AP Physics 1 - Circular Motion and Gravitation Practice Test (Multiple Choice Section) Answer Section

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1 AP Physics 1 - Cicula Motion and Gaitation Pactice est (Multiple Choice Section) Answe Section MULIPLE CHOICE 1. B he centipetal foce must be fiction since, lacking any fiction, the coin would slip off. he fiction is static because the coin is not slipping.. D he net foce and the acceleation on any object in unifom cicula motion ae both always towad the cente of the cicle. 3. D When the block is on the plane, the acceleation is 4 because the block is speeding up while going down and to the ight. When the block is at the bottom, it is actually going along (pat of) a cicula path. his means acceleation must be towad the cente of the cicle, which is B If both cues ae banked at the same angle, then they both poide the same centipetal acceleation: ( }) a = { c { ( same) ( 4) 5. A When an object moes in a cicle, its elocity is continuously changing diection, so since the elocity changes, the object must be acceleating. Velocity is nee the same as speed because elocity has diection and speed does not. o moe in a cicle, thee must be a net foce (called the centipetal foce) that points towad the cente of the cicle (in this case, the tension in the sting). If the sting beaks, the object will moe in a staight line tangent to the cicle. 6. C Objects feel weightless because they ae in fee-fall (the only foce on them in obit is gaity), theefoe the astonauts and the space ship all fall togethe at the same ate John R. Fensley, he College Entance Examination Boad, et.al. All ights eseed.

2 7. B GmM Foce of gaity is both F g = mg and F G =. Set these equal and cancel out m to get the gaity on a planet of mass M: GM g = Half the diamete and one-tenth the mass means that mass and adius ae multiplied by: ( 1/10 } ) G M { g = { (?) ( 1/ ) 1 1 Note that the denominato is squaed, so g is multiplied by 10 4 = 4/10. Multiplying Eath s gaity by 4/10 yields 4 m/s. 8. E Inese-squae law: As distance inceases, the foce deceases as the inese-squae of the distance. If the distance is multiplied by 4, the foce is multiplied by the inese-squae of 4, which is 1/ C ( }) m F c = { ( 4) he speed (which is squaed) must be doubled in the numeato to balance the multiplication of (in the denominato) by fou. 10. D he acceleation must be pointed towad the cente of the cicle, so if the acceleation points west then the ca is at the east end of the tack. If the ca is at the east end of the tack and elocity points noth, then the ca must be going counteclockwise aound the tack. Now sole fo acceleation: a = / () = /(800) = 1600 = 40 m/s 11. D When any ca goes aound a cue on a oadway, the fictional foce is what poides the centipetal foce to make the ca go in a cicle. he lage ca has twice the mass, but half the elocity on the same-adius oad: (}) ( ) 1/ } m { F = ( 1/ ) { ( 1) 014 John R. Fensley, he College Entance Examination Boad, et.al. All ights eseed.

3 1. D If 10 kg is just baely enough to beak the sting, then the sting s beaking stength is 100 N (the weight of the 10 kg). Using the sting to otate an object on a fictionless table will mean that the sting s tension is the centipetal foce causing the cicula motion (the object s weight and nomal foce cancel). Find the maximum speed: m F = ( ) ( 0.5) 100 = ( ) 400 = = 0 m/s 13. D When the ship is the same distance between the Eath and the Moon, the gaitational foce fom the Eath is geate than the Moon s foce because Eath has moe mass. Because these two gaitational foces ae unequal (Eath s is geate), thee is a net foce on the spaceship. 14. A Conside setting up a cicula obit equation by setting gaity foce equal to centipetal foce. how in the fact that speed = cicumfeence/peiod. Let M = sta s mass, and m = planet s mass. GmM m π = and = GM = (note that the planet s mass doesn t matte!) GM π = 3 GM = 4π Note the left-hand side the sta s mass is inesely popotional to the peiod (squaed). hat means that a longe obital peiod belongs to a sta with less mass. 15. C Apply Keple s hid Law, which states that two objects obiting the same massie object hae obital adii and peiods that obey the atio 1 /R 3 1 = /R 3. Let Eath s peiod and adius both be epesented by 1, so the asteoid s adius is : (1) /(1) 3 = /() 3 = 8 =.8 yeas John R. Fensley, he College Entance Examination Boad, et.al. All ights eseed.

