Slide 1 / 67 Slide 2 / 67 1 Two spherical objects have masses of 200 kg and 2 Two spherical objects have masses of 1.5 x 10 5 kg 500 kg. Their centers are separated by a distance and 8.5 x 10 2 kg. Their centers are separated by a of 25 m. Find the gravitational attraction between distance of 2500 m. Find the gravitational them. attraction between them. Slide 3 / 67 Slide 4 / 67 3 Two spherical objects have masses of 3.1 x 10 5 kg 4 Two spherical objects have equal masses and and 6.5 x 10 3 kg. The gravitational attraction experience a gravitational force of 25 N towards between them is 65 N. How far apart are their one another. Their centers are 36cm apart. centers? Determine each of their masses. Slide 5 / 67 Slide 6 / 67 5 A 1 kg object is located at a distance of 6.4 x10 6 m 6 Two spherical objects have masses of 8000 kg from the center of a larger object whose mass is and 1500 kg. Their centers are separated by a 6.0 x 10 24 kg. distance of 1.5 m. Find the gravitational attraction between them. A What is the size of the force acting on the smaller object? B What is the size of the force acting on the larger object? C What is the acceleration of the smaller object when it is released? D What is the acceleration of the larger object when it is released?
Slide 7 / 67 Slide 8 / 67 7 Two spherical objects have masses of 7.5 x 10 5 kg 8 Two spherical objects have masses of 8.1 x 10 2 kg and 9.2 x 10 7 kg. Their centers are separated by a and 4.5 x 10 8 kg. The gravitational attraction distance of 2.5 x 10 3 m. Find the gravitational between them is 1.9 x 10 -3 N. How far apart are attraction between them. their centers? Slide 9 / 67 Slide 10 / 67 9 Two spherical objects have equal masses and 10 A 1 kg object is located at a distance of 7.0 x10 8 m experience a gravitational force of 85 N towards from the center of a larger object whose mass is one another. Their centers are 36mm apart. 2.0 x 10 30 kg. Determine each of their masses. A What is the size of the force acting on the smaller object? B What is the size of the force acting on the larger object? C What is the acceleration of the smaller object when it is released? D What is the acceleration of the larger object when it is released? Slide 11 / 67 Slide 12 / 67 11 Two spherical objects have masses of 8000 kg 12 Two spherical objects have masses of 9.5 x 10 8 kg and 5.0 kg. Their centers are separated by a and 2.5 kg. Their centers are separated by a distance of 1.5 m. Find the gravitational attraction distance of 2.5 x 10 8 m. Find the gravitational between them. attraction between them.
Slide 13 / 67 Slide 14 / 67 13 Two spherical objects have masses of 6.3 x 10 3 kg 14 Two spherical objects have equal masses and and 3.5 x 10 4 kg. The gravitational attraction experience a gravitational force of 25 N towards between them is 6.5 x 10 -3 N. How far apart are one another. Their centers are 36 cm apart. their centers? Determine each of their masses. Slide 15 / 67 Slide 16 / 67 15 A 1 kg object is located at a distance of 1.7 x10 6 m 16 *Compute g at a distance of 4.5 x 10 7 m from the from the center of a larger object whose mass is center of a spherical object whose mass is 3.0 x 10 23 kg. 7.4 x 10 22 kg. A What is the size of the force acting on the smaller object? B What is the size of the force acting on the larger object? C What is the acceleration of the smaller object when it is released? D What is the acceleration of the larger object when it is released? Slide 17 / 67 Slide 18 / 67 17 *Compute g for the surface of the moon. Its 18 *Compute g for the surface of a planet whose radius is 1.7 x10 6 m and its mass is 7.4 x 10 22 kg. radius is twice that of the Earth and whose mass is the same as that of the Earth.
