Slide 1 / 42 Slide 2 / 42 1 The gravitational force between two objects is 2 Two objects attract each other gravitationally. If proportional to the distance between their centers is cut in half, the gravitational force the distance between the two objects. A is cut to one fourth. A the square of the distance between the two B objects. is cut in half. B the product of the two objects. doubles. C C the square of the product of the two objects. quadruples D D Slide 3 / 42 Slide 4 / 42 3 Two objects, with masses m 1 and m 2 , are originally 4 As a rocket moves away from the Earth's surface, a distance r apart. The magnitude of the the rocket's weight gravitational force between them is F. The masses are changed to 2m 1 and 2m 2 , and the distance is changed to 4r. What is the magnitude of the new increases. A gravitational force? decreases. B remains the same. C F/16 A D depends on how fast it is moving. F/4 B 16F C 4F D Slide 5 / 42 Slide 6 / 42 5 A hypothetical planet has a mass of half that of the 6 Two planets have the same surface gravity, but Earth and a radius of twice that of the Earth. What planet B has twice the mass of planet A. If planet is the acceleration due to gravity on the planet in A has radius r, what is the radius of planet B? terms of g, the acceleration due to gravity at the Earth? 0.707r A r B A g C 1.41r g/2 B 4r D g/4 C g/8 D
Slide 7 / 42 Slide 8 / 42 7 Let the average orbital radius of a planet be r. Let 8 A planet is discovered to orbit around a star in the the orbital period be T. What quantity is constant galaxy Andromeda, with the same orbital diameter for all planets orbiting the Sun? as the Earth around our Sun. If that star has 4 times the mass of our Sun, what will the period of revolution of that new planet be, compared to the Earth's orbital period? T/R A T/R 2 B T 2 /R 3 one-fourth as much C A T 3 /R 2 one-half as much D B C twice as much four times as much D Slide 9 / 42 Slide 10 / 42 9 The speed of Halley's Comet, while traveling in its 10 The hydrogen atom consists of a proton of mass 1.67 × 10 -27 kg and an orbiting electron of mass 9.11 elliptical orbit around the Sun, × 10 -31 kg. In one of its orbits, the electron is 5.3 × 10 -11 m from the proton. What is the mutual attractive force between the electron and proton? is constant. A increases as it nears the Sun. B 1.8 × 10 -47 N decreases as it nears the Sun. C A 3.6 × 10 -47 N D is zero at two points in the orbit. B 5.4 × 10 -47 N C 7.0 × 10 -47 N D Slide 11 / 42 Slide 12 / 42 11 The gravitational attractive force between two 12 A spherically symmetric planet has four times the masses is F. If the masses are moved to half of Earth's mass and twice its radius. If a jar of their initial distance, what is the gravitational peanut butter weighs 12 N on the surface of the attractive force? Earth, how much would it weigh on the surface of this planet? 4F A A 6.0 N 2F B 12 N B F/2 C 24 N C D F/4 36 N D
Slide 13 / 42 Slide 14 / 42 13 A satellite encircles Mars at a distance above its 14 A satellite is in a low circular orbit about the Earth surface equal to 3 times the radius of Mars. The (i.e., it just skims the surface of the Earth). What is acceleration of gravity of the satellite, as the speed of the satellite? (The mean radius of the Earth is 6.38 × 10 6 m.) compared to the acceleration of gravity on the surface of Mars, is 5.9 km/s A zero. A 6.9 km/s B the same. B 7.9 km/s C one-third as much. C 8.9 km/s D one-sixteenth as much. D Slide 15 / 42 Slide 16 / 42 The planet Jupiter is 7.78 × 10 11 m from the Sun. 15 Two moons orbit a planet in nearly circular orbits. 16 Moon A has orbital radius r, and moon B has How long does it take for Jupiter to orbit once orbital radius 4r. Moon A takes 20 days to about the Sun? (The distance from the Earth to the Sun is 1.50 × 10 11 m.) complete one orbit. How long does it take moon B to complete an orbit? 1 yr A 20 days A B 3 yr 80 days B 6 yr C 160 days C 12 yr D D 320 days Slide 17 / 42 Slide 18 / 42 The mass of Earth's moon is 7.4 x 10 22 kg and its 17 What is the gravitational force acting on a 70 kg 18 mean radius is 1.75 x 10 3 km. What is the person standing on Earth due to the moon? The mass of the moon is 7.36 x 10 22 kg and the distance acceleration due to gravity at its surface? to the moon is 3.8 x 10 8 m. 2.8 x 10 6 m/s 2 A 0.24 N A 9.8 m/s 2 B 0.024 N B 1.6 m/s 2 C C 0.0024 N 0.80 N D 0.00024 N D
