Three point particles are fixed in place in an xy plane, as shown. Particle A has mass ma, parti- cle B has mass 2.00m A, and particle C has mass 3.00m A. A fourth particle D, with mass 4.00mA, is to be placed near the other three particles. In terms of distance d, at what (a) x coordinate and (b) y coordinate should particle D be placed so that the net gravitational force on particle A from particles B, C, and D is zero? В d 1.5d C A

Three point particles are fixed in place in an xy plane, as shown. Particle A has mass ma, parti- cle B has mass 2.00m A, and particle C has mass 3.00m A. A fourth particle D, with mass 4.00mA, is to be placed near the other three particles. In terms of distance d, at what (a) x coordinate and (b) y coordinate should particle D be placed so that the net gravitational force on particle A from particles B, C, and D is zero? В d 1.5d C A

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.6P

See similar textbooks

Similar questions

A uniform rod of mass 200 g and length 100 cm is free to rotate in a horizontal plane around a fixed vertical axis through its center, perpendicular to its length. Two small beads, each of mass 20 g, are mounted in grooves along the rod. Initially, the two beads are held by catches on opposite sides of the rod’s center, 10 cm from the axis of rotation. With the beads in this position, the rod is rotating with an angular velocity of 10.0 rad/s. When the catches are released, the beads slide outward along the rod. (a) What is the rod’s angular velocity when the beads reach the ends of the rod? (b) What is the rod’s angular velocity if the beads fly off the rod?
A nonrotating frame of reference placed at the center of the Sun is very nearly an inertial one. Why is it not exactly an Inertial frame?
A rocket takes off from Earth and reaches a speed of 100 m/s in 10.0 s. If the exhaust speed is 1500 m/s and the mass of fuel burned is 100 kg, what was the initial mass of the rocket?
The Sun’s mass is 2.01030kg , its radius is 7.0105km , and it has a rotational period of approximately 28 days. If the Sun should collapse into a white dwarf of radius 3.5103km , what would its period be if no mass were ejected and a sphere of uniform density can model the Sun both before and after?
Check Your Understanding Galaxies are not single objects. How does the gravitiational force of one galaxy exerted on the “closer” stars of the other galaxy compare to those farther away? What effect would this have on the shape of the galaxies themselves?
Find the center of mass of a cone of uniform density that has a radius R at the base, height h, and mass M. Let the origin be at the center of the base of the cone and have +z going through the cone vertex.
In a particle accelerator, a proton has mass 1.6710-27kg and an initial speed of 2.00105m/s . It moves in a straight line, and its speed increases to 9.00105m/s in a distance of 10.0 cm. Assume that the acceleration Is constant. Find the magnitude of the force exerted on the proton.
Three point particles are fixed in place in an xyz coordinate system. Particle A, at the origin, has mass mA. Particle B, at xyz coordinates (2.00d, 1.00d, 2.00d), has mass 2.00mA, and particle C, at coordinates (-1.00d, 2.00d, -3.00d), has mass 3.00mA. A fourth particle D, with mass 4.00mA, is to be placed near the other particles. In terms of distance d, at what (a) x, (b) y, and (c) z coordinate should D be placed so that the net gravitational force on Afrom B, C, and Dis zero?
(COLLAB Gauss's Law for Mass) Journey through the Center of the Earth. A 1024-kg blue ball is dropped from an initial z-position of 2.9 x 106 m through the center of a planet with radius 6 x 106 m. If the mass of the planet is 32.1 x 1015 kg, measure the displacement of the ball at time t = 7 s?
Astronomers estimate that a 2.0-km-diameter asteroid collideswith the Earth once every million years. The collision couldpose a threat to life on Earth. (a) Assume a spherical asteroidhas a mass of 3200 kg for each cubic meter of volume andmoves toward the Earth at 15 km/s How much destructiveenergy could be released when it embeds itself in the Earth?(b) For comparison, a nuclear bomb could release about 4.0x1016 JHow many such bombs would have to explodesimultaneously to release the destructive energy of theasteroid collision with the Earth?
Ahockey puck of mass 322 g is siding due east on a fictionless table with a speed of 150 ms Suddenlys constare force of magnitude 4.03 N and deacted due north is applied to the puck f 2.55s Find the magnitude of the moment | 4pm at the end of the 255-s interval (Express your answer to 2 decimal places, with no unit
Pluto and its satellite Charon have masses which are more similar to each other than any other knonw pair of orbiting bodies in the Solar system. How far from the center of pluto is the barycenter or center of mass of the Pluto-Charon system? Take the mass of Pluto to be 1.31 × 10^22 kg, and 1.59 × 10^21 kg for Charon (about one eighth that of Pluto). Assume Pluto and its moon Charon are separated by 19,640 km while the radius of Pluto and Charon are 1190 km and that of Charon are 606 km respectively. Treating Pluto and Charon as spherically symmetric objects, how far from Pluto is the barycenter of the Pluto - Charon pair, and is this point inside are outside of Pluto? Hint: Place Pluto at the origin and Charon on the x axis. A. 289 km; inside B. 781 km; inside C. 2130 km; outside D. 5910 km; outside