A) 2 B) 2 C) 2 2 D) 4 E) 8

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1 Page 1 of 8 CTGavity-1. m M Two spheical masses m and M ae a distance apat. The distance between thei centes is halved (deceased by a facto of 2). What happens to the magnitude of the foce of gavity between them? The foce inceases by a facto of A) 2 B) 2 C) 2 2 D) 4 E) 8 Answe: 4 CTGavity-2. At a paticula instant, two asteoids in inte-galactic space ae a distance = 20 km apat. Asteoid 2 has 10 times the mass of asteoid 1. The magnitudes of the acceleations of asteoids 1 and 2 ae a 1 and a 2, espectively. a 1 What is the atio? a 2 m 1 m 2 = 10 m 1 A) 10 B) 1/10 C) 1 D) cannot be detemined. Answe: 10 Each mass feels the same sized foce. The smalle mass has the bigge acceleation. CTGavity-3. Planet X has the same mass as the Eath, but 1/2 the adius. (Planet X is moe dense than Eath). What is the acceleation of gavity on Planet X? A) g E (same as Eath) B) 2 g E C) 4 g E D) 8 g E E ) None of these. Answe: 4 g E

2 Page 2 of 8 CTGavity-4. A satellite is in cicula obit at an altitude of 100 miles above the suface of the Eath. Eath The satellite s pe-launch weight is its weight measued on the gound. The magnitude of the foce of gavity on the satellite while it is in obit is.. A) slightly geate than its pe-launch weight. B) the same as its pe-launch weight. C) slightly less than its pe-launch weight. D) much less than its pe-launch weight, but not zeo. E) zeo. Answe: slightly less than its pe-launch weight. The satellite is only slightly futhe fom the cente of the eath when it is in obit, compaed to when it is on the gound. CTGavity-5. Two satellites, A and B, ae in cicula obit aound the eath. The distance of satellite B fom the cente of the Eath is twice that of satellite A. What is the atio of the magnitudes of the acceleations of A to B? a A... A) 1 B) 2 C) 4 D) 1/2 E) 1/4 a B B A Answe: 4

3 Page 3 of 8 CTGavity-6. A ock is eleased fom est at a point in space fa fom Eath, beyond the obit of the Moon. The ock falls towad the Eath and cosses the obit of the Moon. When the ock is the same distance fom the Eath as the Moon, the magnitude of the acceleation of the ock is.. (Ignoe the gavitational foce between the ock and the Moon.) A) geate B) smalle C) the same as the acceleation of the Moon. Moon Eath ock Answe: the same as The acceleation of gavity depends only the distance to the cente of the eath. As the ock falls towad the Eath, its acceleation is.. (neglect Moon s gavity) A) constant. B) not constant. Answe: not constant, as the ock gets close to Eath, the acceleation of gavity inceases CTGavity-7. At time t=0, a satellite in cicula obit about the Eath is diectly ove Denve, 300 miles above the city, and taveling eastwad at 16,000 mph. At the same time, a ock is eleased fom est 300 miles above the city, vey nea the satellite. satellite ock Denve Tue o False: at t=0+, the acceleations of the ock and the satellite ae identical. A) Tue B) False Answe: Tue

4 Page 4 of 8 CTGavity-8. Suppose the Eath had no atmosphee and a pojectile was fied fom a mountain top with sufficient speed to put it in cicula obit. The magnitude of the acceleation of the pojectile while in obit would be.. A) much less than g (because it doesn't fall to the gound) B) much geate than g C) appoximately g D) Impossible to tell. Answe: appoximately g T CTGavity-9. Keple's thid law states that the atio 3 is a constant fo all the planets. The peiod T of the Eath is 1 yea. An astonomical unit (1 A.U.) is defined as the mean distance fom the Eath to the Sun, theefoe the mean Eath-Sun distance is 1A.U. Conside an asteoid in cicula obit aound the Sun with adius = 2A.U. The peiod of the asteoid is.. A) 2 yeas. B) 3 yeas C) 2 3/ yeas. D) 2 2/ yeas E) None of these. Answe: 2 3/ yeas. 2

