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.
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- Calculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?Consider two iron spheres, each of diameter 195 mm, which are just touching. At what distance r from the center of the earth will the force of mutual attraction between the contacting spheres be equal to the force exerted by the earth on one of the spheres? Answer: r = (107)kmA solid sphere has a uniformly distributed mass of 1.0 * 104 kg and a radius of 1.0 m.What is the magnitude of the gravitational force due to the sphere on a particle of mass m when the particle is located at a distance of (a) 1.5 m and (b) 0.50 m from the center of the sphere? (c) Write a general expression for the magnitude of the gravitational force on the particle at a distance r < 1.0 m from the center of the sphere.
- 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 = 4.07 × 1024 kg and R = 5.79 x 106 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet? (a) Number i Units (b) Number i UnitsConsider two iron spheres, each of diameter 280 mm, which are just touching. At what distance r from the center of the earth will the force of mutual attraction between the contacting spheres be equal to the force exerted by the earth on one of the spheres? Answer:r = i (107)kmThe moon orbits the earth along a path of radius 3.84 x 108 m , a spaceship of mass 30000 Kg orbits the Earth along a path of radius 2.8 x 108 m. calculate: a) The gravitational force exerted on the spaceship when it is at the line joints the centers of the earth and the moon. b) the gravitational field strength of the Earth at a point that locates at the orbit of the spaceship. G = 6.67 x 10-11 Nm2/Kg2 ME = 6 x 1024 Kg , Mm = 7.35 x 1022 Kg
- In the figure, three 9.74 kg spheres are located at distances d₁ = 0.953 m, and d₂ = 0.215 m. What are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the net gravitational force on sphere B due to spheres A and C? (a) Number i (b) Number i dr B Units Units î ✪The International Space Station has a mass of 4.19 x 10° kg and orbits at a radius of 6.79 x 10° m from the center of Earth. Find the gravitational force exerted by Earth on the space station, the space station's gravitational potential energy, and the weight of a 71.7 kg astronaut living inside the station. HINT (a) the gravitational force (in N) exerted Earth on the space station (Enter the magnitude.) (b) the space station's gravitational potential energy (in J) (c) the weight (in N) of an 71.7 kg astronaut living inside the station Need Help? Watch It Read It(c) Two uniform stars are separated by 2.36 × 1016 m. The star on the left has a mass of 5.33 × 1028 kg and the star on the right has a mass of 2.76 × 1030 kg. Determine the magnitude of the gravitational force on the star on the right. (d)Consider the two stars from part (c) above. Let the dotted line joining their centers be on the x-axis with the origin at the center of the star on the left. Determine the location of the center of mass of the two-star system.
- 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 UnitsThe International Space Station has a mass of 4.19 x 105 kg and orbits at a radius of 6.79 x 10° m from the center of Earth. Find the gravitational force exerted by Earth on be the space station, the space station's gravitational potential energy, and the weight of a 71.7 kg astronaut living inside the station. HINT (a) the gravitational force (in N) exerted by Earth on the space station (Enter the magnitude.) 3.637e7 X N (b) the space station's gravitational potential energy (in J) -2.4696e13 (c) the weight (in N) of an 71.7 kg astronaut living inside the station X N Need Help? Read It Watch ItOn 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.