Slide 19 / 42 Slide 20 / 42 19 An astronaut goes out for a "space walk" at a 20 The radius of Earth is R. At what distance above distance above Earth's surface equal to the radius Earth's surface will the acceleration of gravity be 4.9 m/s 2 ? of Earth. What is her acceleration due to gravity? zero 0.41 R A A B g B 0.50 R g/2 R C C g/4 1.41 R D D Slide 21 / 42 Slide 22 / 42 21 At a distance of 14000 km from a planet's center g = 22 An object weighs 432 N on the surface of Earth. At 32 m/s 2 . What is g at a location which is 28000 km a height of 3R Earth above Earth's surface, what is its from the planet's center? weight? 8 m/s 2 A 432 N A 16 m/s 2 48 N B B 128 m/s 2 27 N C C D cannot be determinded with this information D 0 N Slide 23 / 42 Slide 24 / 42 23 By how many Newtons does the weight of a 100-kg 24 A spherically symmetric planet has a mass two person change in going from sea level to an altitude times that of Earth and a radius that is twice Earth's. of 5000 m (R Earth = 6.4 x 106 m)? If a jar of peanut butter weight 12 N on the surface of Earth, what would it weigh on that planet? A 0.73 N 1 N B 6 N A 0 N C 12 N B 0.34 N D 18 N C D 20 N
Slide 25 / 42 Slide 26 / 42 25 The weight of a satellite on a planet's surface is W. 26 A spacecraft is in a circular orbit with speed v and Which is closest to the weight of the satellite when orbital radius R around a planet of mass M. What it's in orbit? is its orbital velocity? 0.05 W GMR A A (GM/R) 2 B 0.10 W B (GM/R) 1/2 0.50 W C C (R/GM) 1/2 0.95 W D D (MR/G) 2 0 E E Slide 27 / 42 Slide 28 / 42 28 Five different satellites orbit the same planet. The 27 Two satellites, X and Y, orbit the same planet at the same height. The orbital velocity of X is v, what is mass and orbital radius of each is given below. the orbital velocity of Y? Which has the lowest speed? Mass Radius v A 1/2 m 1/2 R A 2v B B m 1/2 R v/2 C m R C D 4v m 2R D v/1.4 E 2m R E Slide 29 / 42 Slide 30 / 42 29 A student who weighs 500 N on Earth travels to a 30 Mars has 1/10 the mass of Earth and 1/2 its planet whose mass and radius are twice that of diameter. What is the surface gravity on Mars? Earth. His weight on that planet is about g A A 1000N 1/2 g B 500 N B 2 g C 1500 N C 2/5 g D 750 N D 1/10 g E 250 N E
Slide 31 / 42 Slide 32 / 42 31 A satellite of mass M moves in a circular orbit of 32 Spacecraft X has twice the mass of Spacecraft Y. radius R with speed v. Which of these must be They orbit Earth at the same radius. Which of these must be true. true for the satellite. I. The net force on it is MR/v 2 I. X feels a greater gravitational force than Y II. X travels twice as fast as Y II. Its acceleration is GM/R II. Its orbital velocity is (GM/R) 1/2 II. X takes twice as long to complete an orbit l only l only A A lll only lll only B B C l and ll only C l and ll only ll and lll only ll and lll only D D l, ll, and lll l, ll, and lll E E Slide 33 / 42 Slide 34 / 42 33 A planets mass can be determined if it is orbited 34 An astronaut inside the space station appears by a small satellite by equating its gravitational weightless. Which statement is true? and centripetal accelerations. Which of the below is not required to do this calculation? The gravitational force on the astronaut is zero A The moon's gravitational pull cancels that of The mass of the satellite A B Earth The radius of the satellite's orbit B The astronaut is in free fall C The period of the satellite's orbit C D The astronaut loses about 95% of her weight The universal gravitational constant, G D In space, astronauts have no mass E All of the above are required E Slide 35 / 42 Slide 36 / 42 35 Two planets have the same surface gravity, but 36 A planet has half the mass and radius of Earth. planet X has twice the mass of Y. Planet X has What is the acceleration due to gravity on the radius r, what is the radius of Y? planet compared to g on Earth A 0.707 r A g r g/2 B B 1.41 r g/4 C C 4r g/8 D D 2r 2g E E
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