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