4 16. D Because the ties ae not sliding on the oadway, the fiction is static and we use µ = 0.8. he fictional foce is F f = µf N = µmg (since F N = mg on a flat suface). he fiction is what poides the centipetal foce, so set fictional foce equal to centipetal foce: µ mg = m = µ g = ( 0.8)( 10)( 50) = 400 = 0 m/s 17. B At the bottom of the swing, thee is an upwad tension (and upwad acceleation) and downwad weight foce: F F = ma (If weight is 4 N, mass is 0.4 kg) g ( 6 ) ( 4) = ( 0.4) a c c a c = 5 m/s = ½g 18. D hink in tems of foces acting on the ca; the only foces acting on the ca ae weight (down) and the nomal foce (to the ight). his makes the net foce down and to the ight. Acceleation has the same diection as net foce, so the acceleation is also down and to the ight. OHER 19. C&D wo objects in the same obit hae the same speed and magnitude of acceleation, since speed and acceleation of an object in obit depends on the planet s mass, not the obiting object s. But because F = ma and K = ½m, foce and kinetic enegy double if the mass of the object is doubled. 0. A&D he net foce is the centipetal foce because the obit is cicula. he ectos and F ae NO constant because thei diections ae continuously changing (een though the speed and stength of the net foce ae both constant). In unifom cicula motion (including cicula obits), the net amount of wok done on the object is always zeo John R. Fensley, he College Entance Examination Boad, et.al. All ights eseed.

5 AP Physics 1 Cicula Motion and Gaitation Pactice est (Fee Response Section SOLUIONS) Poblem 1 (7 Points) (eache Made) (a) 1 point Vecto points tangent to the cicle (eithe diection) and ectos a and F point towad the cente. No points awaded fo unlabeled ectos o if thee ae any extaneous ectos. (b) (c) points he student maks peiod of otation and fequency of otation only. he student indicates that both coins ae on the same otating suface, so they complete cicles in the same time. his point can be awaded fo this easoning een if point was not awaded. points he student maks B = 3 A π he student shows = and explains that thee times the adius esults in thee times the speed. (d) points he student maks µ B = 3µ A m he student indicates that the fictional foce is equal to the centipetal foce, so µ mg =. Masses cancel, so mass does not affect this answe ( µ g = ). If speed is multiplied by thee, then the numeato is multiplied by 9, and if adius is multiplied by 3, then the denominato is multiplied by 3. his means that the coefficient of fiction must be thee ties as much. 015 John Fensley. All ights eseed.

6 Poblem (13 Points) (eache Made) (a-i) points GmM he student shows equations such as F = and he student uses the equations to deie GM = o m F = GM = o an equialent equation. (a-ii) points (b) π he student shows thei esult fom pat (a) as well as the equation =. 3 4π he student uses the equations to deie GM = 4π R, =, o an equialent equation 3 R GM 1 point Radius R (m) Peiod (sec) R 3 (m 3 ) (sec ) he student fills in at least thee coect numbes in each column. 015 John Fensley. All ights eseed.

7 (c) 3 points (d) he scale on each axis is linea and causes at least half of the gaph space to be used etically and hoizontally. Coect indications of scientific notation exponents ae shown. Fou points ae plotted coectly based on the data table. he best-fit does not pass fathe than two small gid-squae lengths fom any point on the gaph. points Fo cubing the gien adius and identifying the point (R 3 = m 3, = sec ) on the best-fit line. could be between sec and sec. Fo taking the squae oot of the alue of, giing seconds (between s and s accepted). (e) 3 points Fo indicating that the slope of the line is (between and is acceptable). 4π Fo setting the slope equal to. GM Fo the mass of the sta between kg and kg 015 John Fensley. All ights eseed.

DYNAMICS OF UNIFORM CIRCULAR MOTION

DYNAMICS OF UNIFORM CIRCULAR MOTION Chapte 5 Dynamics of Unifom Cicula Motion Chapte 5 DYNAMICS OF UNIFOM CICULA MOTION PEVIEW An object which is moing in a cicula path with a constant speed is said to be in unifom cicula motion. Fo an object