Mass M is divided into two parts xM and (1-x)M. For a given separation, the value of x for which the gravitational attraction between the two pieces becomes maximum. Find this maximum value of x.

In the figure below, three point particles are fixed in place in an xy plane. Particle A has mass mA, particle B has mass 2.35mA, and particle C has mass 3.45mA. A fourth particle D, with mass 4.40mA, is to be placed near the other three particles. In terms of distance d, at what coordinates should particle D be placed so that the net gravitational force on particle A from particles B, C, and D is zero? (a) C 1.5d x coordinate d (b) y coordinate Bo A d x

There is a small sphere of mass m at a height H, from the center of a uniform ring of radius R and mass M. The center of the ring is placed at the origin of a Cartesian coordinate system. The x and y directions line in the plane of the ring, while the z-direction is positive upwards.’  Take the x-axis to be directed towards the right (in the plane of the ring). Write an expression for the x-component of the gravitational force Fx on the mass m, where G is the gravitational constant.

(a) Evaluate the gravitational potential energy (in J) between two 4.00 kg spherical steel balls separated by a center-to-center distance of 19.0 cm. (b) Assuming that they are both initially at rest relative to each other in deep space, use conservation of energy to find how fast (in m/s) will they each be traveling upon impact. Each sphere has a radius of 5.50 cm. m/s

On the ground level, the weight of a satellite is W N. The satellite is launched and stays in an orbit that is R/47 above the ground level, where R is radius of the Earth. If the gravitational force on the satellite is xW at this location, determine x.

, are: Three point particles are fixed in position in an xy plane. Two of them, particle A of mass 5 g and particle B of mass 11 g, are shown in the figure with a separation of dAB = 0.519 m at angle O = 30°. Particle C, with mass 9 g, is not shown. The net gravitational force acting on particle A due to particles B and Cis 2.71 x 1014 N at an angle of -163.8°. from the positive x axis. What are (a) the x coordinate and (b) the y coordinate of particle C? В dAB A

A satellite of Mars, called Phobos, has an orbital radius of 9.4 ✕ 106 m and a period of 2.8 ✕ 104 s. Assuming the orbit is circular, determine the mass of Mars. (ans kg)

A coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a m, = 1.9-kg object at the origin of the coordinate system, a m, = 3.3-kg object at (0, 2.0), and a m, = 5.3-kg object at (4.0, 0). Find the resultant gravitational force exerted by the other two objects on the object at the origin. magnitude Your response differs from the correct answer by more than 10%. Double check your calculations. N direction 68.12 o above the +x-axis

Current Attempt in Progress One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M-2.97 x 1024 kg and R-8.31 x 10 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet? (a) Number (b) Number Units Units

(a) How far from the center of Earth would the net gravitational force of Earth and the Moon on an object be zero? (b) Setting the magnitudes of the forces equal should result in two answers from the quadratic. Do you understand why there are two positions, but only one where the net force is zero?