Slide 19 / 67 Slide 20 / 67 19 *Compute g for the surface of the sun. Its radius 20 *Compute g for the surface of Mars. Its radius is is 7.0 x10 8 m and its mass is 2.0 x 10 30 kg. 3.4 x10 6 m and its mass is 6.4 x 10 23 kg. Slide 21 / 67 Slide 22 / 67 21 *Compute g at a height of 6.4 x 10 6 m (R E ) above 22 *Compute g at a height of 2 R E above the surface the surface of Earth. of Earth. Slide 23 / 67 Slide 24 / 67 23 *Compute g for the surface of a planet whose 24 *Compute g at a distance of 8.5 x 10 9 m from the radius is half that of the Earth and whose mass is center of a spherical object whose mass is 5.0 x double that of the Earth. 10 28 kg.
Slide 25 / 67 Slide 26 / 67 25 *Compute g at a distance of 7.3 x 10 8 m from the 26 *Compute g for the surface of Mercury. Its radius center of a spherical object whose mass is 3.0 x is 2.4 x10 6 m and its mass is 3.3 x 10 23 kg. 10 27 kg. Slide 27 / 67 Slide 28 / 67 27 *Compute g for the surface of Venus. Its radius is 28 *Compute g for the surface of Jupiter. Its radius 6.0 x10 6 m and its mass is 4.9 x 10 24 kg. of is 7.1 x10 7 m and its mass is 1.9 x 10 27 kg. Slide 29 / 67 Slide 30 / 67 29 *Compute g at a height of 4 R E above the surface 30 *Compute g at a height of 5 R E above the surface of Earth. of Earth.
Slide 31 / 67 Slide 32 / 67 32 **Compute: 31 *Compute g for the surface of a planet whose radius is double that of the Earth and whose mass a) The velocity of an object orbiting at a is also double that of the Earth. distance of 4.5 x 10 7 m from the center of a spherical object whose mass is 3.0 x 10 23 kg. b) Compute the orbital period of that object. Slide 33 / 67 Slide 34 / 67 33 **Compute: 34 **Mars has two moons, Phobos and Deimos. Phobos has an orbital radius of 9.4 x 10 6 m and an a) The velocity of an object orbiting at a height orbital period of 0.32 days. Deimos has an orbital of 6.4 x 10 6 m above the surface of Earth. radius of 23.5 x 10 6 m. b) Compute the orbital period of that object. a) What is the orbital period of Deimos? b) At what height above the surface of Mars would a satellite have to be placed so that it remains above the same location on the surface of Mars as the planet rotates below it. A Martian day is equal to 1.02 Earth days. Slide 35 / 67 Slide 36 / 67 36 **Compute: 35 **Compute: a) The velocity of an object orbiting at height of a) The velocity of an object orbiting at a 2 R E above the surface of Earth. distance of 8.5 x 10 9 m from the center of a spherical object whose mass is 5.0 x 10 28 kg. b) Compute the orbital period of that object. b) Compute the orbital period of that object.
Slide 37 / 67 Slide 38 / 67 38 **Compute: 37 **Earth orbits the sun in 365.25 days and has an orbital radius of 1.5 x 10 11 m. a) The velocity of an object orbiting at a distance of 7.3 x 10 8 m from the center of a a) How many days will it take Mercury to orbit the sun given that its orbital radius is 5.8x10 10 m? spherical object whose mass is 3.0 x 10 27 kg. b) How many days will it take Mars to orbit the sun given b) Compute the orbital period of that object. that its orbital radius is 2.3x10 11 m? c) It takes Jupiter 4333 days to orbit the sun. What is the average distance from the sun? Slide 39 / 67 Slide 40 / 67 39 **Compute: 40 **Calculate the orbital velocity and the period, in days, for an object orbiting the sun at distance of a) The velocity, both magnitude and direction, 1.5 x 10 11 m. Give the period in days. of an object orbiting at a height of 5 R E above the surface of Earth. b) Compute the orbital period of that object. Slide 41 / 67 Slide 42 / 67 41 **Jupiter has 16 moons. One of them, Io, has an orbital radius of 4.2 x 10 8 m and an orbital period of 1.77 days. a) What is the mass of Jupiter? General Problems b) Another of them, Europa, has an orbital radius of 6.7 x 10 8 m. What is its orbital period? c) Another of them, Ganymede, has an orbital period 7.2 days. What is the radius of its orbit? d) Jupiter rotates once every 0.41 days. At what orbital radius will a satellite maintain a constant position?
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