2013 Checkpoints Chapter 7 GRAVITY

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Harvey Hall
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1 0 Checkpoints Chapte 7 GAVIY Question 64 o do this question you must et an equation that has both and, whee is the obital adius and is the peiod. You can use Keple s Law, which is; constant. his is a vey useful fomula, even thouh it is not stictly on the couse. heefoe any incease in must also have an incease in. Keple s Law shows thee is no dependence on mass. Question 65 constant (. 0 ( ) ) (you could use any othe set of data) Solution of the equation yield 7 days (ANS) Question 66 m F F (0.4) F N (ANS) Question 67 (his is not on the couse) A satellite obits about the cente of the ath. If it is not in the plane of the equato it will be altenately above a point in the Nothen then Southen hemisphee. o emain above a fixed point on the ath it must be above the equato. Question 68 Gavitational Potential eney is iven by m 6.67x0 6.0x0.0x0 U - U x0 U -.x0 J Note that the adius is the adius of the eath plus 00 km. he kinetic eney is half the size of the Potential eney when in stable cicula obit so k 6. x 0 J he othe way of doin this is: mv m m mv m mv K.x0 k 6. x 0 J (ANS)

2 Question 69 Peiod is independent of mass, meely dependent on adius. he answe is Question 70 9 heefoe the shuttle is 0 fom the cente of the ath. at the ath s suface is 9.8ms - We will use as the avitational field at the suface of the ath. We will use as the avitational field at 0 fom the cente of the ath ms - Sub values in fo and 00 et by itself Usin the equation of motion: v u + at > v x 00 v 0 ms - (ANS) Question 7 quatin avitational field stenths, S ( - x) x MS M We can simplify such that ( - x) x Question 7 Use mv 0 k 7 mv.0 0 W m N (ANS) his is anothe example of combinin the Kinetic ney fomula with the Centipetal Foce expession fom cicula motion Question 7 A balance will wok in any place whee thee is a avitational field by compain the avitational attaction on two masses, so it will wok on the Moon. In a satellite in obit, the balance and masses would all be in fee fall so the avitational attaction [appaent weiht] will be zeo.

3 Question 74 he oiinal kinetic eney will be conveted to Gavitational Potential ney as it moves thouh the Gavitational field. If the aph supplied was a Foce vs heiht aph, the eney thus tansfomed would be iven by the aea unde that aph. o convet the vs heiht aph, the values ae multiplied by the mass involved 50 k. he aea is appoximately a apezium. Aea (8 + 66)/ J ½ x 50 x v v 70 ms - (ANS) 80 Question 86 Gavitational Field stenth is iven by so () Afte subtactin the adius of the ath ( ) we et heiht 0 km (ANS) Question 75 m B eaane a fomula involvin G such as m then make G the subject and substitute the units of the othe vaiables. Question 76 See the notes fo the deivation of Keple s Law. his is the standad manipulation of the fomula obtained when equatin the Gavitational field stenth to the centipetal acceleation. Question 77 M G 8 4 π (.8 0 ) ( ) M k (ANS)

4 Question 78 Use the standad fomulae and eaane to ive?? ( ) /( ) m o find the altitude, you need to subtact the adius of the ath, m (ANS) Question 79 Fom this equation the peiod is independent of the mass of the satellite. If they have the same adius of obit and the same peiod, then they must both have the same speed. Question 80 Usin is and ives is On substitution is is A (ANS) is is (6.0 0 ) (0.5 0 ) Question 8 Usin Keple s Law (which is not on the couse, but is vey useful) he atio of is the same o all bodies obitin the Sun. (6.0 0 ) (0.5 0 ) (simplifyin the calculation) ath-yeas (ANS) Question 8 he comet will basically have a constant eney as it obits the Sun. (ven thouh it is losin a minute amount as it buns). he total eney is the sum of the P and K. he comet will ain P as it moves away fom the sun, theefoe it must lose K. his means that it will tavel faste at X than Y. As the comet moves fom X to Y, the speed will decease and the total eney will emain constant (ANS)

5 Question 8 m F (.8 0 ) N (ANS) Question 84 he obit is cicula, mv F m Π ( ) m4π 90 4 Π.8 0 F 90 4 Π sec 7. 0 s (ANS) 6 6 Question 85 Helen s appaent weiht is he nomal eaction fom the lift platfom. Since Helen is tavellin at a constant speed the net foce actin on Helen is 0 N. his means that he weiht is equal in manitude of the nomal eaction actin on he. he manitude of he weiht is m So the appaent weiht actin on he is 600 N. Question 86 hee is only one foce actin on Jason as it obits, that is its weiht foce and this acts towads the cente of the ath. diection of movement ath m Jason Question 87 he peiod can be calculated fom: (. 0 ) s (ANS)

6 Question 88 emiss Weiht (6.7 0 ).69 x 0 6 N (ANS) Question 89 he peiod can be calculated fom Keple s Law: (6.7 0 ) 6 (6.7 0 ) secs (ANS) his question can also be done usin F m4π F m4π F 6 ( ) mv m Π ( ) 5480 secs m4π (ANS) Question 90 Same Fom Keple s Law, the peiod is independent of the mass of the satellite. Question 9 W m, if the visito weihs the same then must equal 0 on both the planet and the ath. 0 Nk - (ANS) Question 9 m Use F m V Visito also ath M V V M V M M V V (.4 0 ) 6 (6.7 0 ) 4 4

7 M V. x 0 0 k (ANS) Question 9 m mv Use v Use v π 9 ( 0 ) x 0. x 0 6 secs (ANS)

Universal Gravitation

Universal Gravitation Chapte 1 Univesal Gavitation Pactice Poblem Solutions Student Textbook page 580 1. Conceptualize the Poblem - The law of univesal gavitation applies to this poblem. The gavitational foce, F g, between