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Unformatted text preview: Graham, Andrew Finalexam 1 Due: Dec 15 2005, noon Inst: Maxim Tsoi 1 This print-out should have 40 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Given: g = 9 . 8 m / s 2 . Consider a boxcar accelerating up a 12 . 4 slope. Inside the boxcar, an object of un- known mass m hangs on a string attached to the boxcars ceiling. When the car accelerates uphill at a steady rate a , the string hangs at a constant angle = 19 . 06 from the perpendicular to the boxcars ceiling and floor. a m 1 9 . 6 12 . 4 Given the angles = 19 . 06 > = 12 . 4 , calculate the boxcars acceleration a . Correct answer: 1 . 2025 m / s 2 . Explanation: Basic Concept: In a non-inertial frame such as an accelerating boxcar, the inertial force- m~a combines with the true gravitational force m~g into a single apparent weight force ~ W app = m ( ~g- ~a frame ) . (1) In fact, the Equivalence Principle says that there is no observable difference between the true gravity and the inertial forces, so in a non-inertial frame there is a net effective grav- ity ~g eff = ~g- ~a frame . (2) Solution: Consider the hanging object in the non-inertial frame of the accelerating boxcar. In the cars frame, the objects hangs without motion so its apparent weight (1) must be balanced by the strings tension. Hence, the direction of the effective gravity (2) must be opposite to the strings pull on the object, which is 12 . 4 from the perpendicular to the boxcars floor and ceiling and 19 . 06 - 12 . 4 = 6 . 66 from the true vertical. At this point, the problem reduces to ge- ometry: Given the directions of vectors ~g , ~a and ~g- ~a and the magnitude g = 9 . 8 m / s 2 , find the magnitude a . We can solve this ques- tion using the sine theorem, but it is just as easy to solve in Carthesian coordinates. Let the x axis run uphull along the boxcarss floor while the y axis is perpendicular the the floor: In these coordinates, a x = a, a y = 0 , (3) g x =- g sin , g y =- g cos (4) where = 12 . 4 is the hills slope. At the same time, the strings direction indicates g eff x =- g eff sin , g eff y =- g eff cos (5) where = 19 . 06 is the angle between the string and the y axis. Consequently, tan = g eff x g eff y = g x- a x g y- a y =- g sin - a- g cos = tan + a g cos . (6) and therefore a = (tan - tan ) g cos (7) = 1 . 2025 m / s 2 . 002 (part 1 of 1) 10 points Many satellites orbit the earth about 1036 km above the earths surface. Geosynchronous satellites orbit at a distance of 4 . 22 10 7 m from the center of the earth....
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This note was uploaded on 10/13/2009 for the course PHY 303K taught by Professor Turner during the Fall '08 term at University of Texas at Austin.
- Fall '08