91影视

(a) At what height above Earth鈥檚 surface is the energy required to lift a satellite to that height equal to the kinetic energy required for the satellite to be in orbit at that height? (b) For relater heights, which is greater, the energy for lifting or the kinetic energy for orbiting?

Planet Roton, with a mass of $\mathbf{7}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{脳}\mathbf{}{\mathbf{10}}^{\mathbf{24}}\mathbf{}\mathit{k}\mathit{g}$and a radius of $\mathbf{1600}\mathbf{}\mathit{k}\mathit{m}$ , gravitationally attracts a meteorite that is initially at rest relative to the planet, at a distance great enough to take as infinite.The meteorite falls toward the planet. Assuming the planet is airless, find the speed of the meteorite when it reaches the planet鈥檚 surface.

The figure shows a spherical hollow inside a lead sphere of radius; $R=4.00\text{cm}$the surface of the hollow passes through the centre of the sphere and 鈥渢ouches鈥� theright side of the sphere. The massof the sphere before hollowing was. $M=2.95\text{kg}$With what gravitational force does the hollowed-out lead sphere attract a small sphere of massrole="math" localid="1655807683275" $m=0.431\text{kg}$that lies at a distance$d=9.00\text{cm}$from the centre of the lead sphere, on the straight line connecting the centres of the spheres and of the hollow?

Three point particles arefixed in position in anx-yplane. Twoof them, particleAof mass 6.00 gand particleBof mass 12.0 g, are shown in the figure, with a separation of${\mathit{d}}_{\mathbf{A}\mathbf{B}}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{500}\mathbf{}\mathbf{m}$at$\mathit{胃}\mathbf{=}\mathbf{30}\mathbf{掳}$angle.ParticleC, with mass, 8.00 g is not shown. The net gravitational forceacting on particleAdue to particlesBandCis$\mathbf{2}\mathbf{.}\mathbf{77}\mathbf{脳}{\mathbf{10}}^{\mathbf{14}}\mathbf{}\mathbf{N}$at an angle$\mathbf{-}\mathbf{163}\mathbf{.}\mathbf{8}\mathbf{掳}$of from the positive direction of thexaxis. What is (a) thexcoordinate and (b) theycoordinate of particleC?

Three dimensions.Three point particles are fixed in place in axyzcoordinate system. ParticleA, at the origin, has mass ${\mathbf{m}}_{\mathbf{A}}$ . ParticleB, atxyzcoordinates $\left(2.00d,1.00d,2.00d\right)$, has mass$\mathbf{2}\mathbf{.}\mathbf{00}{\mathbf{m}}_{\mathbf{A}}$, and particleC, at coordinates$\left(-1.00d,2.00d,-3.00d\right)$, has mass$\mathbf{3}\mathbf{.}\mathbf{00}{\mathbf{m}}_{\mathbf{A}}$. A fourth particleD, with mass $\mathbf{4}\mathbf{.}\mathbf{00}{\mathbf{m}}_{\mathbf{A}}$, is to be placed near the other particles. In terms of distanced, at what (a)x, (b)y, and (c)zcoordinate shouldDbe placed so that the net gravitational force onAfromB,C, andDis zero?

In the figure, a particle of mass$m_1=0.67\text{kg}$is a distance$d=23\text{cm}$from one end of a uniform rod with length$L=3.0\text{m}$and mass$M=5.0\text{kg}$. What is the magnitude of the gravitational forceon the particle from the rod?

(a) What will an object weigh on the Moon鈥檚 surface if it weighs $100\text{N}$on Earth鈥檚 surface? (b) How many Earth radii must this same object be from the centre of Earth if it is to weigh the same as it does on the Moon?

Mountain pulls.A large mountain can slightly affectthe direction of 鈥渄own鈥� as determined by a plumb line. Assumethat we can model a mountain as a sphere of radius$\mathbf{R}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{km}$and density (mass per unit volume).$\mathbf{2}\mathbf{.}\mathbf{6}\mathbf{脳}{\mathbf{10}}^{\mathbf{3}}\mathbf{}\mathbf{kg}\mathbf{/}{\mathbf{m}}^{\mathbf{3}}$Assume alsothat we hang a 0.50mplumb line at a distance offrom the sphere鈥檚 centre and such that the sphere pulls horizontally on thelower end. How far would the lower end move toward the sphere?

what altitude above Earth鈥檚 surface would the gravitational acceleration be$\mathbf{4}\mathbf{.}\mathbf{9}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$?

A massMis split into two parts,$\mathit{m}$and role="math" localid="1657189921712" $\mathit{M}\mathbf{-}\mathit{m}$, which are0 then separated by a certain distance. What ratio$\mathit{m}\mathbf{-}\mathit{M}$maximizes the magnitude of the gravitational force between the parts?