PHYSICS 218 Honors EXAM 2 Retest. Choose 5 of the following 6 problems. Indicate which problem is not to be graded.
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1 PHYSICS 18 Honos EXAM Retest Choose 5 of the following 6 pobles. Indicate which poble is not to be gaded. 1. A ope is affixed at one end to the i of a pulley, and wapped five tuns aound the pulley. The pulley has a ass of 5 kg, a adius of 0., and its ass is distibuted as a unifo disk. A ass of 10 kg is suspended fo the loose end of the ope, so that it hangs fo the floo. The ass is then eleased. What is the velocity of the ass just befoe it stikes the floo? The ope will unwind by an angle θ = L / R = = 10ad 0. We equie Newton's law fo foce and fo toque: (M=10 kg is ass of weight, =5 kg is ass of pulley) Mg T = Ma TR = Iα a = Rα R I = Rα Mg = Ma Mg a = = 8 M + / Now solve the equation of otion: x = at t = 1 x / a v = at = ax = 5.6
2 . A lawn olle in the fo of a thin-walled hollow cylinde of ass M is pulled hoizontally with a constant foce F applied by a handle attached to its axle. If it olls without slipping, find the acceleation and the fiction foce. Thee will be a fiction foce F f opposing the extenal foce F, so as to incease the angula velocity as the linea velocity inceases (no slipping). Requie Newton s law fo both foces and toques: F F = Ma F R = Iα a = Rα I = M F Iα / R = Ma F Ma = Ma a = F / M F f f f (thin cylindical shell, all ass on the suface (adius R) = Ma = F /
3 3. Conside a unifo solid disk of adius 5 c, with a ass of 0 kg. Thee 10 c diaete holes ae boed though the disk as shown. What is the oent of inetia of the holey disk, about its axis? Use the paallel axis theoe: The oent of inetia of the big disk with no holes, about its axis, is 1 I disk = MR = 0.65 kg The oent of inetia of each sall disk (adius, distance fo cente of big disk d, ass = M /R ) that is eoved, about the cental axis, is = I + hole d = = So oveall, I = I disk I holen = kg 3 n= 1
4 4. Two astonauts ust etieve a satellite that has begun to tuble in obit. The satellite is in the shape of a long cylinde, whose ass of 1,000 kg is unifoly distibuted inside. The satellite is tubling end ove end, with a peiod of 5 inutes. The astonauts want to stop the tubling by catching the satellite at its ends. If they each apply constant foce ove a axiu stoke of 0.3, how uch foce ust they apply to stop the satellite? Call the oveall length of the cylindical satellite L. The oent of inetia of a od otating about its cente in a tubling otion is 1 I = ML 1 The toque exeted by the two astonauts is L τ = ( ) The angula acceleation is then α = τ / I = 1F / ML π The initial angula velocity is ω = =.01ad 5in The angle though which the ship otates befoe stopping is 1 θ = ω 0t αt ω = ω αt 0 ω 0 ω = 0 when θ = =.018L / F α We equie that the angle θ coespond to a stoke s = 0.3. L s = ( ) θ =.009L / F = 0.3 F =.03L F
5 5. Counications satellites ae placed in geosynchonous obit: the satellite obit eains ove a fixed location on the Eath s suface. Calculate the adius of a geosynchonous obit. What is the highest latitude on Eath s suface that can eceive line-of-sight signals fo such satellites? The univesal constant of gavitation is 6.67 x N /kg. The ass of the eath is 6 x 10 4 kg. Hint: you don t need these, only g and the adius of the Eath, 6400 k, and the length of a day! Fo geosynchonous obit, we ust have that the obit peiod equals one day: π ω = = ad 4(3600s) Apply Newton s law to equie that the acceleation fo gavity equals that needed to keep it in obit: RE F = GM / = ( GM / RE ) 1443 v F = 3 = gr ω E = = ω = 8 6 ( 9.8 ) ( ) 5 ( ) g = The highest latitude that can eceive line-of-sight signals is an angle β fo the pole, 6 R whee sin β = E = =.034ad = So the highest latitude is 90 o - o = 88 o. 4 3
6 6. A unifo pulley wheel 8 c diaete, ass 1 kg, has a 5 long cod wapped aound its peiphey. Stating fo est, the wheel is given an angula acceleation of 1.47 ad/s. A) though what angle ust the wheel tun fo the cod to unwind? B) how long does it take? C) what is the final angula oentu of the wheel? 5 A) θ = L / R = = 6. 5ad.08 B) 1 θ = αt t = θ / α = 9.s 1 L = Iω = MR ω C) ω = αt = 111ad L =.08kg
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