5 Page 5 of 8 CTGavity-10. A planet in elliptical obit aound a sta moves fom the point in its obit futhest fom the sta (A) to the closest point (P). The wok done by the foce of gavity duing this movement is: A) zeo B) positive C) negative. P A Answe: positive The planet executes one complete obit stating fom point A and etuning to A. The wok done by the foce of gavity duing this obit is: Answe: zeo A) zeo B) Positive C) Negative. CTGavity-11. The gavitational PE, U() = GMm/ of a two mass system (m << M) is plotted. Mass M is stationay at the oigin and mass m is at = 0. Also shown is the total enegy E tot. Which aow epesents the KE of mass m? A B C D) none of these U() 0 B C A E tot Answe: A KE + PE = E tot

6 Page 6 of 8 CTGavity-12. A pojectile is fied fom an ailess wold with a speed = v escape. What is the total enegy (E tot = KE GMm/ ) of the pojectile? A) E tot = 0 B) E tot < 0 C) E tot > 0 Answe: E tot = 0 CTGavity-13.Does escape speed depend on launch angle? That is, if a pojectile is given an initial speed v o, is it moe likely to escape an (ailess) planet, if fied staight up than if fied at an angle? A) Yes B) No Answe: No. The escape speed is independent of angle CTGavity-14. A planet is in elliptical obit aound the Sun. The zeo of potential enegy U is GMm chosen at =, so U( ). How does the magnitude of U U U compae to the KE? A) U > KE B) U < KE C) U =KE D) depends on the position in the obit. Answe: U > KE than the positive KE. Since E tot < 0 (bound obit), the negative U must be lage in magnitude

7 Page 7 of 8 CTGavity-15. Suppose a pojectile is fied staight upwad fom the suface of an ailess planet of adius R with the escape velocity v esc (meaning the pojectile will just baely escape the planet's gavity -- it will asymptotically appoach infinite distance and zeo speed.) What is the pojectile's speed when it is a distance 4R fom the planet's cente (3R fom the suface). A) 1/2 v esc B) 1/4 v esc C) 1/9 v esc D) 1/3 v esc E) None of these is coect. (Ignoe the gavity of the Sun and othe astonomical bodies.) Answe: 1/2 v esc Use consevation of enegy. E tot = 0 (since v = v esc ), so the magnitude of PE = U equals the magnitude of the KE: PE = KE. If inceases by a facto of 4, the PE deceases in magnitude by a facto of 4. If PE deceases by 4, KE must decease by 4. CTGavity-16. A satellite is in cicula obit aound a planet that has a vey tenuous atmosphee extending up to the altitude of the satellite. Due to atmospheic dag, the satellite... A) spials inwad B) spials outwad C) emains in an obit of constant adius Answe: spials inwad. as the obit decays, the speed of the satellite A) inceases B) deceases C) emains constant Answe: inceases! As deceases, the obital speed inceases! Vey non-intuitive! v_obit = (GM / )^1/2. As deceases, v_obit inceases.

8 Page 8 of 8 CTGavity-17. A peson is standing in an elevato in a building on Eath. The elevato is stopped between floos. Anothe peson is in a small oom in a ocket in integalactic space. The ocket is acceleating at 9.8 m/s 2 as shown. a = g Eath Space Which peson feels heavie? A) Eath peson. B) Space peson. C) They feel exactly the same. Answe: They feel exactly the same. CTGavity-18. Astonaut Dave Bowman is standing in the centifuge of the spaceship Discovey. He dops his pen and obseves it fall to the floo. Which statement below is most accuate? A) Afte Bowman eleases the pen, the net foce on the pen is zeo. B) The pen falls because the centifugal foce pulls it towad the floo. C) The pen falls because the atificial gavity pulls it towad the floo. Answe: Afte Bowman eleases the pen, the net foce on the pen is zeo. CTGavity-19. How does the foce of gavity on a space shuttle Astonaut compae to the foce of gavity on the astonaut when she is on the eath? A) Foce of gavity on the space shuttle astonaut is zeo. B) Foce of gavity on the space shuttle astonaut is much, much less than on eath, but not zeo. C) Foce of gavity on the space shuttle astonaut is slightly less than when on eath Answe: Foce of gavity on the space shuttle astonaut is slightly less than when on eath

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