※ [本文轉錄自 NTU-Exam 看板] 作者: SummerWind86 (不能寒訓...) 看板: NTU-Exam 標題: [試題] 94上 李尚凡普物甲 期末考 時間: Fri Jan 13 02:38:52 2006 課程名稱︰普通物理學甲上 課程性質︰ 課程教師︰李尚凡 開課系所︰機械系 考試時間︰2006-1-12 試題 : 1. Suppose our Sun is about to explode. In an effort to escape in a spacecraft at v=0.800c and head toward the star Tau Ceti, 12.0ly away. When we reach two thirds of our journey from the Earth as seen in a frame of reference in which the Sun and Tau Ceti are at rest, we see our Sun explode and, unfortunately, at the same instant we see Tau Ceti explode as well. In the spacedcraft's frame of reference, which occurred first? By how many years? 2. A string is wound around a uniform disk of radius R and mass M. The disk is released from rest with the string vertical and it's top end tied to a fixed bar. Show that(a) the tension in the string is one-third the weight of the disk. (b)the magnitude of the acceleration of the center of mass is 2g/3, and (c)the speed of the center of mass is (4gh/3)^1/2 after the disk has descended through distancd h. 3. Suppose a solid disk of radius R is given an angular speed ωi about an axis through its center and then lowered to a horizontal surface and released. Furthermore, assume that the coefficient of friction between disk and surface is μ. (a)Show that the time interval before pure rolling motion occurs is Rωi/3μg . (b)Show that the distance the disk travels before pure rolling occurs is R^2ωi^2/18μg. 4. A ward of sticky clay with mass m and velocity v is fired at a solid cylinder of mass M and radius R. The cylinder is initially at rest, and is mounted on a fixed horinzontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at a distance d<R from the center. (a)Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder. 5. Two stars of masses M and m, seperated by a distance d, revolve in circular orbits about their center of mass. Show that each star has a period given by T^2 = (4π^2d^3) /〔G(M+m)〕 Proceed as follows: Apply Newton's second law to each star. Note that the center of mass condition requires that Mr2 = Mr1, where r1+r2=d. 6. The water supply of a building is fed through a main pipe 6.00cm in diameter. A 2.00cm diameter faucet tap , located 2.00m above the main pipe, is observed to fill a 25.0L container in 30.0s. (a)What is the speed at which the water leaves the faucet? (b)What is the gauge pressure in the 6cm main pipe? (Assume the faucet is the only "leak" in the building.) 7. A rope of total mass m and length L is suspended vertically. Show that a transverse pulse travels the length of the rope in a time interval Δt = 2〔(L/g)^(1/2)〕 --

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