College Physics Student s Manual Chapte 6 CHAPTER 6: UIORM CIRCULAR MOTIO AD GRAVITATIO 6. ROTATIO AGLE AD AGULAR VELOCITY. Sei- taile tucks hae an odoete on one hub of a taile wheel. The hub is weighted so that it does not otate, but it contains geas to count the nube of wheel eolutions it then calculates the distance taeled. If the wheel has a.5 diaete and goes though 00,000 otations, how any kiloetes should the odoete ead? Gien: d.5.5 0.575, Δθ 00,000 π ad ot ot.57 6 ad ind Δ s using Δ s Δθ 7.6 Δs Δ θ, so that 6 (.57 ad)( 0.575 ) 5 7 k 7. A tuck with 0.0- - adius ties taels at.0 /s. What is the angula elocity of the otating ties in adians pe second? What is this in e/in? Gien: 0.0,.0 s..0 s Use ω 76. ad s. 0.0 Conet to p by using the conesion facto: 9
College Physics Student s Manual Chapte 6 e π ad, ω 76. ad s e π ad 60 s in 78 e in 78 p 6. CETRIPETAL ACCELERATIO 8. Veify that the linea speed of an ultacentifuge is about 0.50 k/s, and Eath in its obit is about 0 k/s by calculating: (a) The linea speed of a point on an ultacentifuge 0.0 fo its cente, otating at 50,000 e/in. (b) The linea speed of Eath in its obit about the Sun (use data fo the text on the adius of Eath s obit and appoxiate it as being cicula). (a) Use ω to find the linea elocity: ω π ad e in 60 s ( 0.0 ) 50,000 e/in 5 /s 0.5 k/s ad y 7 (b) Gien: ω π.988 ad s;.96 7 y.6 s Use ω to find the linea elocity: ω (.96 )(.988 ad s).975 s 9.7 k s 6. CETRIPETAL ORCE 6. What is the ideal speed to take a 0 adius cue banked at a 0.0 angle? 50
College Physics Student s Manual Chapte 6 Using tan θ gies: g tan θ gtan θ g ( 0 )( 9.8 s ) tan 0.0 8.9 s 6.5 EWTO S UIVERSAL LAW O GRAVITATIO. (a) Calculate Eath s ass gien the acceleation due to gaity at the oth Pole is 9.80 /s and the adius of the Eath is 67 k fo pole to pole. (b) Copae this with the accepted alue of 5.979. (a) Using the equation g gies: g g G ( ) ( 9.80 s ) 67 5.979 6.67 M (b) This is identical to the best alue to thee significant figues. 9. Astology, that unlikely and ague pseudoscience, akes uch of the position of the planets at the oent of one s bith. The only known foce a planet exets on Eath is gaitational. (a) Calculate the agnitude of the gaitational foce exeted on a.0 baby by a 0 fathe 0.00 away at bith (he is assisting, so he is close to the child). (b) Calculate the agnitude of the foce on the baby due to upite if it is at its closest distance to Eath, soe 6.9 away. How does the foce of upite on the baby copae to the foce of the fathe on the baby? Othe objects in the oo and the hospital building also exet siila gaitational foces. (Of couse, thee could be an unknown foce acting, but scientists fist need to be coninced that thee is een an effect, uch less that an unknown foce causes it.) 5
College Physics Student s Manual Chapte 6 (a) Use to calculate the foce: f (b) The ass of upite is: (.67 )( 0 )(.0 ) ( 0.00 ) 6 7 7.0 f.90 7 ( 6.67 )(.90 )(.0 ) ( 6.9 ) 7.0.5 7-6 0.5.5 6 6.6 SATELLITES AD KEPLER S LAWS: A ARGUMET OR SIMPLICITY 5. ind the ass of upite based on data fo the obit of one of its oons, and copae you esult with its actual ass. Using T G M π, we can sole the ass of upite: M π G T π - 6.67 8 (. ) 7 [( 0.0085 y)(.6 s y) ].89 7 This esult atches the alue fo upite s ass gien by ASA. 8. Integated Concepts Space debis left fo old satellites and thei launches is becoing a hazad to othe satellites. (a) Calculate the speed of a satellite in an obit 900 k aboe Eath s suface. (b) Suppose a loose iet is in an obit of the sae 5
College Physics Student s Manual Chapte 6 adius that intesects the satellite s obit at an angle of 90 elatie to Eath. What is the elocity of the iet elatie to the satellite just befoe stiking it? (c) Gien the iet is.00 in size, how long will its collision with the satellite last? (d) If its ass is 0.500 g, what is the aeage foce it exets on the satellite? (e) How uch enegy in joules is geneated by the collision? (The satellite s elocity does not change appeciably, because its ass is uch geate than the iet s.) GM (a) Use c ac, then substitute using a and. GM (b) S E (.67 )( 5.979 ) 6 900. s In the satellite s fae of efeence, the iet has two pependicula elocity coponents equal to fo pat (a): (.5 s).98 s + (c) Using kineatics: d t t d.00.0.98 s 7 s Δp Δt t 0.500.98 s 8.0 s ( )( ) (d).8 (e) The enegy is geneated fo the iet. In the satellite s fae of efeence, and 0. So, the change in the kinetic enegy of the iet is: i, f Δ KE i 5 ( 0.500 )(.98 s) 0. 5